SyllabusThe subject will cover the following topics:
Error analysis, round off errors, truncation errors, inherent errors, error propagation;
Evaluation of functions, Taylor series, Chebyshev series, economisation of Taylor series, rational approximations and continued fractions;
Solution of nonlinear equations, graphical solution, bisection method, chord method, Newton's method, direct iteration, complex roots;
Difference calculus, extrapolation of data, interpolation of data, experimental data, differentiation of discrete data and detection of errors in data;
Curve fitting and data smoothing, polynomial curve fitting, least squares curve fitting, smoothing of experimental data;
Numerical integration, difference methods, trapezoidal rule, Simpsonms rule, Gauss quadrature;
Differential equations, variables separable, homogeneous equations, exact equations, first order linear equations, second order linear equations with constant coefficients;
Numerical solution of differential equations, Taylor series method, Euler's method, Runge-Kutta methods, predictor-corrector methods;
Systems of linear equations, Gaussian elimination, Gauss pivotal condensation, Gauss-Seidel iteration. |
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