MATH 360
COURSE SYLLABUS
(2009-2010, Fall Semester)
INTRODUCTION TO THEORY OF ORDINARY DIFFERENTIAL EQUATIONS
(3-0) 3
Instructor: Dr. Abdullah Özbekler
Catalog Data: First Order Ordinary Differential Equations, The Existence and Uniqueness Theorem, Systems and Higher
Order Ordinary Differential Equations, Linear Differential Equations, Boundary Value Problems and Eigenvalue Problems,
Oscillation and Comparison Theorems.
Textbook: Introduction to Theoretical Aspects of Ordinary Differential Equations, A. K. Erkip, METU.
References:
1) Differential Equations, Second Edition, by Shepley L. Ross, John Wiley and Sons, 1984.
2) Lectures on Differential Equations, Yılmaz Akyıldız and Ali Yazıcı.
3) Elementary Differential Equations, Boyce DiPrima
4) Schaum's Easy Outlines - Differential Equations Crash Course - 2003
Prerequisite: Math 262 & Math 231 (or Math 275)
Goals: The course is designed to present other aspects of ordinary differential equations to the student who has so far seen
the basic solution techniques. The emphasis is on existence-uniqueness and related questions; initial value, boundary value
and eigenvalue problems are introduced within that concept. Examples and problems aim to clarify the theory.
Attendance Policy: Attendance is an essential requirement of this course. Any student should attend more than 80% lecture
hours: If you do attend less than 80% of the lecture hours, you will get an NA grade. Students who will get NA grade can
not attend the final exam
Grading Policy: There will be two midterm exams and a final exam. The weights and dates of these are as follows:
Midterm I: November 13, 2009 %30
Midterm II: December 11, 2009 %30
Final:
January 18, 2010 %40
______________________________________
TOTAL 100
Make-up: Make-up exams will be given only if the proper medical documentation for the absence is received. You must
submit the medical report to your department in three days after the last day of the report. Otherwise, it will not be accepted.
Make-up exams for Midterms will be before the final exams and the dates will be announced later.
Make-Up Exam for Midterm I and II: January 05, 2010 (Tuesday) at 18:00
Make-Up for Final Exam
: January 25, 2010 (Monday) at 10:00
IMPORTANT: All students should provide an ID card to serve as identification. Any student without an ID card CAN
NOT take the exam.
COURSE CHART
WEEK
DATE
1
Sep. 23 - 25, 2009
2
Sep. 28 - Oct. 2, 2009
3
Oct. 5 - 9, 2009
4
Oct. 12 - 16, 2009
II. Proof of Existence and Uniqueness (E-U) Theorem: Differential
Inequalities, Integral Inequalities and Gronwall’s Lemma
5
Oct. 19 - 23, 2009
Integral Equations,The Uniquenness Theorem,
6
Oct. 26 - 30, 2009
(Holiday Oct. 29)
Picard’s Method. Preparation of Existence Theorem
7
Nov. 2 - 6, 2009
Proof of Existence Theorem, Continuation of Solution, Dependence on Initial
Value
8
Nov. 9 - 13, 2009
III. Systems and Higher order Ordinary Differential Equations:
Introduction. The Vector Notation, Initial Value Problems
9
Nov. 16 - 20, 2009
The Uniqueness Theorem, Picard’s Method, The Existence Theorem
10
Nov. 23 - 27, 2009
(Holiday Nov. 26-27)
11
Nov. 30 – Dec. 4, 2009
(Holiday Nov. 30)
12
Dec. 7 - 11, 2009
V. Boundary Value Problems and Eigenvalue Problems:
Boundary Value Problems (BVP), Examples
13
Dec. 14 - 18, 2009
The number of Solutions of BVP, Eigenvalue Problems
14
Dec. 21 - 25, 2009
VI. Oscillation and Comparison Theorems: Zeros of Solutions
15
16
Dec. 28 - 31, 2009
(Holiday Jan. 1)
Jan. 4 - 6, 2009
SECTIONS
I. First Order Ordinary Differential Equations: Introduction
Tangent Line Approximation, Cauchy-Euler Method
The Graph Method, Direction Fields, E-U of Solutions of IVP’s
Continuation of Solution, Dependence on Parameter, Complex Valued Equations
IV. Linear Differential Equations: General Theory, Second Order Linear
Equations and the Wronskian Identity
An Eigenvalue Problem
Review (If time permits)