PMAT 22025

>< Type/ Status : Core
>< Title : Infinite Series and Ordinary Differential Equations
>< Pre-requisites : PMAT 12035
>< Objectives :
At the end of this course, the student will understand the nature of the convergence of infinite series, and the methods of solving ordinary differential equations.
>< Course Content :

Infinite Series: Properties of infinite series, Series of non-negative terms, Alternating series, Absolute and conditional convergence, Power Series, Taylor and Maclaurine Series, Binomial Series, Fourier Series.

First Order Non-Linear Differential Equations: Riccarti, Clairaut types.

Linear differential equations of higher degree: Equations with constant coefficients, Operator methods, Laplace transform method, Euler’s equation, Other non-linear equations, Systems of linear equations with constant coefficients, Linear equations with variable coefficients, Method of variation of parameters, Series solutions of ordinary differential equations and the method of Frobenius, Legendre and Bessel equations.

>< Methodology : A combination of lectures and tutorial discussions
>< Scheme of Evaluation : Based on tutorials, tests and end of course examination
>< Recommended Reading :
1. Ross, K.A. (1980). Elementary Analysis: The theory of calculus, Springer- Verlag New York.
2. Arora, S. & Malik, S.C. (1994). Mathematical Analysis, Wiley Eastern.
3. Gupta, S.L. & Rani, N. (1999). Principles of Real Analysis, Vikas, India.
4. Raisinghania, M.D. (1991). Advanced Differential Equations, S.Chands, India.
5. Mondal, C. R. (2003). Ordinary Differential Equation, Prentice Hall, India.

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