PHYSICS 116A
Homework 2 Solutions
I. [optional]
Boas, Ch. 1, 6, Qu. 30 (proof of the ratio test). Just follow the hints.
If , the ratio of succcessive terms for n is less than 1, the hints show that 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
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 ma
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
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 a
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 matr
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|
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
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
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 an
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
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-mechani
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 he
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 com
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 1
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, Pr
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, Pro
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, P
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
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,
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, P
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, P
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, P
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
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 ar
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
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,
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