Introduction to programming in MATLAB, examples. Error definitions, Taylor series and error propagation. Roots of equations – Bisection method, fixed point iteration, Newton-Raphson method, secant method, systems of nonlinear equations. Numerical linear algebra – Gauss elimination, LU decomposition, matric inversion, power method for finding eigen values, QR factorisation.
Curve Fitting – Linear regression, polynomial regression, nonlinear regression, Newton’s divided difference interpolation, Lagrange interpolation.
Numerical Integration and Differentiation – Trapezoidal rules, Simpson’s rules, Newton-Cotes algorithm, Gauss quadrature, high accuracy differentiation formulas, Richardson extrapolation, partial derivatives.
Differential Equations – Euler’s method, improved Euler’s methods, Runge-Kutta method, systems of equations, Finite difference method, solution of Laplace equation by FDM, explicit methods for parabolic equations, simple implicit method, Crank-Nicolson method