MATH 174 - Numerical Methods II
Course Description
This course is about numerical methods with emphasis on algorithms and convergence,
error analysis and computer arithmetic. Other topics that will be discussed are
solutions of nonlinear equations of the form f(x) = 0, polynomial interpolation,
approximation; direct and iterative methods for solving linear systems; numerical
differentiation and integration.
Course Learning Outcomes
After completion of the course, the student should be able to:
- Discuss the different methods in solving solutions of differential, equations, curve fitting, eigenvalues and
eigenvectors, and numerical integration.
- Make a program implementing different problems using a programming language.
- Use appropriate numerical methods in solving complicated mathematical problems numerically.
Course Outline
UNIT 1. Curve Fitting
- Least Squares Line
- Curve Fitting
- Spline Functions
- Fourier Series and Trigonometric Polynomials
UNIT 2. Solutions of Differential Equations
- Review of Differential Equations
- Euler’s Method
- Heun’s (Modified Euler) Method
- Taylor Series Method
- Runge-Kutta Method
- Predictor-Corrector Methods
- Systems of Differential Equations
- Boundary Value Problems
- Finite-difference Method
UNIT 3. Eigenvalues and Eigenvectors
- Homogeneous Systems: The Eigenvalue Problem
- Power Method
- Jacobi’s Metho