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# MATH 351 (Fall 2017): Differential Equations

### Section and Class Number

Section 01 & 16794

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 11:00 am - 12:00 pm or by appointment (email)

### Final Exam

December 13, 2017, Wednesday 8:00 am - 10:00 am, Live Oak Hall Room 1317

### 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 09:30 am - 10:45 am in LO (Live Oak Hall) 1317

### Course text

Elementary Differential Equations (11th edition) or Elementary Differential Equations and Boundary Value Problems (11th edition), by William E. Boyce and Richard C. DiPrima, 2017.

### Announcements

1. Homework assignments and course lecture notes will be posted through CSUN Canvus . Please visit the canvas course webpage frequently.

2. A list of practice problems is posted on this webpage. Please use these for extra practice.

### Course syllabus and tentative timetable

Week Date Topics covered Homework Homework due date Practice Problems Additional Material
1 Aug 28 & 30 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 8):6, 8, 11, 12, 14, 16, 19;

Exercises 1.2 (page 15): 3a, 10, 11, 12;

Exercises 1.3 (page 22): 3, 4,15, 16, 18.

2 Sept 04 & 06 Labor Day Holiday

Sec. 2.1: Linear Equations; Method of Integrating Factors

Exercises 2.1 (page 31): 2c, 3c, 6c, 7c, 10c, 11c, 19, 20, 21;

3 Sept 11 & 13 Sec. 2.2: Separable Differential Equations

Sec. 2.3: Modeling with First Order Equations

Sec. 2.4: Differences Between Linear and Nonlinear Equations

Exercises 2.2 (page 38): 3, 4, 5, 6, 13, 15, 17, 20, 21, 30;

Exercises 2.3 (page 47): 1, 2, 4, 9, 12, 20;

Exercises 2.4 (page 57): 2, 4, 7, 12, 18, 24, 25, 27;

4 Sept 18 & 20 Sec. 2.5: Autonomous Equations and Population Dynamics

Sec. 2.6: Exact Equations and Integrating Factors

Exercises 2.5 (page 67): 2, 4, 5, 6, 7, 8, 9, 14, 15, 17;

Exercises 2.6 (page 75): 2, 4, 6, 8, 10, 11, 19, 20, 21;

5 Sept 25 & 27 Sec. 2.7: Numerical Approximations: Euler's Method

Midterm 1

Exercises 2.7 (page 83): 2, 3, 9, 10, 12;

6 Oct 02 & 04 Sec. 2.8: The Existence and Uniqueness Theorem

Sec. 3.1: Homogeneous Equations with Constant Coefficient

Exercises 2.8 (page 90): 2, 7, 9a, 10a, 11, 14, 15, 16, 17, 18;

Review Problems for Chapter 2 (page 100): 1-24;

Exercises 3.1 (page 109): 1, 3, 4, 6, 7, 9, 10, 11, 15, 16, 18;

7 Oct 09 & 11 Sec. 3.2: Solutions of Linear Homogeneous Equations; the Wronskian

Sec. 3.3: Complex Roots of the Characteristic Equations

Exercises 3.2 (page 119): 2, 3, 8, 9, 14, 15, 18, 20, 21, 24, 25;

Exercises 3.3 (page 125): 4, 5, 9, 10, 11, 15, 26, 28, 30;

8 Oct 16 & 18

Sec. 3.4: Repeated Roots; Reduction of Order

Sec. 3.5: Nonhomogeneous Equations; Method of Undetermined Coefficients

Exercises 3.4 (page 132): 4-6, 8, 10, 12, 19, 20, 22, 25-27;

Exercises 3.5 (page 141): 2, 3, 5, 9, 10, 11, 13, 14, 16a-21a;

9 Oct 23 & 25 Sec. 3.6: Variation of Parameters

Sec. 4.1: General Theory of nth Order Linear Equations

Exercises 3.6 (page 146): 6, 7, 9, 11, 12, 14, 15, 24-26;

Exercises 4.1 (page 173): 1, 5, 7, 11, 13, 15, 16, 17, 20;

10 Oct 30 & Nov 01 Sec. 4.2: Homogeneous Equations with Constant Coefficients

Midterm 2

Exercises 4.2 (page 180): 2, 9-13, 15, 17, 20, 25;

11 Nov 6 & 8 Sec. 7.1: Introduction

Sec. 7.2: Review of Matrices

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

12 Nov 13 & 15 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-Valued Eigenvalues

13 Nov 20 & 22 Sec. 7.7 Fundamental Matrices

Sec. 7.8: Repeated Eigenvalues

Sec. 9.1: The Phase Plane: Linear Systems

14 Nov 27 & 29 Sec. 9.2: Autonomous Systems and Stability

Sec. 9.3: Locally Linear Systems

Sec. 9.4: Competing Species

15 Dec 04 & Dec 06 Sec. 9.5: Predator-Prey Equations

Midterm 3