AMath 231
ASSIGNMENT # 1 Solutions: Review [15 Total]
Fall 2014
Due Monday, September 15, 2014 at 2pm in box 7, slot 11 (A-M) and 12 (N-Z), located
across from MC4066. Late assignments or assignments submitted to the incorrect dropbox
will receive a grade
AMath 231
ASSIGNMENT #7: More
; Gauss & Stokes Thms.
Spring 2014
Due on or before Thursday, July 3rd at noon in the correct drop slot.
1. Show that the velocity v of a particle in cylindrical coordinates is given by:
v=
2.
d
d
dz
e + e + ez
dt
dt
dt
a) A
AMath 231
ASSIGNMENT #8: Applications of Vector Calculus
Spring 2014
Due on or before Thursday, July 10th at noon in the correct drop slot.
1. Determine whether the vector eld F = (y cosh z, x cosh z, xy sinh z) is conservative
and if so, nd a scalar pote
AMath 231
ASSIGNMENT #9: Fourier Series
Spring 2014
Due on or before Thursday, July 17th at noon in the correct drop slot.
1. Let C[a, a] be the space of continuous functions on the interval [a, a]. Given that
f C[a, a] is even and g C[a, a] is odd, show
AMath 231
ASSIGNMENT #10: Fourier Series, Convergence
Spring 2014
Due on or before Thursday, July 24th at noon in the correct drop slot.
1. Use Parsevals formula and a suitable Fourier series to sum
n=1
1
.
(2n 1)2
Hint: Look at Table 5.1 in the course no
AMath 231
ASSIGNMENT #11: Fourier Transforms
Spring 2014
Not due in, but you are responsible for this material for the nal exam.
1. Show that the Fourier transform of
2
.
1 + 2
Sketch the graphs in the time domain and in the frequency domain.
f (t) = e|t|
AMath 231, Spring 2014
Assignment 2 Solutions
Page 1 of 3
1.
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AMath 231, Spring 2014
Assignment 5 Solutions
Page 1 of 2
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AMath 231, Spring 2014
Page 1 of 4
Assignment 3 Solutions
1. (a) The speed of the particle is given by
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and make sure that JavaScript is enabled. t cos
AMath 231, Spring 2014
Assignment 7 Solutions
Page 1 of 4
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AMath 231
ASSIGNMENT # 4: Greens Theorem, Cons. Fields
Spring 2014
Due on or before Thursday, June 5th at noon in the correct drop slot.
1.
(i) Consider the closed curve C, x(t) = (a cos t, b sin t), where a and b are positive
constants, and the velocity
AMath 231
ASSIGNMENT # 3: Line Integrals
Spring 2014
Due on or before Thursday, May 29th at noon in the correct drop slot.
1. Consider a particle with position given by
x = g(t) = (et cos t, et sin t),
0 t 2
(a) Show that the speed of the particle is give
AMATH 231
ASSIGNMENT # 9 Stokes Theorem
Fall 2014
Due Monday, November 24, 2014 at 2pm in box 7, slot 11 (A-M) and 12 (N-Z), located
across from MC4066. Late assignments or assignments submitted to the incorrect dropbox
will receive a grade of zero. Write
AMATH 231
ASSIGNMENT # 6: Surfaces and Surface Integrals
Fall 2014
Due Monday, October 27, 2014 at 2pm in box 7, slot 11 (A-M) and 12 (N-Z), located across
from MC4066. Late assignments or assignments submitted to the incorrect dropbox will
receive a grad
AMATH 231
ASSIGNMENT # 9 Stokes Theorem
Fall 2014
Due Monday, November 24, 2014 at 2pm in box 7, slot 11 (A-M) and 12 (N-Z), located
across from MC4066. Late assignments or assignments submitted to the incorrect dropbox
will receive a grade of zero. Write
AMATH 231
Coordinates
ASSIGNMENT # 7 Vector Identities and Curvilinear
Fall 2014
Due Monday, November 17, 2014 at 2pm in box 7, slot 11 (A-M) and 12 (N-Z), located
across from MC4066. Late assignments or assignments submitted to the incorrect dropbox
will
AMATH 231
Coordinates
ASSIGNMENT # 7 Vector Identities and Curvilinear
Fall 2014
Due Monday, November 10, 2014 at 2pm in box 7, slot 11 (A-M) and 12 (N-Z), located
across from MC4066. Late assignments or assignments submitted to the incorrect dropbox
will
AMATH 231
ASSIGNMENT # 10 Fourier Series
Fall 2014
Due Monday, December 1, 2014 at 2pm in box 7, slot 11 (A-M) and 12 (N-Z), located across
from MC4066. Late assignments or assignments submitted to the incorrect dropbox will
receive a grade of zero. Write
Lecture 30: AMATH 231-F14-001
4.4
November 17, 2014
Maxwells Equations
In this subsection we derive Maxwells equations using the theorems of vector calculus.
4.4.1
Gauss Law
The electrostatic force eld at x0 due to a charge Q at position xQ is,
E(x0 ) =
Q
Lecture 24: AMATH 231-F14-001
4.2
4.2.1
November 3, 2014
Gauss Theorem
The Theorem
Theorem 4.7 Let be a bounded subset of R3 whose boundary, is a single piecewise smooth orientated closed surface. If F is C 1 on then
F dV =
F n d,
where n is the unit out
AMath 231
ASSIGNMENT # 1: Review and Curves
Spring 2014
Due on or before Thursday, May 15th at noon in location to be announced. Late assignments or those put into the wrong drop slot will not be marked.
Comment: The rst two problems are review. If you to
AMath 231
ASSIGNMENT # 2: Vector Fields
Spring 2014
Due on or before Thursday, May 22nd at noon in the correct drop slot.
NOTE: Monday May 19th is a holiday, and there is no tutorial on Wednesday the 21st since
that day follows a Monday schedule for all U
AMath 231, Spring 2014
Assignment 9 Solutions
Page 1 of 4
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and make sure that JavaScript is enabled. You will likely need to download the file first, t
AMath 231
ASSIGNMENT # 1: Review and Curves
Spring 2015
Due on or before Wednesday, May 13th at 1:26pm in location to be announced. Late assignments or those put into the wrong drop slot will not be marked.
Comment: The rst two problems are review. If you
AMath 231
ASSIGNMENT # 5: Surfaces, Scalar Surf. Integrals
Spring 2014
Due on or before Thursday, June 12th at noon in the correct drop slot.
1. Sketch the given surface x = g(u, v), where g : Duv R3 is given below. Discuss
whether the surface is smooth.
AMath 231
ASSIGNMENT # 6: Surface Integrals,
Spring 2015
Due on or before Thursday, June 18th at the usual time and place.
F n dS and circulation
1. Calculate the ux
F dx for the given vector eld F,
where is the triangular piece of the plane x + 2y + 3z =
AMath 231
ASSIGNMENT #7: More
; Gauss & Stokes Thms.
Spring 2015
Due on or before Thursday, June 24th at the usual time and place. This is the last
assignment before the midterm, and you likely wont get it back before then. Consider
keeping a copy for stu
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Assignment 6 - Surfaces, surface integrals and geodesics.
Due February 10, 2017 (1 pm).
~ v) = (u cos v, u sin v, v), (u, v) [0, 5] [0, 2]. Find its area.
1. Sketch the helicoid S(u,
RR
2. Evaluate the surface integral
f dS where,
(a) f (x, y, z) = xz and