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# MATH 351 (Spring 2014): Differential Equations

### Section and Class Number

Section 01 & 15845

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 9:30am - 10:30am or by appointment (email)

### Final Exam

May 14, 2014, Wednesday 10:15 am - 12:15 pm, Live Oak Hall Room 1326

### Midterm Exams

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

### Lecture times and locations

Mondays & Wednesdays 11:00 am - 12:15 pm in LO (Live Oak Hall) 1326

### Course text

Elementary Differential Equations and Boundary Value Problems (10th edition), or the short version of Elementary Differential Equations 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.

Course Syllabus

Week Date Topics covered Homework Homework due date Practice Problems Additional Material
1 Jan 20 & 22 Introduction

Sec. 1.1: Some Basic Mathematical Models; Direction Fields
Exercises 1.1 (page 7): 7, 9, 15, 17, 19, 21, 23 (due Feb 5) Exercises 1.1 (page 7): 8, 10, 16, 18, 20, 22, 24;

Page 1 -- Page 70
2 Jan 27 & 29 Sec. 1.2: Solutions of Some Differential Equations

Sec. 1.3: Classification of Differential Equations

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 Feb 5) 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;

3 Feb 3 & 5 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 Feb 12)

(Exercises 2.2 due Feb 19)
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)

4 Feb 10 & 12

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 Feb 19)

(Exercises 2.4 due Feb 24)
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;

5 Feb 17 & 19 Sec. 2.4 cont'd

Sec. 2.5: Autonomous Equations and Population Dynamics
Exercises 2.5 (page 88): 1, 3, 5, 7, 9, 11, 15, 16, 20, 22;

(Exercises 2.5 due Mar 3 )

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

Quiz 1 Statistics

Solutions for Quiz 1
6 Feb 24 & 26 Sec. 2.5 cont'd

Sec. 2.6: Exact Equations and Integrating Factors
Exercises 2.6 (page 101): 3, 5, 7, 9, 11, 13, 15, 25, 27, 29;

(Exercises 2.6 due Mar 5) Exercises 2.6 (page 101): 2-12 (even), 16, 20, 26, 28, 30;

Lecture Notes for Sec. 2.7
7 Mar 3 & 5

Sec. 2.7: Numerical Approximations: Euler's Method

Midterm 1

Exercises 2.7 (page 110): 1, 3;

(Exercises 2.7 due March 12)
Exercises 2.7 (page 110): 2, 4;

Midterm 1 Statistics

Solutions for Midterm 1

8 Mar 10 & 12

Sec. 2.8: The Existence and Uniqueness Theorem

Sec. 3.1: Homogeneous Equations with Constant Coefficient

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

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

Exercises 3.1 (page 144): 10, 11, 12, 15, 17, 19, 21, 23, 25, 27;

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

(Exercises 2.8 due March 24 )

(Exercises 3.1 due March 24)

(Exercises 3.2 due April 2)
Exercises 2.8 (page 120): 2, 4, 5;

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

Exercises 3.1 (page 144): 1-7, 9, 13, 14, 16, 18, 20, 22, 24, 26, 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;

Lecture Notes for Sec. 2.8

Lecture Notes for Sec. 3.1
9 Mar 17 & 19 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 April 2)

(Exercises 3.4 due April 2)
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;
10 Mar 24 & 26 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 April 2)

(Exercises 3.6 due April 2)

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;
Notes for Sec. 3.6

11 Mar 31 & April 2 Cesar Chavez Holiday

Sec. 4.1: General Theory of nth Order Linear Equations

Sec. 4.2: Homogeneous Equations with Constant Coefficients

Sec. 4.3: The Method of Undetermined Coefficients

Sec. 4.4: The Method of Variation of Parameters
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 4.3 (page 239): 1, 4, 5, 6, 9, 11, 13, 15, 17;

Exercises 4.4 (page 244): 1, 2, 3, 9;
(Exercises 4.1 due April 16)

(Exercises 4.2 due April 16 )

(Exercises 4.3 due April 16)

(Exercises 4.4 due April 16 )
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 4.3 (page 239): 3, 8, 10, 14, 16, 18;

Exercises 4.4 (page 244): 4, 5, 7, 11, 13;
Lecture Notes for Sec. 4.1 & 4.2

Notes for Sec. 4.4
12 April 7 & 9 Spring Recess; No Instruction

Quiz 2 Statistics

Solutions for Quiz 2
13 April 14 & 16 Sec. 7.1: Introduction

Sec. 7.2: Review of Matrices

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

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

(Exercises 7.1 due April 23)

(Exercises 7.2 due April 23)

(Exercises 7.3 due April 30)
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;

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

Lecture Notes for Sec. 7.1

Lecture Notes for Sec. 7.2

Lecture Notes for Sec. 7.3

Midterm 2 Statistics

Solutions for Midterm 2
14 April 21 & 23 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

Sec. 7.8: Repeated Eigenvalues
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 7.8 (page 436): 2, 3, 4, 5, 7, 9;
(Exercises 7.4 due April 30)

(Exercises 7.5 due April 30)

(Exercises 7.6 due April 30)

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;

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

Lecture Notes for Sec. 7.4

Lecture Notes for Sec. 7.5

Lecture Notes for Sec. 7.6

Lecture Notes for Sec. 7.7
15 April 28 & 30 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 (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;
Quiz 3 Statistics

Solutions for Quiz 3
16 May 5 & 7 Midterm 3 Solutions for Midterm 3
17 Final Exam Week