MA6251 – ENGINEERING MATHEMATICS – II SYLLABUS (REGULATION 2013) ANNA UNIVERSITY 

UNIT I: VECTOR CALCULUS 

(MA6251) 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.

UNIT II: ORDINARY DIFFERENTIAL EQUATIONS 

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.

UNIT III: LAPLACE TRANSFORM 

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.

UNIT IV: ANALYTIC FUNCTIONS 

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.

UNIT V: COMPLEX INTEGRATION 

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).