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# MATH 351 (Fall 2013): Differential Equations

### Section and Class Number

Section 01 & 15328

Jing Li

### Contact information:

Office:  Live Oak Hall (LO), Room 1303C
Phone: 818-677-7799
E-mail: jing.li(at)csun(dot)edu

Office hours: Mondays & Wednesdays 3:30 pm - 4:30 pm or by appointment (email)

### Final Exam

December 16, 2013, Wednesday 3:00 pm - 5:00 pm, Chaparral Hall Room 5117

### Midterm Exams

Midterm Exam 1: Wednesday (Oct. 2, 2013).
Midterm Exam 2: (date to be annouced) in class.
Midterm Exam 3: (date to be annouced) in class.

### Lecture times and locations

Mondays & Wednesdays 2:00 pm - 3:15 pm in CR (Chaparral Hall) 5117

### Course text

Elementary Differential Equations and Boundary Value Problems (10th edition), by William E. Boyce and Richard C. DiPrima.

### Announcements

1. Midterm 1 will be in class on Wednesday (Oct. 2, 2013). It is going to cover Chapter 1 (1.1, 1.2, 1.3) and Chapter 2 (2.1 - 2.8).

2. Midterm 2 will be in class on Wednesday (Nov. 13, 2013). It is going to cover Chapter 3 (3.1, 3.2, 3.3, 3.4, 3.5, 3.6), Chapter 4 (4.1, 4.2), and Chapter 5 (5.1, 5.2, 5.3).

3. I will be holding extra office hours from 3pm - 5pm on Tuesday (Nov. 12, 2013).

### Course syllabus and tentative timetable

I will post all assigments, solutions and additional material in this space. You should therefore consult this spot frequently.

Course Syllabus

Week Date Topics covered Homework Homework due date Practice Problems Additional Material
1 Aug 26 & 28 Sec. 1.1: Some Basic Mathematical Models; Direction Fields

Sec. 1.2: Solutions of Some Differential Equations

Sec. 1.3: Classification of Differential Equations
Exercises 1.1 (page 7): 7, 9, 15, 17, 19, 21, 23

Exercises 1.2 (page 15): 3, 7, 9, 13, 15, 17;

Exercises 1.3 (page 24): 1, 3, 5, 7, 11, 14, 17, 19
(due Sept 11) Exercises 1.1 (page 7): 8, 10, 16, 18, 20, 22, 24;

Exercises 1.2 (page 15): 4, 5, 6, 8, 10, 12, 14, 16, 19;

Exercises 1.3 (page 24): 2, 4, 6, 8, 10, 12, 13, 16, 18, 20, 29
2 Sept 2 & 4 Labor Day Holdiay

Sec. 2.1: Linear Equations; Method of Integrating Factors

Sec. 2.2: Separable Equations
Exercises 2.1 (page 39): 13, 15, 17, 19, 31, 33;

Exercises 2.2 (page 48): 3, 5, 7, 9, 13(a)(c), 15(a)(c), 21(solve analytically), 25(solve analytically), 29, 30(a)(b)(c)(d)(e), 31(a)(b), 33(a)(b), 37(a)(b)
(Exercises 2.1 due Sept 11)

(Exercises 2.2 due Sept 18)
Exercises 2.1 (page 39): 14, 16, 18, 20, 30, 32, 38, 39, 41;

Exercises 2.2 (page 48): 2-26 (even), 23, 32(a)(b), 34(a)(b), 36(a)(b), 38(a)(b)

3 Sept 9 & 11 Sec. 2.2 (cont'd): Examples

Sec. 2.3: Modeling with First Order Equations

Sec. 2.4: Differences Between Linear and Nonlinear Equations
Exercises 2.3 (page 60): 1, 4, 8, 16, 19, 24;

Exercises 2.4 (page 76): 1, 3, 7, 9, 11, 15, 22, 28, 33;
(Exercises 2.3 due Sept 18)

(Exercises 2.4 due Sept 18)
Exercises 2.3 (page 60): 2, 3, 5, 7, 9, 11, 32;

Exercises 2.4 (page 76): 2, 4, 5, 6, 8, 10, 12, 13, 21, 23-26, 29;
4 Sept 16 & 18 Sec. 2.5: Autonomous Equations and Population Dynamics

Sec. 2.6: Exact Equations and Integrating Factors
Exercises 2.5 (page 88): 1, 3, 5, 7, 9, 11, 15, 16, 20, 22;

Exercises 2.6 (page 101): 3, 5, 7, 9, 11, 13, 15, 25, 27, 29;

(Exercises 2.5 due Oct 2)

(Exercises 2.6 due Oct 2)
Exercises 2.5 (page 88): 2, 4, 6, 8, 10, 12-14, 17, 21, 23, 24;

Exercises 2.6 (page 101): 2-12 (even), 16, 20, 26, 28, 30;
Solutions for Quiz 1
5 Sept 23 & 25

Sec. 2.7: Numerical Approximations: Euler's Method

Sec. 2.8: The Existence and Uniqueness Theorem

Exercises 2.7 (page 110): 1, 3;

Exercises 2.8 (page 120): 1, 3, 6, 13, 14, 15, 16, 17, 18, 19;

(Exercises 2.7 due Oct 2)

(Exercises 2.8 due Oct 9)

Exercises 2.7 (page 110): 2, 4;

Exercises 2.8 (page 120): 2, 4, 5;

Miscellaneous Problems for Chapter 2 (page 133): 1-35;
Lecture Notes for Sec. 2.7
6 Sept 30 & Oct 2 Sec. 3.1: Homogeneous Equations with Constant Coefficient

Midterm 1
Exercises 3.1 (page 144): 10, 11, 12, 15, 17, 19, 21, 23, 25, 27; (Exercises 3.1 due Oct 16) Exercises 3.1 (page 144): 1-7, 9, 13, 14, 16, 18, 20, 22, 24, 26, 28; Solutions for Midterm 1
7 Oct 7 & 9 Sec. 3.1 cont'd

Sec. 3.2: Solutions of Linear Homogeneous Equations; the Wronskian

Exercises 3.2 (page 155): 5, 6, 9, 11, 12, 14, 15, 17, 19, 22, 26, 31, 34;

(Exercises 3.2 due Oct. 21)

Exercises 3.2 (page 155): 2, 3, 4, 7, 8, 10, 13, 16, 18, 20, 21, 23, 24, 25, 27, 28, 29, 30, 32, 33, 35
8 Oct 14 & 16

Sec. 3.3: Complex Roots of the Characteristic Equations

Sec. 3.4: Repeated Roots; Reduction of Order

Exercises 3.3 (page 164): 5, 8, 9, 12, 13, 18, 19, 20, 25, 34, 39, 40;

Exercises 3.4 (page 172): 2, 4, 6, 8, 9, 11, 14, 15, 23, 27, 28;
(Exercises 3.3 due Oct. 21)

(Exercises 3.4 due Oct. 28)
Exercises 3.3 (page 164): 1-4, 6, 7, 10, 11, 14-16, 17, 21-24, 35-38, 41, 42;

Exercises 3.4 (page 172): 12, 13, 16, 17, 18, 24-26, 29, 30, 40-45;
9 Oct 21 & 23 Sec. 3.5: Nonhomogeneous Equations; Method of Undetermined Coefficients

Sec. 3.6: Variation of Parameters

Exercises 3.5 (page 184): 1, 2, 3, 4, 5, 6, 7, 8, 10, 12, 14, 16, 17, 19, 20, 26;

Exercises 3.6 (page 190): 3, 5, 7, 8, 9, 11, 13, 15, 17, 31;
(Exercises 3.5 due Oct. 30)

(Exercises 3.6 due Nov. 4)
Exercises 3.5 (page 184): 9, 11, 13, 15, 18, 22, 23, 29, 30, 31, 32, 36;

Exercises 3.6 (page 190): 4, 6, 10, 12, 16, 18, 19, 20, 21, 28, 29, 30, 32;
10 Oct 28 & 30 Sec. 4.1: General Theory of nth Order Linear Equations

Sec. 4.2: Homogeneous Equations with Constant Coefficients

Sec. 5.1: Review of Power Series
Exercises 4.1 (page 226): 3, 5, 7, 8, 13;

Exercises 4.2 (page 233): 2, 5, 9, 11, 13, 15, 16, 19, 20;

Exercises 5.1 (page 253): 2, 3, 5, 6, 7, 8, 12, 13, 15, 17, 21, 22, 23, 24, 27;

(Exercises 4.1 due Nov. 4)

(Exercises 4.2 due Nov. 4 )

(Exercises 5.1 due Nov. 13 )
Exercises 4.1 (page 226): 2, 4, 6, 9, 10, 15, 16, 27, 28;

Exercises 4.2 (page 233): 1, 3, 4, 6, 10, 12, 14, 17, 18, 21-24;

Exercises 5.1 (page 253): 1, 4, 9, 10, 11, 14, 16, 18, 19, 20, 25, 26, 28;
Lecture Notes for Sec. 4.1 & 4.2

Solutions for Quiz 2
11 Nov 4 & 6 Sec. 5.2: Series Solutions Near an Ordinary Point, Part I

Sec. 5.3: Series Solutions Near an Ordinary Point, Part II

Sec. 7.1: Introduction

Sec. 7.2: Review of Matrices
Exercises 5.2 (page 263): 4, 7, 8, 9, 10, 11, 12, 19, 21;

Exercises 5.3 (page 269): 2, 3, 6, 7, 10, 12, 13, 16, 19, 22, 23;

Exercises 7.1 (page 363): 2, 3, 4, 5, 7, 9, 11, 15, 16;

Exercises 7.2 (page 376): 2, 8, 9, 11, 13, 15, 17, 21, 23, 25;
(Exercises 5.2 due Nov. 13)

(Exercises 5.3 due Nov. 13)

(Exercises 7.1 due Nov. 25)

(Exercises 7.2 due Nov. 25)

Exercises 5.2 (page 263): 5, 6, 13, 14, 20, 22;

Exercises 5.3 (page 269): 1, 4, 5, 8, 9, 11, 14, 17, 18, 20, 21;

Exercises 7.1 (page 363): 1, 6, 8, 10, 12, 14;

Exercises 7.2 (page 376): 1, 3, 4, 5, 6, 7, 10, 12, 14, 16, 18, 19, 20, 22, 24, 26;
Lecture Notes for Sec. 7.1

Lecture Notes for Sec. 7.2
12 Nov 11 & 13 Veterans' Day Holiday

Midterm 2
Solutions for Midterm 2
13 Nov 18 & 20 Sec. 7.3: Systems of Linear Algebraic Equations: Linear Independence, Eigenvalues, Eigenvectors

Sec. 7.4: Basic Theory of Systems of First Order Linear Equations

Sec. 7.5: Homogeneous Linear Systems with Constant Coefficients

Sec. 7.6: Complex Eigenvalues
Exercises 7.3 (page 388): 2, 3, 4, 5, 7, 11, 13, 16, 17, 22, 23, 25;

Exercises 7.4 (page 394): 2, 4, 5, 6;

Exercises 7.5 (page 405): 2, 3, 6, 7, 9, 10, 11, 13, 16, 17, 25, 27;
(Exercises 7.3 due Nov. 25)

(Exercises 7.4 due Nov. 27)

(Exercises 7.5 due Dec. 2)

Exercises 7.3 (page 388): 6, 8, 9, 10, 14, 18, 19, 20, 21, 24;

Exercises 7.4 (page 394): 1, 3, 7;

Exercises 7.5 (page 405): 1, 4, 5, 8, 12, 14, 15, 18-24, 26, 28, 29, 30;

14 Nov 25 & 27 Sec. 7.6: cont'd

Sec. 7.7: Fundamental Matrices

Sec. 7.8: Repeated Eigenvalues

Exercises 7.6 (page 417): 4, 5, 6, 7, 9, 19;

Exercises 7.7 (page 427): 1, 3, 5, 7, 9, 11;

Exercises 7.8 (page 436): 2, 3, 4, 5, 7, 9;
(Exercises 7.6 due Dec. 4)

(Exercises 7.7 due Dec. 4)

(Exercises 7.8 won't be collected)

Exercises 7.6 (page 417): 1, 2, 3, 8, 10, 11, 12, 13, 14, 15, 16, 17, 18, 20;

Exercises 7.7 (page 427): 2, 4, 6, 8, 10, 12, 17;

Exercises 7.8 (page 436): 1, 6, 8, 10, 11, 12, 15;
Solutions for Quiz 3
15 Dec 2 & 4 Sec. 9.1: The Phase Plane: Linear Systems

Sec. 9.2: Autonomous Systems and Stability

Sec. 9.3: Locally Linear Systems

Sec. 9.4: Competing Species

Sec. 9.5: Predator-Prey Equations
Exercises 9.1 (page 505): 1, 2, 4, 5, 6, 8, 9, 11, 13, 15, 19;

Exercises 9.2 (page 517): 1, 2, 3, 4, 17, 19, 21;

Exercises 9.3 (page 527): 1, 3, 5, 6, 7, 12, 15, 16, 19, 21, 26, 27, 28;

Exercises 9.4 (page 541): 1, 3, 5, 8, 9, 10;

Exercises 9.5 (page 551): 1-5, 9;
(Exercises 9.1 won't be collected)

(Exercises 9.2 won't be collected)

(Exercises 9.3 won't be collected)

(Exercises 9.4 won't be collected)

(Exercises 9.5 won't be collected)
Exercises 9.1 (page 505): 3, 7, 10, 12, 14, 16, 17, 18, 20, 21, 22;

Exercises 9.2 (page 517): 5-16, 18, 20, 22, 23, 24, 25, 26, 27, 28;

Exercises 9.3 (page 527): 2, 4, 8, 9, 10, 11, 13, 14, 17, 18, 20, 23, 24, 25, 30;

Exercises 9.4 (page 541): 2, 4, 6, 11, 12, 13-19;

Exercises 9.5 (page 551): 6, 7, 8, 11, 12, 13, 14, 15, 16;
Solutions for Quiz 4
16 Dec 9 Midterm 3 Solutions for Midterm 3
17 Final Exam Week