Ordinary Differential Equations ( Math 6302)

Transcription

1 Ordinary Differential Equations ( Math 6302) Prof. Dr. Ayman Hashem Sakka Islamic University of Gaza Faculty of Science Department of Mathematics Second Semester

2 Semester: Spring 2014 Instructor: Prof. Dr. Ayman Hashem Sakka Home page: Office: Deanship of Admission and Registration Phone: 1203

3 Textbooks David A. Sanchez, Differential Equations and Stability Theory: An Introduction, Dover Publications, Inc., 1979

4 References References (1) Lawrence Perko, Differential Equations and Dynamical Systems, Third Edition, Springer, 2001

5 References References (1) Lawrence Perko, Differential Equations and Dynamical Systems, Third Edition, Springer, 2001 (2) Rainville and Bedient, Elementary Differential Equations (7th edition),

6 References References (1) Lawrence Perko, Differential Equations and Dynamical Systems, Third Edition, Springer, 2001 (2) Rainville and Bedient, Elementary Differential Equations (7th edition), (3) Gerald Teschl, Ordinary Differential Equations and Dynamical Systems, gerald/

7 References References (1) Lawrence Perko, Differential Equations and Dynamical Systems, Third Edition, Springer, 2001 (2) Rainville and Bedient, Elementary Differential Equations (7th edition), (3) Gerald Teschl, Ordinary Differential Equations and Dynamical Systems, gerald/ (4) E. Hille, Ordinary differential equations in the complex domain, Dover Publications, Inc., 1997

8 References References (1) Lawrence Perko, Differential Equations and Dynamical Systems, Third Edition, Springer, 2001 (2) Rainville and Bedient, Elementary Differential Equations (7th edition), (3) Gerald Teschl, Ordinary Differential Equations and Dynamical Systems, gerald/ (4) E. Hille, Ordinary differential equations in the complex domain, Dover Publications, Inc., 1997 (5) B. P. Parashar, Differential and Integral Equations (2nd edition), CBS Publishers & Distributors, 1992.

9 Exams and Grading Homework and project (30 %) Midterm Exam (30%) Final Exam (40%)

10 Course Description Linear systems of differential equations, Local theory of nonlinear systems, Existence and uniqueness theorem, Stability, Frobenius method, Equations of hypergeometric type.

11 Course outline First Week: Introduction to Ordinary differential equations, An existence and uniqueness theorem. Second Week: The maximum interval of existence, Linear equations. Third Week: Fundamental solutions, The Wronskian. Fourth Week: Nonhomogeneous linear equations, The nth-order linear equation. Fifth Week: Linear equations with constant coefficients, The behavior of solutions. Sixth Week: Solutions of first-order linear systems with constant coefficients. Seventh Week: Matrix exponential.

12 Course outline Eighth Week: Jordan forms. Ninth Week: Autonomous systems and phase space. Stability of nonautonomous systems, Tenth Week: Liapunov s direct method. Eleventh Week: Proof of the Existence-Uniqueness Theorem. Twelfth Week: Continuation of solutions and the maximum interval of existence, The dependence of solutions on parameters and approximate solutions. Thirteenth Week: Differential equations in the complex domain, The Frobenius method for second-order equations. Fourteenth Week: Special functions: Gamma function, Bessel functions. Fifteenth Week: Legendre function, Hypergeometric function. The Frobenius method for systems.