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) , PrenticeHall.
Elementary Differential Equations , C H Edwards, Jr, and
D E Penney, (third edition), PrenticeHall
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 13.4015.30
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 14.4016.30
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 08.4010.30 , SBZ03
Wednesday 08.40.4010.30 , SBZ03
Friday 08.4010.30, SBZ03
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

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