Calculus and Physics for beginners. Suggestions for books [closed]
I would like to start brushing up on some math and physics. Mostly math that theoretical physicist use. Want to start with the basics so wanted some suggestions on books that'll help me with this. I appreciate your replies. Thank yo
calculus reference-request physics self-learning
edited Dec 10 '18 at 5:15
Shaun
8,750113680
asked Dec 10 '18 at 3:42
Jason Dalmeida
4
closed as too broad by TheGeekGreek, Lord Shark the Unknown, Alexander Gruber♦ Dec 12 '18 at 5:04
Please edit the question to limit it to a specific problem with enough detail to identify an adequate answer. Avoid asking multiple distinct questions at once. See the How to Ask page for help clarifying this question. If this question can be reworded to fit the rules in the help center, please edit the question.
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I would like to start brushing up on some math and physics. Mostly math that theoretical physicist use. Want to start with the basics so wanted some suggestions on books that'll help me with this. I appreciate your replies. Thank yo
calculus reference-request physics self-learning
edited Dec 10 '18 at 5:15
Shaun
8,750113680
asked Dec 10 '18 at 3:42
Jason Dalmeida
4
closed as too broad by TheGeekGreek, Lord Shark the Unknown, Alexander Gruber♦ Dec 12 '18 at 5:04
Please edit the question to limit it to a specific problem with enough detail to identify an adequate answer. Avoid asking multiple distinct questions at once. See the How to Ask page for help clarifying this question. If this question can be reworded to fit the rules in the help center, please edit the question.
Mathematical methods for physicists-G. B. Arfken and H. J. Weber
– Thomas Shelby
Dec 10 '18 at 4:00
1
Thank you very much!
– Jason Dalmeida
Dec 10 '18 at 5:02
1
Don't forget the co-author F. E. Harris, @ThomasShelby!
– Shaun
Dec 10 '18 at 5:14
1
@Shaun Sorry, my bad!
– Thomas Shelby
Dec 10 '18 at 5:48
Jason Dalmeida, I've written detailed recommendations. Now I've edited and expanded them. Hope they will be of some help.
– Ken Draco
Dec 12 '18 at 11:41
|
show 1 more comment
I would like to start brushing up on some math and physics. Mostly math that theoretical physicist use. Want to start with the basics so wanted some suggestions on books that'll help me with this. I appreciate your replies. Thank yo
calculus reference-request physics self-learning
edited Dec 10 '18 at 5:15
Shaun
8,750113680
asked Dec 10 '18 at 3:42
Jason Dalmeida
4
I would like to start brushing up on some math and physics. Mostly math that theoretical physicist use. Want to start with the basics so wanted some suggestions on books that'll help me with this. I appreciate your replies. Thank yo
calculus reference-request physics self-learning
calculus reference-request physics self-learning
edited Dec 10 '18 at 5:15
Shaun
8,750113680
asked Dec 10 '18 at 3:42
Jason Dalmeida
4
edited Dec 10 '18 at 5:15
Shaun
8,750113680
asked Dec 10 '18 at 3:42
Jason Dalmeida
4
edited Dec 10 '18 at 5:15
Shaun
8,750113680
edited Dec 10 '18 at 5:15
Shaun
8,750113680
edited Dec 10 '18 at 5:15
Shaun
8,750113680
8,750113680
asked Dec 10 '18 at 3:42
Jason Dalmeida
4
asked Dec 10 '18 at 3:42
Jason Dalmeida
4
asked Dec 10 '18 at 3:42
Jason Dalmeida
4
4
closed as too broad by TheGeekGreek, Lord Shark the Unknown, Alexander Gruber♦ Dec 12 '18 at 5:04
Please edit the question to limit it to a specific problem with enough detail to identify an adequate answer. Avoid asking multiple distinct questions at once. See the How to Ask page for help clarifying this question. If this question can be reworded to fit the rules in the help center, please edit the question.
closed as too broad by TheGeekGreek, Lord Shark the Unknown, Alexander Gruber♦ Dec 12 '18 at 5:04
Please edit the question to limit it to a specific problem with enough detail to identify an adequate answer. Avoid asking multiple distinct questions at once. See the How to Ask page for help clarifying this question. If this question can be reworded to fit the rules in the help center, please edit the question.
Mathematical methods for physicists-G. B. Arfken and H. J. Weber
– Thomas Shelby
Dec 10 '18 at 4:00
1
Thank you very much!
– Jason Dalmeida
Dec 10 '18 at 5:02
1
Don't forget the co-author F. E. Harris, @ThomasShelby!
– Shaun
Dec 10 '18 at 5:14
1
@Shaun Sorry, my bad!
– Thomas Shelby
Dec 10 '18 at 5:48
Jason Dalmeida, I've written detailed recommendations. Now I've edited and expanded them. Hope they will be of some help.
– Ken Draco
Dec 12 '18 at 11:41
|
show 1 more comment
Mathematical methods for physicists-G. B. Arfken and H. J. Weber
– Thomas Shelby
Dec 10 '18 at 4:00
1
Thank you very much!
– Jason Dalmeida
Dec 10 '18 at 5:02
1
Don't forget the co-author F. E. Harris, @ThomasShelby!
– Shaun
Dec 10 '18 at 5:14
1
@Shaun Sorry, my bad!
– Thomas Shelby
Dec 10 '18 at 5:48
Jason Dalmeida, I've written detailed recommendations. Now I've edited and expanded them. Hope they will be of some help.
– Ken Draco
Dec 12 '18 at 11:41
Mathematical methods for physicists-G. B. Arfken and H. J. Weber
– Thomas Shelby
Dec 10 '18 at 4:00
Mathematical methods for physicists-G. B. Arfken and H. J. Weber
– Thomas Shelby
Dec 10 '18 at 4:00
1
1
Thank you very much!
– Jason Dalmeida
Dec 10 '18 at 5:02
Thank you very much!
– Jason Dalmeida
Dec 10 '18 at 5:02
1
1
Don't forget the co-author F. E. Harris, @ThomasShelby!
– Shaun
Dec 10 '18 at 5:14
Don't forget the co-author F. E. Harris, @ThomasShelby!
– Shaun
Dec 10 '18 at 5:14
1
1
@Shaun Sorry, my bad!
– Thomas Shelby
Dec 10 '18 at 5:48
@Shaun Sorry, my bad!
– Thomas Shelby
Dec 10 '18 at 5:48
Jason Dalmeida, I've written detailed recommendations. Now I've edited and expanded them. Hope they will be of some help.
– Ken Draco
Dec 12 '18 at 11:41
Jason Dalmeida, I've written detailed recommendations. Now I've edited and expanded them. Hope they will be of some help.
– Ken Draco
Dec 12 '18 at 11:41
|
show 1 more comment
1 Answer
1
active
oldest
votes
In my recommendations below, I emphasize books that allow understanding things at a deeper level, at conceptual level. Books that cover a lot and provide a sound, deep knowledge. These books are opposite of what rote-learners would need. There won't be concatenations of theorems for rote-learning without a real, deep and intuitive understanding. I don't believe in studying books that don't provide all derivations and crystal clear explanations. No books for dummies are recommended here. Delving deep, contemplating and pushing yourself required. No walk-through, not even with a 300-page book by Gardner. Yet the books below are not overly rigorous or advanced; they are crystal clear/user friendly in exposing the material and they can be studied from scratch by beginners. If only a couple of books are required (not, like, kinda, best 7-10 books), please jump to the summary/conclusions at the bottom.
Part 1 (Math) The best books are Calculus by Larson (≈1300 pages) and Thomas’ Calculus (≈1300 pages). There is also a great precalculus book called Algebra and Trigonometry by Larson (≈1000 pages) or alternatively Precalculus by Stewart (≈1000 pages). A thousand pages of precalculus must not be skipped but 50% of its material is always skipped (as a result students have problems with basic things and are flailing in math although they always claim that they do know precalc). The best book on linear algebra is Elementary Linear Algebra by Kolman (≈600 pages) but it might be a bit challenging; Strang’s Linear Algebra (≈500 pages) is easier and is superb. Calculus by Marsden is the easiest complete course (Berkeley) –it is superb (3 volumes totaling ≈1000 pages); SMs are called Student’s Guides). Analytic geometry is nowadays neglected, however there’s a good book: Analytic Geometry by Douglas (≈500 pages). Boyce and DiPrima (≈700 pages) should be the choice on ODE. Advice: if precalculus and Douglas' Analytic Geometry are to be skipped (bad idea but that's what happens 99% of the time) I suggest simpler books by Marsden rather than Thomas’ Calculus. They still cover everything needed (in terms of calculus) for physics and engineering. Vector Calculus by Marsden’s (≈600 pages; not to be confused with their 3-volum Calculus) is an awesome, slightly more advanced book (covering only Calculus III/IV). These books will all deliver when a deep understanding is in priority. They are all very interesting and sufficiently comprehensive. If a bit more math logic in terms of rigor and theoretical aspects are of interest, then Spivak’s Calculus(≈600 pages) is a superb introduction in that direction (purely logical, mathematical -- rather than applied but very interesting with some beautiful and challenging problems of theoretical type). Please note that Spivak covers only 50% of topics in calculus. If you want more calculus with more rigor -- it is Apostol (I don't recommend it for beginners; it's rigorous but it's an olla podrida of linear algebra, calculus, and analytic geometry or a Jack of all trades but master of non and yet it is a rigorous classical text recommended by many. Don't misconstrue my opinion about Apostol. His text is not bad, not by a long shot. On the flip side it's good for rote learners citing it without real understanding).
Part 2. (Physics). Physics by Young and Freedman (≈1500 pages) is almost the optimal choice as it is not too long, not too short for more or less serious introduction from scratch. Fundamentals of Physics by Halliday and Resnick (≈1500 pages) is just as good; it is an outstanding text in fact! There’s also an excellent and comprehensive Berkeley course: Physics Course (in 5 volumes). It consists of Mechanics by Kittel and Knight (≈400 pages), Electricity and Magnetism by Pursell (≈500 pages), Thermal Physics by Kittel and Kroemer (≈500 pages), Quantum Physics by Wichmann (≈400 pages), Statistical and Thermal Physics by Reif (≈600 pages). These are all extremely interesting books. They are comprehensive enough. Feynman Lectures on Physics are also very good. They are partly college course books and partly just a popular read (but a serious read with problems and SMs). All these books require knowledge of Calculus. That’s it. That’s my advice based off of the hundreds of books on math and physics I have. All the books I recommended I'm familiar with/read. Please note these are all books for college, let’s say, for a serious university when math, physics, and engineering are in priority. These are all suited for beginners and yet provide an in-depth coverage at undergrad level.
IMPORTANT ADDENDUM:
I recon best books for real beginners should be pointed out as well:
1) Differential and Integral Calculus by Granville (this text is 100 years old, it's around 500 pages only. No vector calculus -- one variable, multivariables, and ODE only.
2) Calculus Made Easy by Thompson and Gardner. (≈300 pages, also lacks vector calculus) I'm gonna quote a couple of sentences of the authors: If it [their book] falls into the hands of the professional mathematicians, they will rise up as one man, and damn it...it [their book] commits several grievous and deplorable errors...it shows how ridiculously easy most of the operations of the calculus really are...it gives away so many trade secrets...
3) College Physics by Serway Vuille. Very accessible text. Covers all the basics (1200 pages only) for a serious beginner totally from scratch -- so simple that calculus is not required. Yet it is a fantastic book that still contains all the main derivations of important equations, plus vector algebra. The best first course in physics. It is a sort of precalculus in physics. Suited for someone who had no exposure to physics before, yet comprehensive and serious.
Now slightly more advanced material than what is contained in average college course books for engineering students:
1) Vector Calculus by Colley (≈600 pages). Not only a superb text but comprehensive. She gives recommendations on good books at the end. While her recommendations (will provide a second opinion) are the best I've ever seen -- yet I don't agree with them 100%. The book is superb though and crystal clear -- better then the books she recommends (mostly advanced/intermediate classical texts which are well known). It's an in-depth version (kind of on steroids) of standard Calculus III/IV. Similar in clarity to Mardsen's Vector Calculus. It's topnotch.
2) Calculus: Complete Course by Adams and Essex (≈1100 pages). Standard just as Calculus by Larson and Thomas' Calculus but unlike Thomas' and Larson this book has a lot of challenging problems that standard texts lack. So if you like challenging problems, this is it. Adams and Essex is slightly more advanced than average. Heavy emphasis on applications and physics. Commendable job by the authors.
3) Calculus by Stewart (≈1300 pages). He might skip a few completely elementary steps here and there, and people start to think it’s not as clear as Larson’s text. Well, it is as clear – it just reveals terrible gaps in precalculus, which leads students to rote-learn formulas and concepts expecting everything on a silver platter without thinking i.e. when math is just plugging in numbers. But that’s not math; that is pure dumb rote learning and a waste of time. This book is in between Adam/Essex and Larson in terms of difficulty. The differences between all the three are in fact very, very minor.
4) See recommendations by Colley in her Vector Calculus. Even more advanced level books are recommended there. Emphasis starts to shift on math rigor there.
5) Classical Mechanics by Gregory (only 600 pages of relatively compact book). That's mostly theoretical mechanics but very interesting, crystal clear. Illustrated by hundreds of examples that help figure out things. Mechanics is the core of physics. This text is a little bit advanced and should be started after finishing ODE and vector calculus. It's a fascinated read (!) if you are prepared. Full of crystal clear derivations and superb explanations. Can't praise it enough. Here you will be able to "unleash" everything you studied in calculus but Gregory will incentivize you a bit more to continue studying and delving deeper into math/physics!
CONCLUSION/SUMMARY
No books above are of the exam type that is of the condensed, rote-learner-friendly, aced-the exam-and-forgot kind of style. On the contrary all the books recommended above are for fundamental knowledge, for deep understanding and delving into details, for figuring out the nature (physics) and logic (math). They are not of the style "goes in one ear out the other" My top default recommendations are as follows:
I would recommend Marsden (≈1000 pages) and Larson (≈1300 pages) by default. But if a person has strong math background (plowed through the whole 1000-page precalc book), then Thomas' Calculus (problems are easy there) coupled with a 1100-page Adams and Essex (has enough tough problems that you may skip if you don't want them) is a topnotch choice. Adams and Essex has a very strong conceptual and application-related coverage as well. Calculus by Stewart (≈1300 pages) is a good alternative to Adams and Essex.
Physics: Physics by Young and Freedman (≈1500 pages) + Fundamentals of Physics by Halliday and Resnick (≈1500 pages) are my recommendation by default. These two books on physics both include a number challenging problems if you like to push yourself a little. If not, such problems might be skipped.
It's important to understand that it's best to use at least two quite different books on сalculus. SMs are necessary to check your solutions right away.The same goes for physics. I also believe a good precalc text must not be brushed aside. A 1000-page Algebra and Trigonometry by Larson (not the one that is called precalculus!) is an excellent choice as is Stewart's Precalculus (≈1000 pages)
If these books look daunting or longish, I advise re-thinking that perception. Authors in fact cut back on a lot of material, try make things crystal clear without sacrificing explanations of main concepts and ideas. And opting for small books won't cut it if an in-depth knowledge is in priority. For passing exams something smaller (+some Schaum's book for practicing problems) might be a smart choice but not for the real knowledge and understanding. For example, I have a Calculus book, which doesn't include ODE or complex variables but it is still 2000 pages long. My Advanced Analytic Geometry is 700 pages long. Now, think how it all gets squeezed in, how many things get left out, derivations omitted, less rigor employed etc. At the same time I named a few much shorter books that don't cut back on conceptual understanding and provide all derivations and explanations within their extremely short volumes (Granville's Calculus, Vuille's physics).
Off Topic Remark: Although this is a personal recommendation, even problem solutions have a personal touch when mistakes may go unnoticed or explanations might be horrible and murky. People have no recourse when they need text book recommendations. Okay, I know there are some posts (usually short just like references at the back of the book) and there are policy guidelines in place. The fact that in this specific SE website this question was not banned immediately speaks volumes. Thought to post recommendations in comments but decided to post it as an answer. If to be removed and deleted, well, guidelines and rules are there for a reason. It’s understandable that soft questions tend to be voted down or ignored.
answered Dec 11 '18 at 9:32
Ken Draco
58629
add a comment |
1 Answer
1
active
oldest
votes
1 Answer
1
active
oldest
votes
active
oldest
votes
active
oldest
votes
In my recommendations below, I emphasize books that allow understanding things at a deeper level, at conceptual level. Books that cover a lot and provide a sound, deep knowledge. These books are opposite of what rote-learners would need. There won't be concatenations of theorems for rote-learning without a real, deep and intuitive understanding. I don't believe in studying books that don't provide all derivations and crystal clear explanations. No books for dummies are recommended here. Delving deep, contemplating and pushing yourself required. No walk-through, not even with a 300-page book by Gardner. Yet the books below are not overly rigorous or advanced; they are crystal clear/user friendly in exposing the material and they can be studied from scratch by beginners. If only a couple of books are required (not, like, kinda, best 7-10 books), please jump to the summary/conclusions at the bottom.
Part 1 (Math) The best books are Calculus by Larson (≈1300 pages) and Thomas’ Calculus (≈1300 pages). There is also a great precalculus book called Algebra and Trigonometry by Larson (≈1000 pages) or alternatively Precalculus by Stewart (≈1000 pages). A thousand pages of precalculus must not be skipped but 50% of its material is always skipped (as a result students have problems with basic things and are flailing in math although they always claim that they do know precalc). The best book on linear algebra is Elementary Linear Algebra by Kolman (≈600 pages) but it might be a bit challenging; Strang’s Linear Algebra (≈500 pages) is easier and is superb. Calculus by Marsden is the easiest complete course (Berkeley) –it is superb (3 volumes totaling ≈1000 pages); SMs are called Student’s Guides). Analytic geometry is nowadays neglected, however there’s a good book: Analytic Geometry by Douglas (≈500 pages). Boyce and DiPrima (≈700 pages) should be the choice on ODE. Advice: if precalculus and Douglas' Analytic Geometry are to be skipped (bad idea but that's what happens 99% of the time) I suggest simpler books by Marsden rather than Thomas’ Calculus. They still cover everything needed (in terms of calculus) for physics and engineering. Vector Calculus by Marsden’s (≈600 pages; not to be confused with their 3-volum Calculus) is an awesome, slightly more advanced book (covering only Calculus III/IV). These books will all deliver when a deep understanding is in priority. They are all very interesting and sufficiently comprehensive. If a bit more math logic in terms of rigor and theoretical aspects are of interest, then Spivak’s Calculus(≈600 pages) is a superb introduction in that direction (purely logical, mathematical -- rather than applied but very interesting with some beautiful and challenging problems of theoretical type). Please note that Spivak covers only 50% of topics in calculus. If you want more calculus with more rigor -- it is Apostol (I don't recommend it for beginners; it's rigorous but it's an olla podrida of linear algebra, calculus, and analytic geometry or a Jack of all trades but master of non and yet it is a rigorous classical text recommended by many. Don't misconstrue my opinion about Apostol. His text is not bad, not by a long shot. On the flip side it's good for rote learners citing it without real understanding).
Part 2. (Physics). Physics by Young and Freedman (≈1500 pages) is almost the optimal choice as it is not too long, not too short for more or less serious introduction from scratch. Fundamentals of Physics by Halliday and Resnick (≈1500 pages) is just as good; it is an outstanding text in fact! There’s also an excellent and comprehensive Berkeley course: Physics Course (in 5 volumes). It consists of Mechanics by Kittel and Knight (≈400 pages), Electricity and Magnetism by Pursell (≈500 pages), Thermal Physics by Kittel and Kroemer (≈500 pages), Quantum Physics by Wichmann (≈400 pages), Statistical and Thermal Physics by Reif (≈600 pages). These are all extremely interesting books. They are comprehensive enough. Feynman Lectures on Physics are also very good. They are partly college course books and partly just a popular read (but a serious read with problems and SMs). All these books require knowledge of Calculus. That’s it. That’s my advice based off of the hundreds of books on math and physics I have. All the books I recommended I'm familiar with/read. Please note these are all books for college, let’s say, for a serious university when math, physics, and engineering are in priority. These are all suited for beginners and yet provide an in-depth coverage at undergrad level.
IMPORTANT ADDENDUM:
I recon best books for real beginners should be pointed out as well:
1) Differential and Integral Calculus by Granville (this text is 100 years old, it's around 500 pages only. No vector calculus -- one variable, multivariables, and ODE only.
2) Calculus Made Easy by Thompson and Gardner. (≈300 pages, also lacks vector calculus) I'm gonna quote a couple of sentences of the authors: If it [their book] falls into the hands of the professional mathematicians, they will rise up as one man, and damn it...it [their book] commits several grievous and deplorable errors...it shows how ridiculously easy most of the operations of the calculus really are...it gives away so many trade secrets...
3) College Physics by Serway Vuille. Very accessible text. Covers all the basics (1200 pages only) for a serious beginner totally from scratch -- so simple that calculus is not required. Yet it is a fantastic book that still contains all the main derivations of important equations, plus vector algebra. The best first course in physics. It is a sort of precalculus in physics. Suited for someone who had no exposure to physics before, yet comprehensive and serious.
Now slightly more advanced material than what is contained in average college course books for engineering students:
1) Vector Calculus by Colley (≈600 pages). Not only a superb text but comprehensive. She gives recommendations on good books at the end. While her recommendations (will provide a second opinion) are the best I've ever seen -- yet I don't agree with them 100%. The book is superb though and crystal clear -- better then the books she recommends (mostly advanced/intermediate classical texts which are well known). It's an in-depth version (kind of on steroids) of standard Calculus III/IV. Similar in clarity to Mardsen's Vector Calculus. It's topnotch.
2) Calculus: Complete Course by Adams and Essex (≈1100 pages). Standard just as Calculus by Larson and Thomas' Calculus but unlike Thomas' and Larson this book has a lot of challenging problems that standard texts lack. So if you like challenging problems, this is it. Adams and Essex is slightly more advanced than average. Heavy emphasis on applications and physics. Commendable job by the authors.
3) Calculus by Stewart (≈1300 pages). He might skip a few completely elementary steps here and there, and people start to think it’s not as clear as Larson’s text. Well, it is as clear – it just reveals terrible gaps in precalculus, which leads students to rote-learn formulas and concepts expecting everything on a silver platter without thinking i.e. when math is just plugging in numbers. But that’s not math; that is pure dumb rote learning and a waste of time. This book is in between Adam/Essex and Larson in terms of difficulty. The differences between all the three are in fact very, very minor.
4) See recommendations by Colley in her Vector Calculus. Even more advanced level books are recommended there. Emphasis starts to shift on math rigor there.
5) Classical Mechanics by Gregory (only 600 pages of relatively compact book). That's mostly theoretical mechanics but very interesting, crystal clear. Illustrated by hundreds of examples that help figure out things. Mechanics is the core of physics. This text is a little bit advanced and should be started after finishing ODE and vector calculus. It's a fascinated read (!) if you are prepared. Full of crystal clear derivations and superb explanations. Can't praise it enough. Here you will be able to "unleash" everything you studied in calculus but Gregory will incentivize you a bit more to continue studying and delving deeper into math/physics!
CONCLUSION/SUMMARY
No books above are of the exam type that is of the condensed, rote-learner-friendly, aced-the exam-and-forgot kind of style. On the contrary all the books recommended above are for fundamental knowledge, for deep understanding and delving into details, for figuring out the nature (physics) and logic (math). They are not of the style "goes in one ear out the other" My top default recommendations are as follows:
I would recommend Marsden (≈1000 pages) and Larson (≈1300 pages) by default. But if a person has strong math background (plowed through the whole 1000-page precalc book), then Thomas' Calculus (problems are easy there) coupled with a 1100-page Adams and Essex (has enough tough problems that you may skip if you don't want them) is a topnotch choice. Adams and Essex has a very strong conceptual and application-related coverage as well. Calculus by Stewart (≈1300 pages) is a good alternative to Adams and Essex.
Physics: Physics by Young and Freedman (≈1500 pages) + Fundamentals of Physics by Halliday and Resnick (≈1500 pages) are my recommendation by default. These two books on physics both include a number challenging problems if you like to push yourself a little. If not, such problems might be skipped.
It's important to understand that it's best to use at least two quite different books on сalculus. SMs are necessary to check your solutions right away.The same goes for physics. I also believe a good precalc text must not be brushed aside. A 1000-page Algebra and Trigonometry by Larson (not the one that is called precalculus!) is an excellent choice as is Stewart's Precalculus (≈1000 pages)
If these books look daunting or longish, I advise re-thinking that perception. Authors in fact cut back on a lot of material, try make things crystal clear without sacrificing explanations of main concepts and ideas. And opting for small books won't cut it if an in-depth knowledge is in priority. For passing exams something smaller (+some Schaum's book for practicing problems) might be a smart choice but not for the real knowledge and understanding. For example, I have a Calculus book, which doesn't include ODE or complex variables but it is still 2000 pages long. My Advanced Analytic Geometry is 700 pages long. Now, think how it all gets squeezed in, how many things get left out, derivations omitted, less rigor employed etc. At the same time I named a few much shorter books that don't cut back on conceptual understanding and provide all derivations and explanations within their extremely short volumes (Granville's Calculus, Vuille's physics).
Off Topic Remark: Although this is a personal recommendation, even problem solutions have a personal touch when mistakes may go unnoticed or explanations might be horrible and murky. People have no recourse when they need text book recommendations. Okay, I know there are some posts (usually short just like references at the back of the book) and there are policy guidelines in place. The fact that in this specific SE website this question was not banned immediately speaks volumes. Thought to post recommendations in comments but decided to post it as an answer. If to be removed and deleted, well, guidelines and rules are there for a reason. It’s understandable that soft questions tend to be voted down or ignored.
answered Dec 11 '18 at 9:32
Ken Draco
58629
add a comment |
In my recommendations below, I emphasize books that allow understanding things at a deeper level, at conceptual level. Books that cover a lot and provide a sound, deep knowledge. These books are opposite of what rote-learners would need. There won't be concatenations of theorems for rote-learning without a real, deep and intuitive understanding. I don't believe in studying books that don't provide all derivations and crystal clear explanations. No books for dummies are recommended here. Delving deep, contemplating and pushing yourself required. No walk-through, not even with a 300-page book by Gardner. Yet the books below are not overly rigorous or advanced; they are crystal clear/user friendly in exposing the material and they can be studied from scratch by beginners. If only a couple of books are required (not, like, kinda, best 7-10 books), please jump to the summary/conclusions at the bottom.
Part 1 (Math) The best books are Calculus by Larson (≈1300 pages) and Thomas’ Calculus (≈1300 pages). There is also a great precalculus book called Algebra and Trigonometry by Larson (≈1000 pages) or alternatively Precalculus by Stewart (≈1000 pages). A thousand pages of precalculus must not be skipped but 50% of its material is always skipped (as a result students have problems with basic things and are flailing in math although they always claim that they do know precalc). The best book on linear algebra is Elementary Linear Algebra by Kolman (≈600 pages) but it might be a bit challenging; Strang’s Linear Algebra (≈500 pages) is easier and is superb. Calculus by Marsden is the easiest complete course (Berkeley) –it is superb (3 volumes totaling ≈1000 pages); SMs are called Student’s Guides). Analytic geometry is nowadays neglected, however there’s a good book: Analytic Geometry by Douglas (≈500 pages). Boyce and DiPrima (≈700 pages) should be the choice on ODE. Advice: if precalculus and Douglas' Analytic Geometry are to be skipped (bad idea but that's what happens 99% of the time) I suggest simpler books by Marsden rather than Thomas’ Calculus. They still cover everything needed (in terms of calculus) for physics and engineering. Vector Calculus by Marsden’s (≈600 pages; not to be confused with their 3-volum Calculus) is an awesome, slightly more advanced book (covering only Calculus III/IV). These books will all deliver when a deep understanding is in priority. They are all very interesting and sufficiently comprehensive. If a bit more math logic in terms of rigor and theoretical aspects are of interest, then Spivak’s Calculus(≈600 pages) is a superb introduction in that direction (purely logical, mathematical -- rather than applied but very interesting with some beautiful and challenging problems of theoretical type). Please note that Spivak covers only 50% of topics in calculus. If you want more calculus with more rigor -- it is Apostol (I don't recommend it for beginners; it's rigorous but it's an olla podrida of linear algebra, calculus, and analytic geometry or a Jack of all trades but master of non and yet it is a rigorous classical text recommended by many. Don't misconstrue my opinion about Apostol. His text is not bad, not by a long shot. On the flip side it's good for rote learners citing it without real understanding).
Part 2. (Physics). Physics by Young and Freedman (≈1500 pages) is almost the optimal choice as it is not too long, not too short for more or less serious introduction from scratch. Fundamentals of Physics by Halliday and Resnick (≈1500 pages) is just as good; it is an outstanding text in fact! There’s also an excellent and comprehensive Berkeley course: Physics Course (in 5 volumes). It consists of Mechanics by Kittel and Knight (≈400 pages), Electricity and Magnetism by Pursell (≈500 pages), Thermal Physics by Kittel and Kroemer (≈500 pages), Quantum Physics by Wichmann (≈400 pages), Statistical and Thermal Physics by Reif (≈600 pages). These are all extremely interesting books. They are comprehensive enough. Feynman Lectures on Physics are also very good. They are partly college course books and partly just a popular read (but a serious read with problems and SMs). All these books require knowledge of Calculus. That’s it. That’s my advice based off of the hundreds of books on math and physics I have. All the books I recommended I'm familiar with/read. Please note these are all books for college, let’s say, for a serious university when math, physics, and engineering are in priority. These are all suited for beginners and yet provide an in-depth coverage at undergrad level.
IMPORTANT ADDENDUM:
I recon best books for real beginners should be pointed out as well:
1) Differential and Integral Calculus by Granville (this text is 100 years old, it's around 500 pages only. No vector calculus -- one variable, multivariables, and ODE only.
2) Calculus Made Easy by Thompson and Gardner. (≈300 pages, also lacks vector calculus) I'm gonna quote a couple of sentences of the authors: If it [their book] falls into the hands of the professional mathematicians, they will rise up as one man, and damn it...it [their book] commits several grievous and deplorable errors...it shows how ridiculously easy most of the operations of the calculus really are...it gives away so many trade secrets...
3) College Physics by Serway Vuille. Very accessible text. Covers all the basics (1200 pages only) for a serious beginner totally from scratch -- so simple that calculus is not required. Yet it is a fantastic book that still contains all the main derivations of important equations, plus vector algebra. The best first course in physics. It is a sort of precalculus in physics. Suited for someone who had no exposure to physics before, yet comprehensive and serious.
Now slightly more advanced material than what is contained in average college course books for engineering students:
1) Vector Calculus by Colley (≈600 pages). Not only a superb text but comprehensive. She gives recommendations on good books at the end. While her recommendations (will provide a second opinion) are the best I've ever seen -- yet I don't agree with them 100%. The book is superb though and crystal clear -- better then the books she recommends (mostly advanced/intermediate classical texts which are well known). It's an in-depth version (kind of on steroids) of standard Calculus III/IV. Similar in clarity to Mardsen's Vector Calculus. It's topnotch.
2) Calculus: Complete Course by Adams and Essex (≈1100 pages). Standard just as Calculus by Larson and Thomas' Calculus but unlike Thomas' and Larson this book has a lot of challenging problems that standard texts lack. So if you like challenging problems, this is it. Adams and Essex is slightly more advanced than average. Heavy emphasis on applications and physics. Commendable job by the authors.
3) Calculus by Stewart (≈1300 pages). He might skip a few completely elementary steps here and there, and people start to think it’s not as clear as Larson’s text. Well, it is as clear – it just reveals terrible gaps in precalculus, which leads students to rote-learn formulas and concepts expecting everything on a silver platter without thinking i.e. when math is just plugging in numbers. But that’s not math; that is pure dumb rote learning and a waste of time. This book is in between Adam/Essex and Larson in terms of difficulty. The differences between all the three are in fact very, very minor.
4) See recommendations by Colley in her Vector Calculus. Even more advanced level books are recommended there. Emphasis starts to shift on math rigor there.
5) Classical Mechanics by Gregory (only 600 pages of relatively compact book). That's mostly theoretical mechanics but very interesting, crystal clear. Illustrated by hundreds of examples that help figure out things. Mechanics is the core of physics. This text is a little bit advanced and should be started after finishing ODE and vector calculus. It's a fascinated read (!) if you are prepared. Full of crystal clear derivations and superb explanations. Can't praise it enough. Here you will be able to "unleash" everything you studied in calculus but Gregory will incentivize you a bit more to continue studying and delving deeper into math/physics!
CONCLUSION/SUMMARY
No books above are of the exam type that is of the condensed, rote-learner-friendly, aced-the exam-and-forgot kind of style. On the contrary all the books recommended above are for fundamental knowledge, for deep understanding and delving into details, for figuring out the nature (physics) and logic (math). They are not of the style "goes in one ear out the other" My top default recommendations are as follows:
I would recommend Marsden (≈1000 pages) and Larson (≈1300 pages) by default. But if a person has strong math background (plowed through the whole 1000-page precalc book), then Thomas' Calculus (problems are easy there) coupled with a 1100-page Adams and Essex (has enough tough problems that you may skip if you don't want them) is a topnotch choice. Adams and Essex has a very strong conceptual and application-related coverage as well. Calculus by Stewart (≈1300 pages) is a good alternative to Adams and Essex.
Physics: Physics by Young and Freedman (≈1500 pages) + Fundamentals of Physics by Halliday and Resnick (≈1500 pages) are my recommendation by default. These two books on physics both include a number challenging problems if you like to push yourself a little. If not, such problems might be skipped.
It's important to understand that it's best to use at least two quite different books on сalculus. SMs are necessary to check your solutions right away.The same goes for physics. I also believe a good precalc text must not be brushed aside. A 1000-page Algebra and Trigonometry by Larson (not the one that is called precalculus!) is an excellent choice as is Stewart's Precalculus (≈1000 pages)
If these books look daunting or longish, I advise re-thinking that perception. Authors in fact cut back on a lot of material, try make things crystal clear without sacrificing explanations of main concepts and ideas. And opting for small books won't cut it if an in-depth knowledge is in priority. For passing exams something smaller (+some Schaum's book for practicing problems) might be a smart choice but not for the real knowledge and understanding. For example, I have a Calculus book, which doesn't include ODE or complex variables but it is still 2000 pages long. My Advanced Analytic Geometry is 700 pages long. Now, think how it all gets squeezed in, how many things get left out, derivations omitted, less rigor employed etc. At the same time I named a few much shorter books that don't cut back on conceptual understanding and provide all derivations and explanations within their extremely short volumes (Granville's Calculus, Vuille's physics).
Off Topic Remark: Although this is a personal recommendation, even problem solutions have a personal touch when mistakes may go unnoticed or explanations might be horrible and murky. People have no recourse when they need text book recommendations. Okay, I know there are some posts (usually short just like references at the back of the book) and there are policy guidelines in place. The fact that in this specific SE website this question was not banned immediately speaks volumes. Thought to post recommendations in comments but decided to post it as an answer. If to be removed and deleted, well, guidelines and rules are there for a reason. It’s understandable that soft questions tend to be voted down or ignored.
answered Dec 11 '18 at 9:32
Ken Draco
58629
add a comment |
In my recommendations below, I emphasize books that allow understanding things at a deeper level, at conceptual level. Books that cover a lot and provide a sound, deep knowledge. These books are opposite of what rote-learners would need. There won't be concatenations of theorems for rote-learning without a real, deep and intuitive understanding. I don't believe in studying books that don't provide all derivations and crystal clear explanations. No books for dummies are recommended here. Delving deep, contemplating and pushing yourself required. No walk-through, not even with a 300-page book by Gardner. Yet the books below are not overly rigorous or advanced; they are crystal clear/user friendly in exposing the material and they can be studied from scratch by beginners. If only a couple of books are required (not, like, kinda, best 7-10 books), please jump to the summary/conclusions at the bottom.
Part 1 (Math) The best books are Calculus by Larson (≈1300 pages) and Thomas’ Calculus (≈1300 pages). There is also a great precalculus book called Algebra and Trigonometry by Larson (≈1000 pages) or alternatively Precalculus by Stewart (≈1000 pages). A thousand pages of precalculus must not be skipped but 50% of its material is always skipped (as a result students have problems with basic things and are flailing in math although they always claim that they do know precalc). The best book on linear algebra is Elementary Linear Algebra by Kolman (≈600 pages) but it might be a bit challenging; Strang’s Linear Algebra (≈500 pages) is easier and is superb. Calculus by Marsden is the easiest complete course (Berkeley) –it is superb (3 volumes totaling ≈1000 pages); SMs are called Student’s Guides). Analytic geometry is nowadays neglected, however there’s a good book: Analytic Geometry by Douglas (≈500 pages). Boyce and DiPrima (≈700 pages) should be the choice on ODE. Advice: if precalculus and Douglas' Analytic Geometry are to be skipped (bad idea but that's what happens 99% of the time) I suggest simpler books by Marsden rather than Thomas’ Calculus. They still cover everything needed (in terms of calculus) for physics and engineering. Vector Calculus by Marsden’s (≈600 pages; not to be confused with their 3-volum Calculus) is an awesome, slightly more advanced book (covering only Calculus III/IV). These books will all deliver when a deep understanding is in priority. They are all very interesting and sufficiently comprehensive. If a bit more math logic in terms of rigor and theoretical aspects are of interest, then Spivak’s Calculus(≈600 pages) is a superb introduction in that direction (purely logical, mathematical -- rather than applied but very interesting with some beautiful and challenging problems of theoretical type). Please note that Spivak covers only 50% of topics in calculus. If you want more calculus with more rigor -- it is Apostol (I don't recommend it for beginners; it's rigorous but it's an olla podrida of linear algebra, calculus, and analytic geometry or a Jack of all trades but master of non and yet it is a rigorous classical text recommended by many. Don't misconstrue my opinion about Apostol. His text is not bad, not by a long shot. On the flip side it's good for rote learners citing it without real understanding).
Part 2. (Physics). Physics by Young and Freedman (≈1500 pages) is almost the optimal choice as it is not too long, not too short for more or less serious introduction from scratch. Fundamentals of Physics by Halliday and Resnick (≈1500 pages) is just as good; it is an outstanding text in fact! There’s also an excellent and comprehensive Berkeley course: Physics Course (in 5 volumes). It consists of Mechanics by Kittel and Knight (≈400 pages), Electricity and Magnetism by Pursell (≈500 pages), Thermal Physics by Kittel and Kroemer (≈500 pages), Quantum Physics by Wichmann (≈400 pages), Statistical and Thermal Physics by Reif (≈600 pages). These are all extremely interesting books. They are comprehensive enough. Feynman Lectures on Physics are also very good. They are partly college course books and partly just a popular read (but a serious read with problems and SMs). All these books require knowledge of Calculus. That’s it. That’s my advice based off of the hundreds of books on math and physics I have. All the books I recommended I'm familiar with/read. Please note these are all books for college, let’s say, for a serious university when math, physics, and engineering are in priority. These are all suited for beginners and yet provide an in-depth coverage at undergrad level.
IMPORTANT ADDENDUM:
I recon best books for real beginners should be pointed out as well:
1) Differential and Integral Calculus by Granville (this text is 100 years old, it's around 500 pages only. No vector calculus -- one variable, multivariables, and ODE only.
2) Calculus Made Easy by Thompson and Gardner. (≈300 pages, also lacks vector calculus) I'm gonna quote a couple of sentences of the authors: If it [their book] falls into the hands of the professional mathematicians, they will rise up as one man, and damn it...it [their book] commits several grievous and deplorable errors...it shows how ridiculously easy most of the operations of the calculus really are...it gives away so many trade secrets...
3) College Physics by Serway Vuille. Very accessible text. Covers all the basics (1200 pages only) for a serious beginner totally from scratch -- so simple that calculus is not required. Yet it is a fantastic book that still contains all the main derivations of important equations, plus vector algebra. The best first course in physics. It is a sort of precalculus in physics. Suited for someone who had no exposure to physics before, yet comprehensive and serious.
Now slightly more advanced material than what is contained in average college course books for engineering students:
1) Vector Calculus by Colley (≈600 pages). Not only a superb text but comprehensive. She gives recommendations on good books at the end. While her recommendations (will provide a second opinion) are the best I've ever seen -- yet I don't agree with them 100%. The book is superb though and crystal clear -- better then the books she recommends (mostly advanced/intermediate classical texts which are well known). It's an in-depth version (kind of on steroids) of standard Calculus III/IV. Similar in clarity to Mardsen's Vector Calculus. It's topnotch.
2) Calculus: Complete Course by Adams and Essex (≈1100 pages). Standard just as Calculus by Larson and Thomas' Calculus but unlike Thomas' and Larson this book has a lot of challenging problems that standard texts lack. So if you like challenging problems, this is it. Adams and Essex is slightly more advanced than average. Heavy emphasis on applications and physics. Commendable job by the authors.
3) Calculus by Stewart (≈1300 pages). He might skip a few completely elementary steps here and there, and people start to think it’s not as clear as Larson’s text. Well, it is as clear – it just reveals terrible gaps in precalculus, which leads students to rote-learn formulas and concepts expecting everything on a silver platter without thinking i.e. when math is just plugging in numbers. But that’s not math; that is pure dumb rote learning and a waste of time. This book is in between Adam/Essex and Larson in terms of difficulty. The differences between all the three are in fact very, very minor.
4) See recommendations by Colley in her Vector Calculus. Even more advanced level books are recommended there. Emphasis starts to shift on math rigor there.
5) Classical Mechanics by Gregory (only 600 pages of relatively compact book). That's mostly theoretical mechanics but very interesting, crystal clear. Illustrated by hundreds of examples that help figure out things. Mechanics is the core of physics. This text is a little bit advanced and should be started after finishing ODE and vector calculus. It's a fascinated read (!) if you are prepared. Full of crystal clear derivations and superb explanations. Can't praise it enough. Here you will be able to "unleash" everything you studied in calculus but Gregory will incentivize you a bit more to continue studying and delving deeper into math/physics!
CONCLUSION/SUMMARY
No books above are of the exam type that is of the condensed, rote-learner-friendly, aced-the exam-and-forgot kind of style. On the contrary all the books recommended above are for fundamental knowledge, for deep understanding and delving into details, for figuring out the nature (physics) and logic (math). They are not of the style "goes in one ear out the other" My top default recommendations are as follows:
I would recommend Marsden (≈1000 pages) and Larson (≈1300 pages) by default. But if a person has strong math background (plowed through the whole 1000-page precalc book), then Thomas' Calculus (problems are easy there) coupled with a 1100-page Adams and Essex (has enough tough problems that you may skip if you don't want them) is a topnotch choice. Adams and Essex has a very strong conceptual and application-related coverage as well. Calculus by Stewart (≈1300 pages) is a good alternative to Adams and Essex.
Physics: Physics by Young and Freedman (≈1500 pages) + Fundamentals of Physics by Halliday and Resnick (≈1500 pages) are my recommendation by default. These two books on physics both include a number challenging problems if you like to push yourself a little. If not, such problems might be skipped.
It's important to understand that it's best to use at least two quite different books on сalculus. SMs are necessary to check your solutions right away.The same goes for physics. I also believe a good precalc text must not be brushed aside. A 1000-page Algebra and Trigonometry by Larson (not the one that is called precalculus!) is an excellent choice as is Stewart's Precalculus (≈1000 pages)
If these books look daunting or longish, I advise re-thinking that perception. Authors in fact cut back on a lot of material, try make things crystal clear without sacrificing explanations of main concepts and ideas. And opting for small books won't cut it if an in-depth knowledge is in priority. For passing exams something smaller (+some Schaum's book for practicing problems) might be a smart choice but not for the real knowledge and understanding. For example, I have a Calculus book, which doesn't include ODE or complex variables but it is still 2000 pages long. My Advanced Analytic Geometry is 700 pages long. Now, think how it all gets squeezed in, how many things get left out, derivations omitted, less rigor employed etc. At the same time I named a few much shorter books that don't cut back on conceptual understanding and provide all derivations and explanations within their extremely short volumes (Granville's Calculus, Vuille's physics).
Off Topic Remark: Although this is a personal recommendation, even problem solutions have a personal touch when mistakes may go unnoticed or explanations might be horrible and murky. People have no recourse when they need text book recommendations. Okay, I know there are some posts (usually short just like references at the back of the book) and there are policy guidelines in place. The fact that in this specific SE website this question was not banned immediately speaks volumes. Thought to post recommendations in comments but decided to post it as an answer. If to be removed and deleted, well, guidelines and rules are there for a reason. It’s understandable that soft questions tend to be voted down or ignored.
answered Dec 11 '18 at 9:32
Ken Draco
58629
In my recommendations below, I emphasize books that allow understanding things at a deeper level, at conceptual level. Books that cover a lot and provide a sound, deep knowledge. These books are opposite of what rote-learners would need. There won't be concatenations of theorems for rote-learning without a real, deep and intuitive understanding. I don't believe in studying books that don't provide all derivations and crystal clear explanations. No books for dummies are recommended here. Delving deep, contemplating and pushing yourself required. No walk-through, not even with a 300-page book by Gardner. Yet the books below are not overly rigorous or advanced; they are crystal clear/user friendly in exposing the material and they can be studied from scratch by beginners. If only a couple of books are required (not, like, kinda, best 7-10 books), please jump to the summary/conclusions at the bottom.
Part 1 (Math) The best books are Calculus by Larson (≈1300 pages) and Thomas’ Calculus (≈1300 pages). There is also a great precalculus book called Algebra and Trigonometry by Larson (≈1000 pages) or alternatively Precalculus by Stewart (≈1000 pages). A thousand pages of precalculus must not be skipped but 50% of its material is always skipped (as a result students have problems with basic things and are flailing in math although they always claim that they do know precalc). The best book on linear algebra is Elementary Linear Algebra by Kolman (≈600 pages) but it might be a bit challenging; Strang’s Linear Algebra (≈500 pages) is easier and is superb. Calculus by Marsden is the easiest complete course (Berkeley) –it is superb (3 volumes totaling ≈1000 pages); SMs are called Student’s Guides). Analytic geometry is nowadays neglected, however there’s a good book: Analytic Geometry by Douglas (≈500 pages). Boyce and DiPrima (≈700 pages) should be the choice on ODE. Advice: if precalculus and Douglas' Analytic Geometry are to be skipped (bad idea but that's what happens 99% of the time) I suggest simpler books by Marsden rather than Thomas’ Calculus. They still cover everything needed (in terms of calculus) for physics and engineering. Vector Calculus by Marsden’s (≈600 pages; not to be confused with their 3-volum Calculus) is an awesome, slightly more advanced book (covering only Calculus III/IV). These books will all deliver when a deep understanding is in priority. They are all very interesting and sufficiently comprehensive. If a bit more math logic in terms of rigor and theoretical aspects are of interest, then Spivak’s Calculus(≈600 pages) is a superb introduction in that direction (purely logical, mathematical -- rather than applied but very interesting with some beautiful and challenging problems of theoretical type). Please note that Spivak covers only 50% of topics in calculus. If you want more calculus with more rigor -- it is Apostol (I don't recommend it for beginners; it's rigorous but it's an olla podrida of linear algebra, calculus, and analytic geometry or a Jack of all trades but master of non and yet it is a rigorous classical text recommended by many. Don't misconstrue my opinion about Apostol. His text is not bad, not by a long shot. On the flip side it's good for rote learners citing it without real understanding).
Part 2. (Physics). Physics by Young and Freedman (≈1500 pages) is almost the optimal choice as it is not too long, not too short for more or less serious introduction from scratch. Fundamentals of Physics by Halliday and Resnick (≈1500 pages) is just as good; it is an outstanding text in fact! There’s also an excellent and comprehensive Berkeley course: Physics Course (in 5 volumes). It consists of Mechanics by Kittel and Knight (≈400 pages), Electricity and Magnetism by Pursell (≈500 pages), Thermal Physics by Kittel and Kroemer (≈500 pages), Quantum Physics by Wichmann (≈400 pages), Statistical and Thermal Physics by Reif (≈600 pages). These are all extremely interesting books. They are comprehensive enough. Feynman Lectures on Physics are also very good. They are partly college course books and partly just a popular read (but a serious read with problems and SMs). All these books require knowledge of Calculus. That’s it. That’s my advice based off of the hundreds of books on math and physics I have. All the books I recommended I'm familiar with/read. Please note these are all books for college, let’s say, for a serious university when math, physics, and engineering are in priority. These are all suited for beginners and yet provide an in-depth coverage at undergrad level.
IMPORTANT ADDENDUM:
I recon best books for real beginners should be pointed out as well:
1) Differential and Integral Calculus by Granville (this text is 100 years old, it's around 500 pages only. No vector calculus -- one variable, multivariables, and ODE only.
2) Calculus Made Easy by Thompson and Gardner. (≈300 pages, also lacks vector calculus) I'm gonna quote a couple of sentences of the authors: If it [their book] falls into the hands of the professional mathematicians, they will rise up as one man, and damn it...it [their book] commits several grievous and deplorable errors...it shows how ridiculously easy most of the operations of the calculus really are...it gives away so many trade secrets...
3) College Physics by Serway Vuille. Very accessible text. Covers all the basics (1200 pages only) for a serious beginner totally from scratch -- so simple that calculus is not required. Yet it is a fantastic book that still contains all the main derivations of important equations, plus vector algebra. The best first course in physics. It is a sort of precalculus in physics. Suited for someone who had no exposure to physics before, yet comprehensive and serious.
Now slightly more advanced material than what is contained in average college course books for engineering students:
1) Vector Calculus by Colley (≈600 pages). Not only a superb text but comprehensive. She gives recommendations on good books at the end. While her recommendations (will provide a second opinion) are the best I've ever seen -- yet I don't agree with them 100%. The book is superb though and crystal clear -- better then the books she recommends (mostly advanced/intermediate classical texts which are well known). It's an in-depth version (kind of on steroids) of standard Calculus III/IV. Similar in clarity to Mardsen's Vector Calculus. It's topnotch.
2) Calculus: Complete Course by Adams and Essex (≈1100 pages). Standard just as Calculus by Larson and Thomas' Calculus but unlike Thomas' and Larson this book has a lot of challenging problems that standard texts lack. So if you like challenging problems, this is it. Adams and Essex is slightly more advanced than average. Heavy emphasis on applications and physics. Commendable job by the authors.
3) Calculus by Stewart (≈1300 pages). He might skip a few completely elementary steps here and there, and people start to think it’s not as clear as Larson’s text. Well, it is as clear – it just reveals terrible gaps in precalculus, which leads students to rote-learn formulas and concepts expecting everything on a silver platter without thinking i.e. when math is just plugging in numbers. But that’s not math; that is pure dumb rote learning and a waste of time. This book is in between Adam/Essex and Larson in terms of difficulty. The differences between all the three are in fact very, very minor.
4) See recommendations by Colley in her Vector Calculus. Even more advanced level books are recommended there. Emphasis starts to shift on math rigor there.
5) Classical Mechanics by Gregory (only 600 pages of relatively compact book). That's mostly theoretical mechanics but very interesting, crystal clear. Illustrated by hundreds of examples that help figure out things. Mechanics is the core of physics. This text is a little bit advanced and should be started after finishing ODE and vector calculus. It's a fascinated read (!) if you are prepared. Full of crystal clear derivations and superb explanations. Can't praise it enough. Here you will be able to "unleash" everything you studied in calculus but Gregory will incentivize you a bit more to continue studying and delving deeper into math/physics!
CONCLUSION/SUMMARY
No books above are of the exam type that is of the condensed, rote-learner-friendly, aced-the exam-and-forgot kind of style. On the contrary all the books recommended above are for fundamental knowledge, for deep understanding and delving into details, for figuring out the nature (physics) and logic (math). They are not of the style "goes in one ear out the other" My top default recommendations are as follows:
I would recommend Marsden (≈1000 pages) and Larson (≈1300 pages) by default. But if a person has strong math background (plowed through the whole 1000-page precalc book), then Thomas' Calculus (problems are easy there) coupled with a 1100-page Adams and Essex (has enough tough problems that you may skip if you don't want them) is a topnotch choice. Adams and Essex has a very strong conceptual and application-related coverage as well. Calculus by Stewart (≈1300 pages) is a good alternative to Adams and Essex.
Physics: Physics by Young and Freedman (≈1500 pages) + Fundamentals of Physics by Halliday and Resnick (≈1500 pages) are my recommendation by default. These two books on physics both include a number challenging problems if you like to push yourself a little. If not, such problems might be skipped.
It's important to understand that it's best to use at least two quite different books on сalculus. SMs are necessary to check your solutions right away.The same goes for physics. I also believe a good precalc text must not be brushed aside. A 1000-page Algebra and Trigonometry by Larson (not the one that is called precalculus!) is an excellent choice as is Stewart's Precalculus (≈1000 pages)
If these books look daunting or longish, I advise re-thinking that perception. Authors in fact cut back on a lot of material, try make things crystal clear without sacrificing explanations of main concepts and ideas. And opting for small books won't cut it if an in-depth knowledge is in priority. For passing exams something smaller (+some Schaum's book for practicing problems) might be a smart choice but not for the real knowledge and understanding. For example, I have a Calculus book, which doesn't include ODE or complex variables but it is still 2000 pages long. My Advanced Analytic Geometry is 700 pages long. Now, think how it all gets squeezed in, how many things get left out, derivations omitted, less rigor employed etc. At the same time I named a few much shorter books that don't cut back on conceptual understanding and provide all derivations and explanations within their extremely short volumes (Granville's Calculus, Vuille's physics).
Off Topic Remark: Although this is a personal recommendation, even problem solutions have a personal touch when mistakes may go unnoticed or explanations might be horrible and murky. People have no recourse when they need text book recommendations. Okay, I know there are some posts (usually short just like references at the back of the book) and there are policy guidelines in place. The fact that in this specific SE website this question was not banned immediately speaks volumes. Thought to post recommendations in comments but decided to post it as an answer. If to be removed and deleted, well, guidelines and rules are there for a reason. It’s understandable that soft questions tend to be voted down or ignored.
answered Dec 11 '18 at 9:32
Ken Draco
58629
edited Dec 13 '18 at 1:36
answered Dec 11 '18 at 9:32
Ken Draco
58629
answered Dec 11 '18 at 9:32
Ken Draco
58629
answered Dec 11 '18 at 9:32
Ken Draco
58629
58629
add a comment |
add a comment |
Mathematical methods for physicists-G. B. Arfken and H. J. Weber
– Thomas Shelby
Dec 10 '18 at 4:00
1
Thank you very much!
– Jason Dalmeida
Dec 10 '18 at 5:02
1
Don't forget the co-author F. E. Harris, @ThomasShelby!
– Shaun
Dec 10 '18 at 5:14
1
@Shaun Sorry, my bad!
– Thomas Shelby
Dec 10 '18 at 5:48
Jason Dalmeida, I've written detailed recommendations. Now I've edited and expanded them. Hope they will be of some help.
– Ken Draco
Dec 12 '18 at 11:41