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Course: Ordinary Differential Equations Instructor: Sudip Ranjan Bhuia Room: Second floor auditorium Level: Undergraduate Time: Currently offered |
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Syllabus Past Exams Syllabus: i) First order differential equations, Picards theorem, existence and uniqueness of solution to first order ordinary differential equations (Peanos existence theorem, Osgoods uniqueness theorem), Systems of first order differential equations, higher order linear differential equations, solving higher order linear DE with constant coefficients. ii) Introduction to power series solutions, Equations with regular singular points, Special ordinary differential equations arising in physics and some special functions (eg. Bessels functions, Legendre polynomials, Gamma functions). iii) Sturm -Liouville problems, Sturm comparison principle, Critical points and stability in linear systems. iv) Nonlinear equations - Lyapunovs method for detecting stability in systems, simple critical points of nonlinear systems, Periodic solutions, statement of the Poincare-Bendixson theorem (no proof). v) Numerical methods and error analysis - Euler method, Second order Taylor method, Trapezoid method, Improved Euler method, Runge-Kutta method. Reference Texts: (a) G.F. Simmons: Differential equations with applications and historical notes. (b) Dmitry Panchenko: Lecture notes on Ordinary Differential Equations. (AMS open notes). (c) Garrett Birkhoff and Gian-Carlo Rota: Ordinary Differential Equations. (d) Peter J. Olver: Lecture notes on Nonlinear Ordinary Differential Equations. (e) W. Boyce and R. C. DiPrima: Elementary Differential Equations. (f) E. A. Coddington and N. Levinson: Theory of Ordinary Differential Equations. Evaluation:
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