Gradient, divergence and curl – Directional derivative – Irrotational and solenoidal vector fields – Vector integration – Green‟s theorem in a plane, Gauss divergence theorem and Stokes‟ theorem (excluding proofs) – Simple applications involving cubes and rectangular parallelopipeds.

Higher order linear differential equations with constant coefficients – Method of variation of parameters – Cauchy‟s  and  Legendre‟s  linear  equations  – Simultaneous first order linear equations with constant coefficients.

Laplace transform – Sufficient condition for existence – Transform of elementary functions – Basic properties – Transforms of derivatives and integrals of functions – Derivatives and integrals of transforms – Transforms of unit step function and impulse functions – Transform of periodic functions. Inverse Laplace transform -Statement of Convolution theorem  – Initial and final value theorems – Solution of linear ODE of second order with constant coefficients using Laplace transformation techniques.

Functions of a complex variable – Analytic functions: Necessary conditions – Cauchy-Riemann equations and sufficient conditions (excluding proofs) – Harmonic and orthogonal properties of analytic function – Harmonic conjugate – Construction of analytic functions – Conformal mapping: w = z+k, kz, 1/z, z2, ez  and bilinear transformation.

Complex integration – Statement  and  applications  of  Cauchy‟s  integral  theorem  and  Cauchy‟s integral formula – Taylor‟s  and  Laurent‟s  series  expansions  – Singular points – Residues – Cauchy‟s residue theorem – Evaluation of real definite integrals as contour integrals around unit circle and semi-circle (excluding poles on the real axis).

Lecture Notes

• Lecture Notes Collections 1 – DOWNLOAD 

Part B – 16 Marks

 

• UNIT 1 to UNIT 5 – 16ARKS  – DOWNLOAD  

Question Papers

MA6152 Mathematics – II Question Bank

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