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 review and begin reading Chapter 14. By
the end of this
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 concise summary of the
content of the paper?
Does the
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 NOTES EXAM. DO NOT OPEN THE TEST UNTIL
YOU ARE INSTRUC
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 that (ab )c can have more values than abc . First remember
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, Section, and Number (C.S.N).
2.5.26: Find the absolute val
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 NOTES EXAM. DO NOT OPEN THE TEST UNTIL
YOU ARE INSTRUC
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 defined with a fundamental period given by < x < . We
sket
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 by the Chapter, Section, and Number (C.S.N). Highlight
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 by the Chapter, Section, and Number (C.S.N). Highlight
.
(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 the functions f (t) = 1 and g(t) = t .
(b). Apply the Lap
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) + sin(b)cos(a)
(1+ n) = n!
(z 1) t
t
0
e dt
1
(z) = (
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 . As
described in class, x(t) satisfies:
d 2 x(t)
dx(t)
2
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
solutions to Laplaces equation 2=0. The solutions are called
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
described in class, x(t) satisfies:
d 2 x(t)
dx(t)
+ 2
+
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, we can generate another solution via conformal mapping.
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 by the Chapter, Section, and Number (C.S.N). Highlight
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 can write
f (z) =
g(z)
,
(z z0 )p
where g(z0 ) is finit
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 using the techniques of sections 3 and 4.
Problems
Our
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
1 + iz
1 iz
1 + iz
=
1 + iz
1
log
2i
1 iz
2iw = log
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 HW, but it is good for you
to see it. The material from
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 plotted on the next page.
w=
2
(1.1)
Ch. 14, 9, 8
ex cos(
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 mostly involves problems
on complex analysis from Chapter
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(3i/2) = cos(3/2) + isin(3/2)
2
Ch. 2, 5A, p. 52, 6
1+i
1
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 49. Principle values and the later
material in section
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 and z = 1. Since these are both simple poles, we can si
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
(1.1)
sin z
sin z
about two dierent curves, |z| = 1 an
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 changes, indicated as Svap, in going
B. P.
Svap
(K)
(J / Kmol
Study of Airplane Flight using 2-Dimensional Airfoil Model
Abstract: The optimization of airplane flight performance relies heavily on calculations of
the aerodynamic of an airfoil. Problems related to airfoils and fluid flows are generally
highly complex