PHY100B HW #1
Due Friday, 1/11/13 at 5pm
Review of Complex Numbers
These problems should be mostly review and are due on Friday!
Start these right away.
Reading and Review
Read Chapter 2 of Boas for r
Final Paper Grading Rubric
Physics 101 Mathematical Methods in the Physical Sciences
Name:_ Perm:_ Section:_
Paper Title:_
Title/Abstract/Introduction
Does the title and abstract provide a clear and
UNIVERSITY OF CALIFORNIA SANTA BARBARA
Department of Physics
Physics 101
Prof. Jean Carlson
Winter 2015
MIDTERM EXAM # 1
THIS IS A FIFTY MINUTE EXAM. THIS IS A CLOSED BOOK, CLOSED
HOMEWORK, AND CLOSED
UNIVERSITY OF CALIFORNIA, SANTA BARBARA
Department of Physics
Physics 101 (Winter 2017)
TAs: Jason Wien, Eric Mefford
Homework 2 Solutions
Boas 2.14.24
(p. 74)
The point of this problem is to show tha
Physics 101 (Winter 2017)
Problem Set 1: Solutions
Eric Mefford
Problems are from Mathematical Methods in the Physical Sciences, 3rd Edition by Mary Boas. The problems
are labelled by the Chapter, Sec
UNIVERSITY OF CALIFORNIA SANTA BARBARA
Department of Physics
Physics 101
Prof. Jean Carlson
Winter 2017
MIDTERM EXAM # 2
THIS IS A FIFTY MINUTE EXAM. THIS IS A CLOSED BOOK, CLOSED
HOMEWORK, AND CLOSED
(1). 2 (21/ 3 1) / 3
(2). (a). V ky, kx, V + ikz
(b). V k1/ 2 sin( /2), k1/ 2 cos( /2), V + ikw1/ 2 , = u 2 + v 2 , = tan 1 (v /u)
(3). (a). n!/sn +1
a n!
n
(b).
n =0 s n +1
(4). (a). Sketch square
UNIVERSITY OF CALIFORNIA, SANTA BARBARA
Department of Physics
Physics 101 (Winter 2017)
TA: Jason Wien, Eric Mefford
Homework 8 Solutions
Boas 7.8.12
(p. 363)
(a) Consider the periodic function ex def
Physics 101 (Winter 2017)
Problem Set 7: Solutions
TAs: Eric Mefford and Jason Wien
Problems are from Mathematical Methods in the Physical Sciences, 3rd Edition by Mary Boas. The problems
are labelled
Physics 101 (Winter 2017)
Problem Set 5: Solutions
TAs: Eric Mefford and Jason Wien
Problems are from Mathematical Methods in the Physical Sciences, 3rd Edition by Mary Boas. The problems
are labelled
.
(1). Solve the following set of equations for t 0 using the Laplace Transform method:
dy(t) dz(t)
+
2y(t) = 1
dt
dt
dy(t)
z(t)
=t
dt
with y(0) = z(0) =
1.
(a). Compute the Laplace Transform of th
FORMULAS
e i = cos( ) + isin( )
e i e i
2i
i
e + e i
cos( ) =
2
n
t
1
= n =0
tn
e t = n =0
1 t
n!
sin( ) =
ux = v y , uy = v x
limz z0 [(z z0 ) f (z)]
p(z0 )
q'(z0 )
limz z0
sin(a + b) = sin(a)cos(b)
Additional Required Problems:
(1). Use Fourier Transforms to find the complete solution x(t) for the displacement of
the
damped, driven harmonic oscillator for the case of critical damping 2 = 0 2 . A
PDE & Complex Variables
P15-1
Lesson 15 Potential Theory Using Complex Analysis (EK 18)
Introduction
Potentials in physics can simplify the derivation of forces. They are typically described by
soluti
Additional Recommended Problem:
(1) Use Fourier Transforms to find the complete solution x(t) for the displacement of the
damped, driven harmonic oscillator for the case of overdamping 2 > 0 2 . As
de
UNIVERSITY OF CALIFORNIA, SANTA BARBARA
Department of Physics
Physics 101 (Winter 2017)
TA: Jason Wien, Eric Mefford
Homework 6 Solutions
Boas 14.10.4
(p. 716)
Given a solution of Laplaces equation, w
Physics 101 (Winter 2017)
Problem Set 3: Solutions
TAs: Eric Mefford and Jason Wien
Problems are from Mathematical Methods in the Physical Sciences, 3rd Edition by Mary Boas. The problems
are labelled
UNIVERSITY OF CALIFORNIA, SANTA BARBARA
Department of Physics
Physics 101 (Winter 2017)
TA: Jason Wien, Eric Mefford
Homework 4 Solutions
Boas 14.6.4
(p. 686)
To find the Laurent series about z0 , we
PHY101 HW #3
Due Friday, 1/25/13 @ 5pm
Cauchys integral formula and Laurent series
Reading
Read Section 4 of Chapter 14 of Boas. Although there are problems below
from later sections, they are solved
Physics 101 Homework 2 Solutions
Michael Gary, modied by Michael Johnson, modied by Jason Kaufman
January 18, 2013
1
Ch. 2, 17, p. 81, 19
We want to show tan1 z =
1
2i
log
1+iz
1iz .
Let
w
1 + iz
1 iz
PHY101 HW #5
Due Friday, 2/8/13 @ 5pm
Principal Values and Branch Cuts
Reading
Read the rest of Section 7 as well as sections 8,9, and 10 of Chapter 14
of Boas. (I wont lecture on section 8 or assign
Physics 101 Homework 6 Solutions
Michael Gary, modied by Michael Johnson, modied by Jason Kaufman
February 15, 2013
1
Ch. 14, 9, 2
x + iy + 1
y
x+1
z+1
=
= i
2i
2i
2
2
Lines of constant u and v are pl
PHY101 HW #2
Due Friday, 1/18/13 @ 5pm
Functions of a Complex Variable
Reading
Read Sections 1-3 of Chapter 14 of Boas.
Problems
This problem set has a few more review problems from Chapter 2, but mos
Physics 101 Homework 1 Solutions
Michael Gary, modied by Michael Johnson, rechecked by Jason Kaufman
January 9, 2013
1
Ch. 2, 4, p. 51, 13
y
z
x
z
Figure 1: (x, y) = (0, 1), i, (r, ) = (1, 3/2), exp(3
PHY101 HW #4
Due Friday, 2/1/13 @ 5pm
Clever tricks for evaluating integrals
Reading
Read Sections 5-7 of Chapter 14 of Boas. Actually, this assignment will
only use section 7 through the top of page
Physics 101 Homework 4 Solutions
Michael Gary, modied by Michael Johnson, modied by Jason Kaufman
January 29, 2013
1
Ch. 14, 6, p. 686, 16
We want the residues of
z2
2z
=
z(1 z)
z(z 1)
(1.1)
at z = 0
Physics 101 Homework 3 Solutions
Michael Gary, modied by Michael Johnson, Jason Kaufman, and Don Marolf
January 23, 2013
1
Ch. 14, 3, p. 677, 17
We want to evaluate the contour integral
C
sin z
dz
2z
7A Quiz 9
Last 6 digits of ID #
Name:
Signature:
DL Sec.
No books or notes. Calculators OK. Show all your work below. Answers alone do not receive credit!
The table shows measured molar entropy change