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# MATH 351 (Fall 2015): Differential Equations

### Section and Class Number

Section 01 & 16147

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 1:00 pm - 2:00 pm or by appointment (email)

### Final Exam

December 9, 2015, Wednesday 10:15 am - 12:15 pm, Chaparral Hall Room 5117

### Midterm Exams

Midterm Exam 1: (date to be announced) in class.
Midterm Exam 2: (date to be announced) in class.
Midterm Exam 3: (date to be announced) in class.

### Lecture times and locations

Mondays & Wednesdays 11:00 am - 12:15 pm in CR (Chaparral Hall) 5117

### Course text

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

### Course syllabus and tentative timetable

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

Week Date Topics covered Homework Homework due date Practice Problems Additional Material
1 Aug 24 & 26 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 2nd
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 Aug 31 & Sept 2 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)
due Sept 9
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 7 & 9 Labor Day Holiday

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 16)

(Exercises 2.4 due Sept 28)

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 14 & 16 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 Sept 30)

(Exercises 2.6 due Oct 7)
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

Statistics for Quiz 1
5 Sept 21 & 23 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 14)

(Exercises 2.8 due Oct 21)
Exercises 2.7 (page 110): 2, 4;

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

Miscellaneous Problems for Chapter 2 (page 133): 1-35;

6 Sept 28 & 30 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 26)
Exercises 3.1 (page 144): 1-7, 9, 13, 14, 16, 18, 20, 22, 24, 26, 28; Solutions for Midterm 1
Statistics for Midterm 1
7 Oct 5 & 7 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. 28)
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 12 & 14

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. 28)

(Exercises 3.4 due Nov. 2nd, extended due Nov. 4)
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 19 & 21 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 Nov. 2nd, extended due Nov. 4)

(Exercises 3.6 due Nov. 9)
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 26 & 28 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. 9)

(Exercises 4.2 due Nov. 9)

(Exercises 5.1 due Nov. 9)

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;

Solutions for Quiz 2

Statistics for Quiz 2
11 Nov 2 & 4 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

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 5.2 due Nov. 23)

(Exercises 5.3 due Nov. 23)

(Exercises 7.1 due Nov. 23)

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;

12 Nov 9 & 11 Midterm 2

Veterans' Day Holiday

Solutions for Midterm 2

Statistics for Midterm 2
13 Nov 16 & 18 Sec. 7.2: Review of Matrices

Sec. 7.3: Systems of Linear Algebraic Equations: Linear Independence, Eigenvalues, Eigenvectors

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

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

(Exercises 7.2 due Nov. 23)

(Exercises 7.3 due Nov. 25)

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

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

14 Nov 23 & 25 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
Sec. 7.7: Fundamental Matrices
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 7.6 (page 417): 4, 5, 6, 7, 9, 19;

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

(Exercises 7.4 due Nov. 30)

(Exercises 7.5 due Nov. 30)

(Exercises 7.6 due Dec. 2nd)

(Exercises 7.7 won't be collected)

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;

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;

Solutions for Quiz 3
15 Nov 30 & Dec 2

Sec. 7.8: Repeated Eigenvalues

Sec. 9.1: The Phase Plane: Linear Systems

Sec. 9.2: Autonomous Systems and Stability

Sec. 9.3: Locally Linear Systems
Exercises 7.8 (page 436): 2, 3, 4, 5, 7, 9;

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 7.8 won't be collected)

(Exercises 9.1 won't be collected)

(Exercises 9.2 won't be collected)

(Exercises 9.3 won't be collected)

Exercises 7.8 (page 436): 1, 6, 8, 10, 11, 12, 15;

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;

16 Dec 7

Sec. 9.4: Competing Species

Sec. 9.5: Predator-Prey Equations
Midterm 3

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

Exercises 9.5 (page 551): 1-5, 9;
(Exercises 9.4 won't be collected)

(Exercises 9.5 won't be collected)
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;

17 Final Exam Week Final Exam on Dec 9 on Classroom CH 5117