Differential Equations
This is a course for 3rd year B.Math(undergraduate) students. For more details on timings and past exams, click here.
Syllabus : Ordinary differential equations - first order equations, Picard's theorem (existence and uniqueness of solution to first order ordinary differential equation), Second order linear equations - second order linear differential equations with constant coefficients, Systems of first order differential equations, Equations with regular singular points, Introduction to power series and power series solutions, Special ordinary differential equations arising in physics and some special functions (eg. Bessel's functions, Legendre polynomials, Gamma functions). Partial differential equations - elements of partial differential equations and the three equations of physics i.e. Laplace, Wave and the Heat equations, at least in 2 - dimensions. Lagrange's method of solving first order quasi linear equations.
Assignments : #1, #2, #3, #4, #5, #6, #7
Teaching Assistant : Tiju Cherian. Office : A-7 SMU Annexe. Email : tiju [AT] isibang.ac.in
References:
1. Differential Equations : Theory, Technique and Practice - G. F. Simmons and S. G. Krantz.
2. differential equations DeMystified - S. G. Krantz.
3. Elementary Differential Equations - W. Boyce and R. C. DiPrima.
4. Theory of Ordinary Differential Equations - E. A. Coddington and N. Levinson.
Additional Material :
(unless mentioned, none of it is written by me)
1. Direction Fields - There are many softwares available online to generate direction fields. For ex., see this one. Orthogonal Trajectories.
2. Pursuit Curves and how to draw them. On Tractrix.
3. Generalized Dog-Rabbit Chase.
4. Cauchy-Peano Theorem. ; A fixed point theorem for iterated mappings. ; Picard-Lindelof Theorem. (Alternative Proof) ; Gronwall's inequality.
5. Picone's identity. Sturm-Picone Comparison Theorem.
6. Transport Equation ; Method of Characteristics.
7. Heat Equation. (See Section 2.3.2 for Fourier Transform and Section 2.4.1 and 2.4.2 for Solution of the Heat equation.) Scanned copy of my notes where I've sketched results about Fourier transforms needed and the rest of the proof is verbatim from Section 2.4.1 and 2.4.2 of the online notes.
Grading :
Class Quizzes : 30/25 Dates : 29th Jan, 19th Feb, 24th Feb, 19th March, 26th March, 16th April.
Mid-Semester : 20/25. Date : March 5th, 2015, 10 AM - 1 AM. Venue : Auditorium.
End-Semester : 50