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, Simpson's 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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