|Specific Objectives of course:
To introduce various techniques for solving linear, non-linear and difference equations using various numerical methods.
Solution of Non-Linear Equations: Bisection method, Newton’s method, Secant method, Method of false position, Method of successive approximation.
Finite Differences: Finite differences, Difference operators and tables, Differences of polynomials, Newton’s and Gauss interpolating techniques for equally spaced data, Simple theorems on divided differences, Newton’s formula for unequal intervals, Lagrange’s formula of interpolation, Numerical differentiation.
Numerical Integration: Review of integration concept and their physical significance for Engineering, Trapezoidal and Simpson’s rule numerical integration techniques.
Solution of Linear Simultaneous Equations: Jacobi’s method, Gauss-Seidal method, Sparse matrices, Solution of differential equations, Euler and modified Euler methods, Runge Kutta method.
Complex Variables: Limit, continuity, zeros and poles, Cauchy-Reimann Equations, Conformal transformations, contour integration.
1. Complex Variables by Murray R. Spiegel, Schaum Series
2. Numerical Analysis by Scheid, Schaum Series