Thought process behind vector valued functions and parameterisation
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Can someone please confirm whether my intuitive notions behind what vector-valued functions and parameterisation is correct. Below are some questions.
Are vector-valued functions like functions of a single variable with domain of real values and range of vectors in an $n$-dimensional space? Does the vector-valued function involve a formula for a position vector which traces out a curve when the range of input values varies?
Do we use parameterisation's to describe curves which cannot be expressed as functions like $y=f(x)$ and $x=g(y)$? How are vector-valued functions and parameterisation's related?
I'm studying physics and these are some math preliminary topics for when I study motion of point Particles, dynamics and conservation laws.
functions vectors intuition parametrization
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add a comment |
$begingroup$
Can someone please confirm whether my intuitive notions behind what vector-valued functions and parameterisation is correct. Below are some questions.
Are vector-valued functions like functions of a single variable with domain of real values and range of vectors in an $n$-dimensional space? Does the vector-valued function involve a formula for a position vector which traces out a curve when the range of input values varies?
Do we use parameterisation's to describe curves which cannot be expressed as functions like $y=f(x)$ and $x=g(y)$? How are vector-valued functions and parameterisation's related?
I'm studying physics and these are some math preliminary topics for when I study motion of point Particles, dynamics and conservation laws.
functions vectors intuition parametrization
$endgroup$
add a comment |
$begingroup$
Can someone please confirm whether my intuitive notions behind what vector-valued functions and parameterisation is correct. Below are some questions.
Are vector-valued functions like functions of a single variable with domain of real values and range of vectors in an $n$-dimensional space? Does the vector-valued function involve a formula for a position vector which traces out a curve when the range of input values varies?
Do we use parameterisation's to describe curves which cannot be expressed as functions like $y=f(x)$ and $x=g(y)$? How are vector-valued functions and parameterisation's related?
I'm studying physics and these are some math preliminary topics for when I study motion of point Particles, dynamics and conservation laws.
functions vectors intuition parametrization
$endgroup$
Can someone please confirm whether my intuitive notions behind what vector-valued functions and parameterisation is correct. Below are some questions.
Are vector-valued functions like functions of a single variable with domain of real values and range of vectors in an $n$-dimensional space? Does the vector-valued function involve a formula for a position vector which traces out a curve when the range of input values varies?
Do we use parameterisation's to describe curves which cannot be expressed as functions like $y=f(x)$ and $x=g(y)$? How are vector-valued functions and parameterisation's related?
I'm studying physics and these are some math preliminary topics for when I study motion of point Particles, dynamics and conservation laws.
functions vectors intuition parametrization
functions vectors intuition parametrization
edited Jan 11 at 1:53
asked Jan 10 at 19:39
user606466
add a comment |
add a comment |
1 Answer
1
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$begingroup$
Are vector-valued functions like functions of a single variable with
domain of real values and range of vectors in an n-dimensional space?
Yes, but a vector-valued function can have any number of variables, e.g., ${bf v}(r, s, t, w)$.
Does the vector-valued function involve a formula for a position
vector which traces out a curve when the range of input values varies?
Yes, but again, there may be several variables involved. For a continuous vector-valued function the "tip of the vector" in general sweeps out a line, surface, volume, etc., depending upon the number of variables.
Do we use parameterisation's to describe curves which cannot be
expressed as functions like y=f(x) and x=g(y)? How are vector-valued
functions and parameterisation's related? What are parametric equation and are they similar to vector valued functions in any way?
One can parameterize a vector-valued function as ${bf v} = (v_1, v_2, ldots, v_k) = (f_1(t), f_2(t), ldots, f_k(t))$.
answered Jan 10 at 19:46
David G. StorkDavid G. Stork
12.2k41836
$endgroup$
$begingroup$
I was asking regarding parametric equations, curves and their traces and how vector valued functions fit in with them. Apologies if I'm unclear. That's why I'm trying to make sense of it by asking.
$endgroup$
– user606466
Jan 10 at 20:00
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It is clear you were asking "regarding" parametric equations, but it is not clear what you were asking.
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– David G. Stork
Jan 10 at 20:02
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Let me rephrase and ask what parametric equations are and if they are similar to vector valued function's in any way.
$endgroup$
– user606466
Jan 10 at 20:13
add a comment |
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1 Answer
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1 Answer
1
active
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active
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active
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votes
$begingroup$
Are vector-valued functions like functions of a single variable with
domain of real values and range of vectors in an n-dimensional space?
Yes, but a vector-valued function can have any number of variables, e.g., ${bf v}(r, s, t, w)$.
Does the vector-valued function involve a formula for a position
vector which traces out a curve when the range of input values varies?
Yes, but again, there may be several variables involved. For a continuous vector-valued function the "tip of the vector" in general sweeps out a line, surface, volume, etc., depending upon the number of variables.
Do we use parameterisation's to describe curves which cannot be
expressed as functions like y=f(x) and x=g(y)? How are vector-valued
functions and parameterisation's related? What are parametric equation and are they similar to vector valued functions in any way?
One can parameterize a vector-valued function as ${bf v} = (v_1, v_2, ldots, v_k) = (f_1(t), f_2(t), ldots, f_k(t))$.
answered Jan 10 at 19:46
David G. StorkDavid G. Stork
12.2k41836
$endgroup$
$begingroup$
I was asking regarding parametric equations, curves and their traces and how vector valued functions fit in with them. Apologies if I'm unclear. That's why I'm trying to make sense of it by asking.
$endgroup$
– user606466
Jan 10 at 20:00
$begingroup$
It is clear you were asking "regarding" parametric equations, but it is not clear what you were asking.
$endgroup$
– David G. Stork
Jan 10 at 20:02
$begingroup$
Let me rephrase and ask what parametric equations are and if they are similar to vector valued function's in any way.
$endgroup$
– user606466
Jan 10 at 20:13
add a comment |
$begingroup$
Are vector-valued functions like functions of a single variable with
domain of real values and range of vectors in an n-dimensional space?
Yes, but a vector-valued function can have any number of variables, e.g., ${bf v}(r, s, t, w)$.
Does the vector-valued function involve a formula for a position
vector which traces out a curve when the range of input values varies?
Yes, but again, there may be several variables involved. For a continuous vector-valued function the "tip of the vector" in general sweeps out a line, surface, volume, etc., depending upon the number of variables.
Do we use parameterisation's to describe curves which cannot be
expressed as functions like y=f(x) and x=g(y)? How are vector-valued
functions and parameterisation's related? What are parametric equation and are they similar to vector valued functions in any way?
One can parameterize a vector-valued function as ${bf v} = (v_1, v_2, ldots, v_k) = (f_1(t), f_2(t), ldots, f_k(t))$.
answered Jan 10 at 19:46
David G. StorkDavid G. Stork
12.2k41836
$endgroup$
$begingroup$
I was asking regarding parametric equations, curves and their traces and how vector valued functions fit in with them. Apologies if I'm unclear. That's why I'm trying to make sense of it by asking.
$endgroup$
– user606466
Jan 10 at 20:00
$begingroup$
It is clear you were asking "regarding" parametric equations, but it is not clear what you were asking.
$endgroup$
– David G. Stork
Jan 10 at 20:02
$begingroup$
Let me rephrase and ask what parametric equations are and if they are similar to vector valued function's in any way.
$endgroup$
– user606466
Jan 10 at 20:13
add a comment |
$begingroup$
Are vector-valued functions like functions of a single variable with
domain of real values and range of vectors in an n-dimensional space?
Yes, but a vector-valued function can have any number of variables, e.g., ${bf v}(r, s, t, w)$.
Does the vector-valued function involve a formula for a position
vector which traces out a curve when the range of input values varies?
Yes, but again, there may be several variables involved. For a continuous vector-valued function the "tip of the vector" in general sweeps out a line, surface, volume, etc., depending upon the number of variables.
Do we use parameterisation's to describe curves which cannot be
expressed as functions like y=f(x) and x=g(y)? How are vector-valued
functions and parameterisation's related? What are parametric equation and are they similar to vector valued functions in any way?
One can parameterize a vector-valued function as ${bf v} = (v_1, v_2, ldots, v_k) = (f_1(t), f_2(t), ldots, f_k(t))$.
answered Jan 10 at 19:46
David G. StorkDavid G. Stork
12.2k41836
$endgroup$
Are vector-valued functions like functions of a single variable with
domain of real values and range of vectors in an n-dimensional space?
Yes, but a vector-valued function can have any number of variables, e.g., ${bf v}(r, s, t, w)$.
Does the vector-valued function involve a formula for a position
vector which traces out a curve when the range of input values varies?
Yes, but again, there may be several variables involved. For a continuous vector-valued function the "tip of the vector" in general sweeps out a line, surface, volume, etc., depending upon the number of variables.
Do we use parameterisation's to describe curves which cannot be
expressed as functions like y=f(x) and x=g(y)? How are vector-valued
functions and parameterisation's related? What are parametric equation and are they similar to vector valued functions in any way?
One can parameterize a vector-valued function as ${bf v} = (v_1, v_2, ldots, v_k) = (f_1(t), f_2(t), ldots, f_k(t))$.
answered Jan 10 at 19:46
David G. StorkDavid G. Stork
12.2k41836
edited Jan 10 at 20:17
answered Jan 10 at 19:46
David G. StorkDavid G. Stork
12.2k41836
answered Jan 10 at 19:46
David G. StorkDavid G. Stork
12.2k41836
answered Jan 10 at 19:46
David G. StorkDavid G. Stork
12.2k41836
12.2k41836
$begingroup$
I was asking regarding parametric equations, curves and their traces and how vector valued functions fit in with them. Apologies if I'm unclear. That's why I'm trying to make sense of it by asking.
$endgroup$
– user606466
Jan 10 at 20:00
$begingroup$
It is clear you were asking "regarding" parametric equations, but it is not clear what you were asking.
$endgroup$
– David G. Stork
Jan 10 at 20:02
$begingroup$
Let me rephrase and ask what parametric equations are and if they are similar to vector valued function's in any way.
$endgroup$
– user606466
Jan 10 at 20:13
add a comment |
$begingroup$
I was asking regarding parametric equations, curves and their traces and how vector valued functions fit in with them. Apologies if I'm unclear. That's why I'm trying to make sense of it by asking.
$endgroup$
– user606466
Jan 10 at 20:00
$begingroup$
It is clear you were asking "regarding" parametric equations, but it is not clear what you were asking.
$endgroup$
– David G. Stork
Jan 10 at 20:02
$begingroup$
Let me rephrase and ask what parametric equations are and if they are similar to vector valued function's in any way.
$endgroup$
– user606466
Jan 10 at 20:13
$begingroup$
I was asking regarding parametric equations, curves and their traces and how vector valued functions fit in with them. Apologies if I'm unclear. That's why I'm trying to make sense of it by asking.
$endgroup$
– user606466
Jan 10 at 20:00
$begingroup$
I was asking regarding parametric equations, curves and their traces and how vector valued functions fit in with them. Apologies if I'm unclear. That's why I'm trying to make sense of it by asking.
$endgroup$
– user606466
Jan 10 at 20:00
$begingroup$
It is clear you were asking "regarding" parametric equations, but it is not clear what you were asking.
$endgroup$
– David G. Stork
Jan 10 at 20:02
$begingroup$
It is clear you were asking "regarding" parametric equations, but it is not clear what you were asking.
$endgroup$
– David G. Stork
Jan 10 at 20:02
$begingroup$
Let me rephrase and ask what parametric equations are and if they are similar to vector valued function's in any way.
$endgroup$
– user606466
Jan 10 at 20:13
$begingroup$
Let me rephrase and ask what parametric equations are and if they are similar to vector valued function's in any way.
$endgroup$
– user606466
Jan 10 at 20:13
add a comment |
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