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


    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


  • (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


    For exercises please see exercises

    For midterms please see midterms

    Metin Gürses
    Office: fen A126
    Bilkent University
    Bilkent, Ankara 06533 Turkey
    Office: (312) 2901924
    Home: (312) 2664560
    Fax:(312) 2664579
    Office: (90)(312) 2901924
    Home:Bilkent Universitesi Lojmanlari 8/3
    Bilkent, Ankara 06533 Turkey

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    Last update June 2002

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