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, 2.9-2.101
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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