Show that the vector path is regular?
$begingroup$
Let ${tilde{i}, tilde{j}, tilde{k}}$ be the standard basis of vectors for IR3. If the path $tilde{x}$ : IR → IR3
is defined by
$$tilde{x}= cos 4t tilde{i}+ sin 4t tilde{j}+ 2t^2 tilde{k},$$
then show that $tilde{x}$ is regular.
I looked online and couldn't find what 'regular' meant in this context. Does it just mean continuous?
calculus multivariable-calculus
edited Jul 21 '16 at 21:00
janmarqz
6,20241630
asked Jul 21 '16 at 20:33
Ciaran SCiaran S
247
$endgroup$
add a comment |
$begingroup$
Let ${tilde{i}, tilde{j}, tilde{k}}$ be the standard basis of vectors for IR3. If the path $tilde{x}$ : IR → IR3
is defined by
$$tilde{x}= cos 4t tilde{i}+ sin 4t tilde{j}+ 2t^2 tilde{k},$$
then show that $tilde{x}$ is regular.
I looked online and couldn't find what 'regular' meant in this context. Does it just mean continuous?
calculus multivariable-calculus
edited Jul 21 '16 at 21:00
janmarqz
6,20241630
asked Jul 21 '16 at 20:33
Ciaran SCiaran S
247
$endgroup$
2
$begingroup$
From where did you get the word "regular"? If you got it from a book, which book is?
$endgroup$
– MonsieurGalois
Jul 21 '16 at 20:41
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highly probable it means that the derivative is non zero
$endgroup$
– janmarqz
Jul 21 '16 at 21:06
1
$begingroup$
@janmarqz I think you're right, my friend came to a similar conclusion. Thanks!!
$endgroup$
– Ciaran S
Jul 25 '16 at 22:06
add a comment |
$begingroup$
Let ${tilde{i}, tilde{j}, tilde{k}}$ be the standard basis of vectors for IR3. If the path $tilde{x}$ : IR → IR3
is defined by
$$tilde{x}= cos 4t tilde{i}+ sin 4t tilde{j}+ 2t^2 tilde{k},$$
then show that $tilde{x}$ is regular.
I looked online and couldn't find what 'regular' meant in this context. Does it just mean continuous?
calculus multivariable-calculus
edited Jul 21 '16 at 21:00
janmarqz
6,20241630
asked Jul 21 '16 at 20:33
Ciaran SCiaran S
247
$endgroup$
Let ${tilde{i}, tilde{j}, tilde{k}}$ be the standard basis of vectors for IR3. If the path $tilde{x}$ : IR → IR3
is defined by
$$tilde{x}= cos 4t tilde{i}+ sin 4t tilde{j}+ 2t^2 tilde{k},$$
then show that $tilde{x}$ is regular.
I looked online and couldn't find what 'regular' meant in this context. Does it just mean continuous?
calculus multivariable-calculus
calculus multivariable-calculus
edited Jul 21 '16 at 21:00
janmarqz
6,20241630
asked Jul 21 '16 at 20:33
Ciaran SCiaran S
247
edited Jul 21 '16 at 21:00
janmarqz
6,20241630
asked Jul 21 '16 at 20:33
Ciaran SCiaran S
247
edited Jul 21 '16 at 21:00
janmarqz
6,20241630
edited Jul 21 '16 at 21:00
janmarqz
6,20241630
edited Jul 21 '16 at 21:00
janmarqz
6,20241630
6,20241630
asked Jul 21 '16 at 20:33
Ciaran SCiaran S
247
asked Jul 21 '16 at 20:33
Ciaran SCiaran S
247
asked Jul 21 '16 at 20:33
Ciaran SCiaran S
247
247
2
$begingroup$
From where did you get the word "regular"? If you got it from a book, which book is?
$endgroup$
– MonsieurGalois
Jul 21 '16 at 20:41
$begingroup$
highly probable it means that the derivative is non zero
$endgroup$
– janmarqz
Jul 21 '16 at 21:06
1
$begingroup$
@janmarqz I think you're right, my friend came to a similar conclusion. Thanks!!
$endgroup$
– Ciaran S
Jul 25 '16 at 22:06
add a comment |
2
$begingroup$
From where did you get the word "regular"? If you got it from a book, which book is?
$endgroup$
– MonsieurGalois
Jul 21 '16 at 20:41
$begingroup$
highly probable it means that the derivative is non zero
$endgroup$
– janmarqz
Jul 21 '16 at 21:06
1
$begingroup$
@janmarqz I think you're right, my friend came to a similar conclusion. Thanks!!
$endgroup$
– Ciaran S
Jul 25 '16 at 22:06
2
2
$begingroup$
From where did you get the word "regular"? If you got it from a book, which book is?
$endgroup$
– MonsieurGalois
Jul 21 '16 at 20:41
$begingroup$
From where did you get the word "regular"? If you got it from a book, which book is?
$endgroup$
– MonsieurGalois
Jul 21 '16 at 20:41
$begingroup$
highly probable it means that the derivative is non zero
$endgroup$
– janmarqz
Jul 21 '16 at 21:06
$begingroup$
highly probable it means that the derivative is non zero
$endgroup$
– janmarqz
Jul 21 '16 at 21:06
1
1
$begingroup$
@janmarqz I think you're right, my friend came to a similar conclusion. Thanks!!
$endgroup$
– Ciaran S
Jul 25 '16 at 22:06
$begingroup$
@janmarqz I think you're right, my friend came to a similar conclusion. Thanks!!
$endgroup$
– Ciaran S
Jul 25 '16 at 22:06
add a comment |
1 Answer
1
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$begingroup$
From Anthony Tromba and Jerry Mardsen's book, "Vector Calculus," a path c is said to be regular at a point t0 if the derivative of c at t0 does not equal 0. If the derivative of c at t0 does not equal 0 for all t, we say that c is a regular path.
answered Mar 13 '18 at 0:58
vectorcalc23Avectorcalc23A
1
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add a comment |
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$begingroup$
From Anthony Tromba and Jerry Mardsen's book, "Vector Calculus," a path c is said to be regular at a point t0 if the derivative of c at t0 does not equal 0. If the derivative of c at t0 does not equal 0 for all t, we say that c is a regular path.
answered Mar 13 '18 at 0:58
vectorcalc23Avectorcalc23A
1
$endgroup$
add a comment |
$begingroup$
From Anthony Tromba and Jerry Mardsen's book, "Vector Calculus," a path c is said to be regular at a point t0 if the derivative of c at t0 does not equal 0. If the derivative of c at t0 does not equal 0 for all t, we say that c is a regular path.
answered Mar 13 '18 at 0:58
vectorcalc23Avectorcalc23A
1
$endgroup$
add a comment |
$begingroup$
From Anthony Tromba and Jerry Mardsen's book, "Vector Calculus," a path c is said to be regular at a point t0 if the derivative of c at t0 does not equal 0. If the derivative of c at t0 does not equal 0 for all t, we say that c is a regular path.
answered Mar 13 '18 at 0:58
vectorcalc23Avectorcalc23A
1
$endgroup$
From Anthony Tromba and Jerry Mardsen's book, "Vector Calculus," a path c is said to be regular at a point t0 if the derivative of c at t0 does not equal 0. If the derivative of c at t0 does not equal 0 for all t, we say that c is a regular path.
answered Mar 13 '18 at 0:58
vectorcalc23Avectorcalc23A
1
answered Mar 13 '18 at 0:58
vectorcalc23Avectorcalc23A
1
answered Mar 13 '18 at 0:58
vectorcalc23Avectorcalc23A
1
answered Mar 13 '18 at 0:58
vectorcalc23Avectorcalc23A
1
1
add a comment |
add a comment |
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$begingroup$
From where did you get the word "regular"? If you got it from a book, which book is?
$endgroup$
– MonsieurGalois
Jul 21 '16 at 20:41
$begingroup$
highly probable it means that the derivative is non zero
$endgroup$
– janmarqz
Jul 21 '16 at 21:06
1
$begingroup$
@janmarqz I think you're right, my friend came to a similar conclusion. Thanks!!
$endgroup$
– Ciaran S
Jul 25 '16 at 22:06