MA203 : MATHEMATICS - III

AUTUMN - 2001

Teaching Plan :

[K] refers to the text book by E. Kreyszig, ``Advanced Engineering Mathematics", 8th Edition, John Wiley and Sons(1999).

 No. Topic § in [K] No.of Lec. 1. Basic concepts, Geometric meaning, Direction fields 1.1-1.2 1 2. 1st order linear equations, homogeneous and non homogeneous 1 3. Solution Method for Nonlinear equations, Separation of variables 1.3-1.4 1 4. Exact Differential equations, integrating factors Bernoulli Equation, Orthogonal trajectories 1.5-1.8 2 5. Existence Uniqueness: Picards iteration 1.9 1 6. 2nd order Linear Differential equations: homogeneous equation with constant coefficients 2.1-2.3 1 Mass spring system 2.5-2.6 1 Existence Uniqueness, Wronskian, Non homogeneous equation 2.7-2.8 2 Method of undetermined coefficients, 2.9-2.10 1 variation of parameters method 2.11-2.12 1 7. Higher Order equations: Wronskian Existence of solution: Solution Methods for constant coefficients 2.13-2.14 2 8. System of ODE: Conversion of higher order ode, basic concepts 3.1-3.2 1 Homogeneous systems 3.3-3.4 1 Nonhomogeneous System 3.6 1 9. Laplace Transform 5.1-5.7 5 10. Linear equation with variable coefficients: Solution Motivation for Power series Method 2.6, 4.1 1

After Mid Semester

 No Topic in [K] No. of Lec. 1 Sequence and Series,       Convergence Tests 14.1, A- 3.3 2 2 Improper Integrals Handout 2 1 3 Uniform convergence, and Power Series 14.5, 14.2 3 4 Series solution: Legendre's Equation, Legendre polynomials 4.3 1 5 Frobenius method, Bessels Function, Bessel Function of 2nd kind 4.4 - 4.6 3 6 Convergence of Picard's iterates Handout 3 1 7 Qualitative Theory: Stability of Linear systems, Phase plane analysis Critical points, Linearised stability Handout 4                    3.3 - 3.4, 3.5 3 8 Sturm - Liouville Problems: Eigenvalues and Eigenfunctions and properties Handout 5                    4.7 - 4.8 3 9 Fourier Series: expansions, approximation by trigonometric polynomials Fourier integrals with Applications 10.1- 10.4,                 10.7 - 10.10 4

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