Textbook
John H. Mathews & Kurtis D. Fink. Numerical Methods Using MATLAB. Pearson Education Inc. 4th Edition, 2004.
Course Contents
1.1 Review of Calculus
1.3 Error Analysis and Order of Approximation
2.1 Fixed Point Iteration and Upper Bound of Error
2.2 Bracketing Methods_Bisection Method
2.2 Bracketing Methods_False Position Method
2.4 Newton Raphson Method, Secant Method, Multiplicity of Roots, Speed of Convergence
Ch3 Cost of Solving Linear Systems
Ch3 Cost of Backward Substitutions
Ch3 Cost of Gaussian Elimination
Ch3 Cost of LU Factorization
Ch3 Cost of Cramer's Rule
Ch3 Cost of Gauss Jordan Reduction
Ch3 Cost of Inverse Method
Ch3 Solving Nonlinear Systems Using Newton Raphson Method
Ch3 Solving Nonlinear Systems Using Fixed Point Iteration
Ch3 Solving Nonlinear Systems Using Seidel Iteration
Ch4 Interpolation
Ch4 Lagrange Polynomial
Ch4 Newton Polynomial
Ch4 Error Terms and Error Bound
Ch5 Curve Fitting
Ch5 Least Squares
Ch5 Linearization
Ch6 Numerical Differentiation
Ch6 Difference Formulas
Ch6 Derivation of Difference Formulas
Ch6 Error Analysis and Optimal Step Size
Ch7 Numerical Integration
Ch7 The Degree of Precision
Ch7 Composite Trapezoidal Rule
Ch7 Composite Simpson Rule
Ch7 Gauss Legegendre Integration
Ch5 Spline Functions
Ch7 Gauss Legegendre Translation
Ch9 Numerical Approximation for IVPs
Ch9 Euler Method
Ch9 Taylor Method of Order 2
Ch9 Heun Method
Ch9 Rung Kutta