# Differential Equations (MATH 471 A)

## Spring 2013

Instructor:   Dr. Seongchun (Michelle) Kwon
e-mail:   kwonseon at hotmail dot com
Office:   Miller Science Center 103-C
Office hours:   10:00- 11:00 AM on MWF and 3:00- 4:00 PM on TTR or by appointment
Class hours:   TTR 1:30 PM-2:50 PM at Miller Hall 208

Text:    Elementary Differential Equations, ISBN: 0-13-508011-8
Authors: Earl D.Rainville; Phillip E. Bedient; Richard E. Bedient Publisher: Prentice Hall

Materials covered:    Differential equations of first order and first degree, differential equations of first order and higher degree, differential operators and linear differential equations, reduction of order.

Final Exam:   May 2(Thursday)   8:00 – 10:00 AM

• Syllabus;     Tentative Schedule
• Suggested Problems
• Lecture Note (Chap 8. Examples Solution) ;     Graphic;     DFIELD and PPLANE,     ODE Software for MATLAB,

## Progress, Problems and Solutions

 Date Progress Problems,Solutions Jan 8 T Introduction Jan 10 TR Chapter 1. Definitions, Families of Curves ( Reference for the geometric interpretation of the solutions of differential equations: MIT Open Courseware ) Group Quiz Jan 15 T 2. Equations of order one: 2.1. Separation of variables Quiz Jan 17 TR 2.2. Homogeneous Functions, 2.3. Equations with homogeneous coefficients (Reference about implicit differentiation: Watch the Kahn Academy video clip) Group Quiz( Please turn this in on Jan 22) Jan 22 T 2.3. Equations with homogeneous coefficients, 2.4. Exact equations Quiz ( Jan 24 TR 2.4. Exact equations, Re-doing the Group quiz (Jan 22's), Working on the group quiz ( Jan 24's) Group Quiz Jan 29 T Keep working on the group quiz ( Jan 24 ) Jan 31 TR 2.5. The linear equation of order one Quiz Feb 5 T 5.1. Integrating factors found by inspection Group Quiz Feb 7 TR 6.1. The general linear equation, 6.2. An existence and uniqueness theorem Quiz Feb 12 T 6.3. Linear independence, 6.4. Wronskian Group Quiz Feb 14 TR 6.4. Wronskian, 6.5. General solution of a homogeneous equation, 6.7. Differential operators Quiz Feb 19 T 6.7. Differential operators, 6.8. The fundamental laws of operation, 6.9. Some properties of differential operators Feb 21 TR Take Home Exam Take home exam( February 26 Due date ) Feb 26 T 7. Linear equations with constant coefficients: 7.1. Introduction, 7.2. The auxiliary equation: distinct roots, 7.3. The auxiliary equation: repeated roots Group Quiz Feb 28 TR 7.4. A definition of exp z for imaginary z, 7.5. The auxiliary equation: imaginary roots Mar 5 T 6.6. General Solutiopn of a nonhomogeneous equation, 8.1. Construction of a homogeneous equation from a specific solution Group Quiz Mar 7 TR 8.2. Solution of a nonhomogeneous equation, 8.3. The method of undetermined coefficients Group Quiz Mar 12, Mar 14 Spring Break Mar 19 T Problem solving Mar 21 TR 8.3. The method of undetermined coefficients Group Quiz Mar 26 T 9.2. Reduction of Order Group Quiz Mar 28 TR Problem Solving Apr 2 T Assessment Day( No day classes ) Apr 4 TR Take Home Exam Day Take home exam(Due date: April 9) Apr 9 T Keep working on the take home test problems with help... Apr 11 TR 9.3. Variation of Parameters Apr 16 T 9.4. Solution of y''+y=f(x) Group Quiz , Take home Quiz ( Due on Apr 18 TR) Apr 18 TR 11. Linear Systems of Equations: 11.1. Introduction, 11.2. First-Order systems with constant coefficients, 11.3. Solution of a first-order system, 11.4. Some matrix algebra Group Quiz , Take home Quiz ( Due on Apr 23 T) Apr 23 T 11.5. First-order system revisited Apr 25 TR 11.5. First-order system revisited