### MA2161 - MATHEMATICS – II–Topics–Marks Division according to Topics

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

1. 2. 