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MATH 351 (Fall 2015): Differential Equations



Section and Class Number

Section 01 & 16147

Instructor

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.

Announcements

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 (Please read it very carefully!!!)

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



Copyright © 2009 Jing Li