Engineering Mathematics-III

4 Credits

5 Modules

Updated 12/31/2024

Numerical Solution of Ordinary Differential Equations

7 Lectures

Taylor series method Picard’s method Euler’s method Modified Euler’s method Runge‐Kutta method. Predictor corrector methods Adam Bashforth and Milnes method convergence criteria Finite difference method.

Numerical Solution of Linear and Non Linear Equations

6 Lectures

Non Linear Equations: Bisection Method RegulaFalsi Method Newton-Raphson Method Iteration method. Linear Equations: Jacobi and Gauss Seidel Iteration methods Relaxation method.

Functions of Complex Variable

12 Lectures

Applications of De Moivre’s theorem Exponential Circular Hyperbolic and Logarithmic functions of a complex variable Inverse Hyperbolic functions Real and imaginary parts of Circular and Hyperbolic functions Summation of the series-‘C+iS’ method. Limit and derivative of complex functions Cauchy-Riemann equations Analytic functions and its applications Complex integration Cauchy’s theorem Cauchy’s integral formula Series of complex function Taylor series singularities and Laurent’s series Cauchy’s residue theorem and its application for the evaluation of real definite integrals.

Interpolation

6 Lectures

Least square curve fit and trigonometric approximations Finite differences and difference operators Newton’s interpolation formulae Gauss forward and backward formulae Sterling and Bessel's formulae Lagrange's interpolation.

Numerical Integration

5 Lectures

Integration by trapezoidal and Simpson’s rules 1/3 and 3/8 rule Romberg integration and Gaussian quadrature rule Numerical integration of function of two variables.