Math 54 - Section 8 - Summer 2015

Welcome! Please take a look at the Syllabus.

You can always reach me by email at (my last name)@math.berkeley.edu.

Or during my office hours (starting June 22nd): Mondays, Wednesdays, and Thursdays 10:10-11:00am in 1057 Evans.

Homework:

• Homework 1 (due Fri. 6/26):
1.1: 4, 14, 18
1.2: 8, 12, 14
1.3: 8, 12, 18, 22
1.4: 2, 4, 10, 16
1.5: 6, 18, 32
1.7: 2, 10, 34, 36, 38
1.8: 32, 34, 36
1.9: 2, 6, 10

• Homework 2 (due Tues. 6/30):
2.1: 2, 4, 10, 12, 18, 22, 24, 26, 32
2.2: 2, 8, 12, 16, 24, 32, 38
2.3: 2, 4, 6, 8, 18, 20, 30, 34, 38

• Homework 3 (due Thurs. 7/2):
3.1: 2, 14, 18, 38
3.2: 2, 4, 8, 22, 26, 34, 36
3.3: 20, 28, 32

• Homework 4 (due Tues. 7/7):
4.1: 2, 6, 12, 16, 32, 33, 34
4.2: 2, 6, 16, 18, 22, 28, 32
4.3: 2, 4, 6, 8, 12, 16, 24, 34

• Homework 5 (due Tues. 7/14): This assignment is not due until after Midterm 1, but I recommend you start it before the exam - it will be good practice on the most recent material we've coverd.
The material on coordinates (4.4), change of basis (4.7), and the matrix of a linear transformation (part of 5.4) is all closely related, but unfortunately it's spread out through these sections of the book. I've chosen to group these sections in class (covered on Tuesday 7/7) and on the homework.
4.4: 2, 8, 10, 14, 18, 28, 32
4.7: 2, 10, 14
5.4: 2, 6, 8
4.5: 2, 6, 8, 12, 14, 18, 26
4.6: 2, 6, 8, 10, 14, 16, 28, 29

• Homework 6 (due Fri. 7/17):
5.1: 2, 4, 6, 8, 16, 25, 26, 31, 32
5.2: 2, 10, 18, 20
5.3: 2, 6, 8, 12, 20, 24, 25, 31, 32
5.4: 12, 14, 20, 22

• Homework 7 (due Tues. 7/21):
5.5: 2, 6, 10, 12, 14, 20
6.1: 2, 6, 10, 14, 16, 18, 28, 31
6.2: 2, 6, 8, 12, 16, 20, 29, 30, 31, 33

• Homework 8 (due Tues. 7/28):
6.3: 2, 4, 8, 12, 16, 24
6.4: 4, 8, 12, 22 [Note: We are not covering QR factorization of matrices]
6.7: 4, 6, 8, 14, 16, 17, 20, 22, 24, 26
7.1: 14, 22, 24, 28, 36

• Homework 9 (due Fri. 7/31): From now on, the section numbers will be from the differential equations part of the textbook - unfortunately, these section numbers overlap with the section numbers from the linear algebra part of the book.
6.1: 2, 4, 6, 16, 18, 26, 28, 29
4.2: 2, 14, 18, 21, 22, 26
4.3: 4, 26, 28, 38
6.2: 2, 6, 14, 20, 26

• Homework 10 (due Tues. 8/4):
4.4: 10, 18, 22, 28, 30, 32, 36
4.5: 2, 4, 8, 18, 28, 41, 46, 48
4.6: 2, 8, 9, 12

• Homework 11 (due Fri. 8/7):
9.1: 4, 8, 12
9.4: 20, 21, 22, 26, 31
9.5: 14, 32, 42, 44
9.6: 2, 14
9.7: 4, 14, 25
9.8: 18, 28

• Homework 12 (due Wed. 8/12 - we'll also have the quiz on Wed. 8/12): Some of the integrals involved in computing Fourier coefficients are rather tedious. It's ok with me if you use Wolfram Alpha or some other computational tool to compute these integrals. Remember to simplify the answer as much as possible, though!
Problems 12 and 14 in 10.3 ask you to use a computer to plot a few partial sums of the Fourier series. This is optional, and you certainly don't need to draw the plots on your homework. However, it is rather fun to see the fruits of your labor. I've made an animation of the first 21 partial sums in the Fourier series for these problems, which you can watch here.
10.2: 10, 14, 20, 24, 28
10.3: 12, 14, 20, 22, 28
10.4: 2, 4, 6, 12, 18

Section materials:

• Monday 6/22: Worksheet 1 - Linear equations and row reduction
• Tuesday 6/23: Worksheet 2 - Vector equations and matrix equations
• Wednesday 6/24: Worksheet 3 - Linear transformations
• Friday 6/26: Worksheet 4 - Inverses
• Tuesday 6/30: Worksheet 5 - Transposes
• Thursday 7/2: Worksheet 6 - Null space and column space
• Tuesday 7/7: Worksheet 7 - Matrices and coordinates
• Wednesday 7/15: Worksheet 8 - Matrix powers and dynamical systems
• Friday 7/17: Worksheet 9 - Geometry in R^n
• Tuesday 7/21: Worksheet 10 - Least-squares solutions
• Monday 7/27: Differential Equations Lecture Notes
• Wednesday 7/29: Worksheet 11 - Vandermonde matrices and linear independence
• Monday 8/3: Worksheet 12 - Linear differential equations and matrix equations
• Friday 8/7: Worksheet 13 - The heat equation
• Tuesday 8/11: Worksheet 14 - Generalized Fourier series
• Thursday 8/13: Final Review

Exam resources: I will post solutions here after each exam.
Also, for each exam, I have uploaded the corresponding exam that I gave when I taught Math 54 in Summer 2011, together with my solutions. Following this are four exams from semesters of Math 54 gone by, two of which have solutions. Note that in classes taught by other professors, different material may have been covered and different language may be used. I'm happy to answer questions about issues like this, but I can't make any general comments about how the exams this summer will be similar or different to the exams below.

• Midterm 1: Exam and Solutions
My old Midterm 1 and solutions.
Ribet, Fall '05 and solutions.
Lenstra, Fall '94 and solutions.
Gu, Fall '07.
Vojta, Spring '01.

• Midterm 2: Exam and Solutions
My old Midterm 2 and solutions.
Ribet, Fall '05 and solutions.
Lenstra, Fall '94.
Bergman, Spring '96.
Vojta, Spring '01 and solutions.

• Final: Solutions
My Final and solutions.
Ribet, Fall '05 and solutions.
Lenstra, Fall '94.
Tener, Summer '09.
Tucker-Simmons, Summer '09 and solutions. Note: In the first problem (1.1), there is a typo: the differential equation should be y'' + 10y' + 25y = 0.