PHYSICS 116A
Homework 2
Due in class, Friday, January 24
I. [optional]
Boas, Ch. 1, 6, Qu. 30 (proof of the ratio test).
II. [optional]
Boas, Ch. 1, 16, Qu. 1, part (a) (stacking books and relation to the harmonic series).
It is surprising that, in princi
Physics 116A
Solutions to Homework Set #2
1. Boas, problem 1.1023. Transform the series
determine the interval of convergence
3n (n+1)
n=0 (x+1)n
Winter 2012
to a power series and
First we want to make the replacement u = x + 1, which allows us to read t
PHYSICS 116A
Homework 2
Due in class, Friday, January 24
I. [optional]
Boas, Ch. 1, 6, Qu. 30 (proof of the ratio test).
II. [optional]
Boas, Ch. 1, 16, Qu. 1, part (a) (stacking books and relation to the harmonic series).
It is surprising that, in princi
Physics 116A
Solutions to Homework Set #8
Winter 2012
1. Boas, problem 3.129. For Equations 2-7, nd the rottion matrix which relates
the principal axes and the original axes.
I will show the method here for problems 2 and 5 (two variable and three variabl
Physics 116A
Solutions to Homework Set #5
Winter 2012
1. Boas, problem 3.214. Use an augmented matrix to solve the following equation
2x + 3y z = 2
x + 2y z = 4
4x + 7y 3z = 11
(1)
We can write this as a 3 x 4 matrix using the coecient in front of each va
Physics 116A
Solutions to Homework Set #7
Winter 2012
1. Boas, p. 141, problem 3.95. Show that the product AAT is a symmetric
matrix.
Using eq. (9.10) on p. 139 of Boas, (AB)T = B TAT for any two matrices A and
B. Hence,
(AAT )T = (AT )T AT = AAT ,
(1)
wh
Physics 116A
Solutions to Homework Set #4
Winter 2012
1. Boas, p. 105, problem 3.412. Find the angle between the vectors A = -2i + j 2k and B = 2i - 2j
We can invert equation 4.2 which gives A B = |A|B|cos() and solve for theta. The
dot product of A and B
Physics 116A
Solutions to Homework Set #6
Winter 2012
1 . Boas, p. 147, problem 3.10-5(a). Given two vectors,
A = (3 + i , 1 , 2 i , 5i , i + 1) and B = (2i , 4 3i , 1 + i , 3i , 1) ,
nd the norms of A and B and the inner product of A and B , and note tha
Physics 116A
Solutions to Homework Set #3
Winter 2012
1. Boas, p. 57, problem 2.611. Test the following series for convergence:
n=0
2n
2+i
3 4i
.
(1)
This is a geometric series. By the ratio test, z n converges for |z | < 1 and diverges
n=0
for |z | > 1.
Physics 116A
Solutions to Homework Set #1
Winter 2012
1. Boas, problem 1.18 Use equation 1.8 to nd a fraction describing
0.694444444.
a
Start with the formula S = 1r , and notice that we can remove any number of
nite decimals from the front into their own
Physics 116A
Mathematical Methods in Physics
Winter 2012
Final Exam
Instructions:
Solve (or try to solve!) the following ten problems.
Please, write out all intermediate steps quoting the nal answer only will
not be accepted as a valid solution!
You ca
Physics 116A
Mathematical Methods in Physics
Winter 2012
Practice Final
Solve the following ten problems:
1. Test the following innite series for convergence:
n=1
1
.
n n1/n
2. One statistical-mechanical theory of solutions of strong electrolytes
(such as
Physics 116A
Mathematical Methods in Physics
Homework Set #1.
Due Date: Wednesday January 18, 2011
Solve the following exercises:
1. Boas, Chapter 1, Section 1, Problem 8.
2. Boas, Chapter 1, Section 1, Problem 16.
3. Boas, Chapter 1, Section 2, Problem 6
PHYSICS 116A
Homework 4
Due in class, Friday February 7
MIDTERM: In class on Monday February 10. It will cover the material in Chapters 1, 2 and 11 in
Boas.
To get credit you must show your working.
1. Boas, Ch. 11, 7, Qu. 6.
2. Boas, Ch. 11, 7, Qu. 9.
3.
PHYSICS 116A
Homework 3
Due in class, Friday January 31
Note: You can ignore the parts of questions which ask you to use the computer. However, you may
check any of your homework answers using the computer if you wish.
To get credit you must show your wor
PHYSICS 116A
Homework 1
Due in class, Friday January 17
Review carefully the material in Chapter 1 of Boas.
Unless otherwise stated, all problems are from Boas.
1. A ball is dropped from a height of 1m. on to a hard oor. After the rst bounce it rises to a
Physics 116A
Mathematical Methods in Physics
Homework Set #9.
Due Date: Wednesday, March 14
Solve the following exercises:
1. Boas, Chapter 11, Section 3, Problem 5.
2. Boas, Chapter 11, Section 3, Problem 13.
3. Boas, Chapter 11, Section 5, Problem 3.
4.
Physics 116A
Mathematical Methods in Physics
Homework Set #8.
Due Date: Wednesday, March 7
Solve the following exercises:
1. Boas, Chapter 3, Section 12, Problem 9.
2. Boas, Chapter 3, Section 12, Problem 23.
3. Boas, Chapter 3, Section 13, Problem 1.
4.
Physics 116A
Mathematical Methods in Physics
Homework Set #7.
Due Date: Wednesday, February 29
Solve the following exercises:
1. Boas, Chapter 3, Section 9, Problem 5.
2. Boas, Chapter 3, Section 9, Problem 17.
3. Boas, Chapter 3, Section 9, Problem 19(c)
Physics 116A
Mathematical Methods in Physics
Homework Set #6.
Due Date: Wednesday, February 22
Solve the following exercises:
1. Boas, Chapter 3, Section 10, Problem 5(a).
2. Boas, Chapter 3, Section 11, Problem 3.
3. Boas, Chapter 3, Section 11, Problem
Physics 116A
Mathematical Methods in Physics
Homework Set #5.
Due Date: Wednesday, February 15
Solve the following exercises:
1. Boas, Chapter 3, Section 2, Problem 14.
2. Boas, Chapter 3, Section 2, Problem 18.
3. Boas, Chapter 3, Section 3, Problem 6.
4
Physics 116A
Mathematical Methods in Physics
Homework Set #4.
Due Date: Wednesday, February 8
Solve the following exercises:
1. Boas, Chapter 3, Section 4, Problem 12.
2. Boas, Chapter 3, Section 4, Problem 19.
3. Boas, Chapter 3, Section 4, Problem 21.
4
Physics 116A
Mathematical Methods in Physics
Homework Set #3.
Due Date: Wednesday, February 1
Solve the following exercises:
1. Boas, Chapter 2, Section 6, Problem 11.
2. Boas, Chapter 2, Section 7, Problem 13.
3. Boas, Chapter 2, Section 9, Problem 9.
4.
Physics 116A
Mathematical Methods in Physics
Winter 2012
Homework Set #2.
Due Date: Wednesday, January 25th (your Instructors birthday)
Solve the following exercises:
1. Boas, Chapter 1, Section 10, Problem 23.
2. Boas, Chapter 1, Section 13, Problem 4.
3
Physics 116A
Final Exam Solutions
Winter 2011
1. The inverse hyperbolic tangent can be dened via the following integral:
1
arctanh x
=
x
0
dt
.
1 x2 t2
(1)
(a) Derive the power series expansion for arctanh x about x = 0. Determine the
general form for the
Physics 116A
Mathematical Methods in Physics
Winter 2009
Last Collaborative Learning Session, March 2009
Second Practice Final
1. Test the following series for convergence and absolute convergence
n=1
cos n
n2
[absolutely convergent and convergent]
2. Sho
PHYSICS 116A
Homework 5
Due in class, Friday February 14
The Midterm is in class on Monday, Feb. 10.
This homework assignment is short because of the Midterm.
To get credit you must show your working.
1. Review Boas Ch. 3, 4 and 5, and solve Boas, Ch. 3,
PHYSICS 116A
Homework 6
Due in class, Friday February 21
To get credit you must show your working.
For the rst 4 questions, if there is a solution, you should nd it.
1. Boas, Ch. 3, 2, Qu. 8.
2. Boas, Ch. 3, 2, Qu. 9.
3. Boas, Ch. 3, 2, Qu. 12.
4. Boas, C
PHYSICS 116A
Homework 8
Due in class, Friday March 7
Note: There will be one more homework.
To get credit you must show your working.
1. Boas, Ch. 3, 9, Qu. 4.
2. Boas, Ch. 3, 9, Qu. 5.
3. Boas, Ch. 3, 9, Qu. 17.
4. Boas, Ch. 3, 10, Qu. 5(a).
5. Boas, Ch.