MATH-3 (B-TECH computer science engineering 4th)

MATHEMATICS - III

Review of the prerequisites such as limits of sequences and functions. Continuity, uniform continuity and differentiability. Rolls theorem, mean value theorems and Taylor's theorem. Newton method for approximate solution Riemann integral and the fundamental theorem of integral calculus. Approximate integration. Applications to length area, volume, surface area of revolution, Moments, centers of Mass and Gravity.

Repeated and multiple integrals with applications to volume, surface area, moments of inertia etc. Analytic functions, Cauchy-Riemann equations, Laplace equation, elementary functions, Cauchy's integral theorem(Proof by using Greens theorem), Cauchy's integral formula, Taylor series and Laurent series. [33%

Residues and applications to evaluating real improper integrals and inverse Laplace transforms. Conformal mapping, linear fractional transformations. [17%]

Boundary value problems involving partial differential equations such as wave equation, heat equation, Laplace equations . Solutions by the method of separation of variables and by Fourier and Laplace transforms. [33%]

Numerical Methods for ODEs and PDEs. [17%]