Mathematical Computing

Course: AMT 221 2.0 Mathematical Computing (Compulsory)

Course content:

Revisiting iterative methods and convergence analysis; Improved Newton’s method and other variants of Newton’s method; Fixed-point method; Solving systems of non-linear equations; Revisiting polynomial interpolation; Concept of Splines; Cubic Splines (Natural, Clamped and others); Gauss-Jacobi method; Gauss-Seidel method; SOR method; Comparison of iterative methods; Gershgorin Circle Theorem; Power method and its variants; QR method; Existence and uniqueness of solutions for ODEs; Euler’s method; Runge-Kutta methods; Least squares approximation; Chebyshev polynomials; Rational function approximation

Recommended Readings:

1. 1. Fink, K.D. & Mathews, J.H.(2004). Numerical Methods using MATLAB (6^th ed).Prentice-Hall Inc.
   2. Burden, R.L. & Faires J.D. (2005). Numerical Analysis (8^th ed). Thomson Brooks/Cole.
   3. Atkinson, K.E. (1989). An Introduction to Numerical Analysis (8^th ed). John Wiley & Sons, Inc.