MATH 173 - Numerical Methods I
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 basic syntax of the programming language and make a program implementing different
problems using the programming language.
- Discuss the different methods in solving solutions of nonlinear equations of the form f(x) = 0, polynomial
interpolation and approximation, direct and iterative methods for solving linear systems, and numerical
differentiation and integration.
- Use appropriate numerical methods in solving complicated mathematical problems numerically.
Course Outline
UNIT 1. Introduction to SciLab
UNIT 2. Error Analysis
UNIT 3. Solution of Nonlinear Equations f(x) = 0
- Bisection Method
- Fixed Point Method
- Regula Falsi (False Position) Method
- Secant Method (Modified Regula Falsi)
- Newton Method
UNIT 4. Solutions of Linear Systems AX = B
- Introduction to Vectors and Matrices
- Upper triangular systems and Back Substitution
- Gaussian elimination
- Triangular Factorization
- Iterative Methods for linear systems
- Iterative Methods for nonlinear systems
UNIT 5. Polynomial Interpolation and Approximation
- Taylor Series
- Lagrange Approximation
- Newton Polynomials
- Chebyshev Polynomials
- Padé Approximations
UNIT 6. Numerical Differentiation and Integration
- Approximating the Derivative
- Numerical Differentiation Formulas
- Richardson’s Extrapolation
- Trapezoidal Rule
- Simpson's Rule 1/3 Rule
- Simpson's 3/8 Rule
- Boole's Rule
- Composite Trapezoidal and Simpson Rule