Anna University
MA2161 - MATHEMATICS – II
Semester : II
Year : 1st
Branch : Common to all branch
UNIT I ORDINARY DIFFERENTIAL EQUATIONS
1. Higher order linear differential equations with constant coefficients –(8 +2)marks
2. Method of variation of parameters -8 marks
3. Cauchy’s and Legendre’s linear equations-(8+2) marks
4. Simultaneous first order linear equations with constant coefficients -8 marks
UNIT II VECTOR CALCULUS
1. Gradient Divergence and Curl ,Directional derivative,Irrotational, solenoidal-8 marks
2. Green’s theorem ,Gauss divergence theorem,stokes’ theorem -16+8 marks
UNIT III ANALYTIC FUNCTIONS
1. Harmonic and orthogonal properties of analytic function-8 marks
2. conjugate Construction of analytic functions -8 marks
3. Conformal mapping : w= z+c, cz, 1/z, -8 marks
4. Bilinear transformation. -8 marks
UNIT IV COMPLEX INTEGRATION
1. Cauchy’s integral formula -8 marks
2. Taylor and Laurent expansions -8 marks
3. Residue theorem -8 marks
4. Contour integration-8 marks
UNIT V LAPLACE TRANSFORM
1. properties ,derivatives, integrals,unit step function ,impulse functions, Initial and Final value theorems-8marks
2. periodic functions-8 marks
3. Inverse Laplace transform –partial fraction and Convolution theorem -8 marks
4. Solution of linear ODE -8 marks
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