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MATH 240 - DIFFERENTIAL EQUATIONS

Summer 2002

Math240 : Differential Equations.

Text book

Elementary Differential Equations and Boundary value problems , W E Boyce and R C DiPrima,. John Wiley (sixth edition).

Other Books

Elementary Differential equations , E D Rainvillen, P E Bediennt and R E Bedient,( 8th edition) , Prentice-Hall.

Elementary Differential Equations , C H Edwards, Jr, and D E Penney, (third edition), Prentice-Hall

Content

Subjects covered

June 10:
Classification of differential equations
Linear equations (first order)
Further discussion of linear equations
Seperable equations
Difference between linear and nonlinear equations

June 17:
Modelling with linear equations and population dynamics
Exact equations and integrating factors
Homogenous equations
The existence and uniqueness theorem
First order difference equations

June 24:
Homogeneous equations with constant coefficients
Complex roots of the characteristic equation
Repeated Roots: Reduction of order
Some special cases
Fundamental solutions of linear homogeneous equations
First midterm exam 28/6 , Friday 13.40-15.30

July 1
Linear independence and the Wronskian
Non homogeneous equations.
General theory of nth order linear equations
Homogeneous equations with constant coefficients
The method of undetermined coefficients
The method of variation of parameters

optional homework 1 ps file for Math and Phys students

July 8
Review of power series
Series solutions near an ordinary point
Regular singular points
Series solutions near a regular singular point

optional homework 2 ps file for math and Phys students

July 15
Second midterm exam 15/7, Monday 14.40-16.30
Laplace Transform
Solutions of initial value problems
Step functions
Solution of Differential equations by Laplace Transform

July 22
Review of matrices
Systems of linear algebraic equations
Linear independence, eigenvalues and eigenvectors
Systems of first order linear equations
Homogeneous linear systems with constant coefficients
Complex eigenvalues, repeated eigenvalues

Suggested reading for Math and Phys students
Chapter 9: Nonlinear Differential Equations and Stability

See also the "Course Syllabus" below

Course Schedule

Monday 08.40-10.30 , SBZ03

Wednesday 08.40.40-10.30 , SBZ-03

Friday 08.40-10.30, SBZ-03

Exams

(20%) First Midterm Exam June 28

(20 %) Second Midterm Exam July 15

(40 %) Final Exam July 29

(20%) Quizes+ Homeworks : ps file of set I

optional homework 1 ps file for Math and Phys students

optional homework 2 ps file for Math and Phys students

see exercises for homeworks

see grades for midterm, final, and homework grades

see quizgrades for quiz grades

First midterm exam questions and their solutions first midterm solutions ps file

Second midterm exam questions and their solutions second midterm solutions ps file

Course Syllabus

For the Summer School Courses 2 weeks below will be condensed to one week

1. Introduction, First order Differential equations
2. Separable Equations, Linear Equations (first order)
3. Applications
4. Exact Solutions, Homogenous Equations, Existence and Uniqueness of solutions
5. Numerical Solutions
6. Linear Equations, Fundamenatl Solution.
7. Linear Equations with Constant Coefficients
8. Nonhomogenous Linear Equations
9. Applications
10. The Laplace Transform
11. The Laplace Transform, Systems of First Order Linear Equations
12. Homogenous Linear Systems with Constant Coefficients
13. Series Solutions of Second Order Linear Equations
14. Series Solution of Second Order Linear Equations
15. Review

Students

For exercises please see exercises

For midterms please see midterms

Metin Gürses
Office: fen A126: Bilkent University; Bilkent, Ankara 06533 Turkey
Phone:: Office: (312) 2901924; Home: (312) 2664560
Fax:(312) 2664579: Office: (90)(312) 2901924
Email:gurses@fen.bilkent.edu.tr
Home:Bilkent Universitesi Lojmanlari 8/3: Bilkent, Ankara 06533 Turkey

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