Week 1: Mathematical Preliminaries and Error Analysis
Week 2: Algorithms and Convergence, Introduction to Matlab
Week 3: Bisection Method, Fixed-point Iteration, Newton's Method
Week 4: Secant Method, Method of False Position, Order of Convergence
Week 5: Muller's Method, Interpolation, Lagrange Polynomial
Week 6: Data Approximation, Neville's Method, Divided Differences
Week 7: Hermite Interpolation, Cubic Spline Interpolation
Week 8: Numerical Differentiation, Three-Point Formulas, Five-Point Formulas
Week 9: Richardson's Extrapolation, Numerical Integration, Degree of Precision
Week 10: Composite Numerical Integration, Composite Trapezoidal and Simpson's rules
Week 11: Romberg Integration, Gaussian Quadrature
Week 12: Multiple Integrals, Composite Simpson's Rule for Double Integration
Week 13: Initial-Value Problems, Euler's Method, Higher-Order Taylor Methods
Week 14: Runge-Kutta Methods, Systems of Differential Equations