# Math 54, Summer 2016

This is the homepage for the Summer 2016 Math 54 (Lecture 3) and its discussion section.

Instructor: Kyle Miller
E-mail: kmill at math.berkeley.edu
Meeting times:
Lecture: MTWHF 12-1 pm in 109 Morgan
Discussion: MTWHF 1-2 pm in 109 Morgan
Office hours: Wed/Thu 3-5 pm in 1066 Evans, or by appointment
bCourses: https://bcourses.berkeley.edu/courses/1451943
Piazza: https://piazza.com/berkeley/summer2016/math54/home

The math department publishes a rough course overview. There is also a collection of some past exams.

## 1. Syllabus

Prerequisites: Math 1A-1B or equivalent. Students who have taken such courses at another institution may not have studied differential equations and should learn the relevant material (Stewart Single Variable Calculus chapters 9 and 17) on their own by the time we get to the differential equations portion of Math 54.

Official description: Basic linear algebra; matrix arithmetic and determinants. Vector spaces; inner product spaces. Eigenvalues and eigenvectors; linear transformations. Homogeneous ordinary differential equations; first-order differential equations with constant coefficients. Fourier series and partial differential equations.

Textbook: Lay-Nagle-Saff-Snider, Linear Algebra & Differential Equations. A specially priced UC Berkeley paperback edition is available. This is a combination of

• Lay, Linear Algebra and Its Applications (4th ed.); and
• Nagle, Saff, and Snider, Fundamentals of Differential Equations (8th ed.).

### 1.1. Homework, quizzes, and exams

Homework will be due once per week, at the end of discussion Friday. Late homework will be given points according to the formula ${2}^{-n}s$, rounded down, where $s$ is the score the homework would have received when not late, and $n$ is the number of days late.

We will have fifteen-minute quizzes every Friday at the beginning of discussion. There will be no make-up quizzes.

A one-hour midterm will be given July 22nd during lecture.

A two-hour final will be given August 12 during lecture, through discussion.

The lowest quiz score and the lowest homework score will be dropped.

The final grade will be determined according to the following: 15% homeworks, 20% quizzes, 25% midterm, 40% final exam.

### 1.3. Special accommodations

All students requesting special accommodations need to be registered with the Disabled Student Services and need to provide a letter indicating the necessary accommodations. Because it is very difficult to arrange accommodations at the last minute, all requests must be received at least 8 days prior to the exams.

### 1.4. Piazza

This term we will be using Piazza for class discussion. I encourage you to ask questions on Piazza rather than via e-mails for our collective benefit. Find our class page at https://piazza.com/berkeley/summer2016/math54/home.

## 2. Schedule

Note: Answers to odd-number exercises for Lay begin on page 363. For the second textbook, page 657.

This schedule is subject to change. Homework, once posted, will remain constant.

### 2.1. Week 1 (Jun 20–24)

Homework 1: (Lay) due June 24
1.1: 1, 3, 9, 11, 17, 18, 23
1.2: 1, 3, 4, 13, 15, 19, 21
1.3: 1, 5, 7, 12, 14, 25
1.4: 1, 2, 5, 11, 23, 29, 30
1.5: 1, 5, 7, 10, 23, 33
1.7: 1, 3, 6, 11, 15, 21

### 2.2. Week 2 (Jun 27–Jul 1)

Reading: sections 2.1–2.3, 3.1–3.3, 4.1 (Lay)

Homework 2: (Lay) due July 1
1.8: 1, 3, 5, 7, 9, 32, 24
1.9: 1, 3, 5, 7, 17, 23
2.1: 1, 5, 7, 8, 9, 17
2.2: 1, 4, 5, 8, 9, 31
2.3: 1, 8, 15, 16, 20, 33
3.1: 1, 2, 6, 9, 25, 27, 29
3.2: 5, 11, 22, 27, 37, 39
3.3: 1, 8, 12, 19, 29

### 2.3. Week 3 (Jul 5–8)

Note: July 4 is a holiday.

Homework 3: (Lay) due July 8
4.1: 1, 3, 6, 11, 13, 21, 31
4.2: 1, 4, 8, 12, 24, 31, (35, 36)
4.3: 11, 13, 19, 23, 24, 31, 32
4.4: 1, 9, 12, 13, 15
4.5: 1, 10, 11, 13, 14, 29

### 2.4. Week 4 (Jul 11–15)

Homework 4: (Lay) due July 15
4.6: 1, 5, 8, 16, 28
4.7: 7
5.1: 1, 3, 11, 13, 16, 26
5.2: 1, 2, 9, 10, 18, 20
5.3: 1, 7, 10, 17, 18, 27
5.4: 10, 13, 14, 22, 25, 26
(5.5: 7, 17, 21, 22, 23)
6.1: 1, 2, 15, 16, 27, 28
Problems in parentheses are optional and ungraded. They are fairly important, so it is worth at least reading them.

### 2.5. Week 5 (Jul 18–22)

Reading: sections 6.2–6.5, 6.7, 7.1 (Lay)

Homework 5: (Lay) due July 25 (Monday)
6.2: 1, 2, 8, 11, 19
6.3: 1, 3, 12, 18
6.4: 1, 2, 13, 18
6.5: 1, 10, 19, 20, 21
6.7: 3, 13, 25 (clarification: Gram-Schmidt $1$, $t$ ,${t}^{2}$)
7.1: 13, 14, 23

Midterm exam schemata

Midterm: July 22 in lecture.

### 2.6. Week 6 (Jul 25–29)

Homework 6: (NSS) due July 29
4.1: 4, 7
4.2: 1, 2, 13, 14, 22, 29, 37
4.3: 2, 3, 9, 21, 38
4.4: 9, 12, 14, 18, 28, 30, 34
4.5: 1, 4, 7, 9, 18, 23
4.6: 3, 4, 20

### 2.7. Week 7 (Aug 1–5)

Homework 7: (NSS) due August 5
6.1: 7, 9, 23
6.2: 1, 6, 15, 19
9.1: 1, 3, 7, 11
9.4: 14, 28, 30
9.5: 2, 9, 12, 31, 32, 50
9.6: 1, 13
9.7: 1, 2, 8, 21(a), 24
9.8: 7, 8, 12, 17, 22

### 2.8. Week 8 (Aug 8–12)

Final: August 12 in lecture.

Final exam planning

Final exam

## 4. Programs

The following are some programs to illustrate some computations and concepts from the course. These are linked to in the Lecture notes section.

## 5. Worksheets

The department publishes worksheets on the Lower Division Course Outlines page, Math 54 Worksheet (pdf).

## 6. How to study

Step 1. Read the book, go to lecture, section, and office hours, solve examples. Check your understanding.

Step 2. Solve homework problems. If you get stuck, you did not complete Step 1, so go back and figure out exactly what you still need to understand.

Mathematics does not end with words written on a page, rather an answer is an artifact or byproduct of understanding. Furthermore, you are trying to convice the reader that you are correct: thus revise! It is your responsibility to make your answers clear. In fact, if on a quiz or exam the grader does not notice you are “right,” this is your fault, and you will lose points for it.

[1] Erratum: the heat equation derivation is incorrect and should have $1/{n}^{2}$ in the denominator rather than ${n}^{2}$.