MATH 4364 - Introduction to Numerical Analysis in Scientific Computing - University of Houston

# MATH 4364 - Introduction to Numerical Analysis in Scientific Computing

***This is a course guideline.  Students should contact instructor for the updated information on current course syllabus, textbooks, and course content***

Prerequisites: MATH 3331 or MATH 3321

Course Description: Root finding, interpolation and approximation, numerical differentiation and integration, numerical linear algebra, numerical methods for differential equations

*Note: Students should have the ability to do computer assignments in FORTRAN, C, Matlab, Pascal, Mathematica or Maple. Formerly MATH 4364 Numerical Analysis

Textbook: Numerical Analysis (9th edition), by R.L. Burden and J.D. Faires, Brooks-Cole Publishers. ISBN: 978-0538733519

Topics Covered:

This is an one semester course which introduces core areas of numerical analysis and scientific computing along with basic themes such as solving nonlinear equations, interpolation and splines fitting, curve fitting, numerical differentiation and integration, initial value problems of ordinary differential equations, direct methods for solving linear systems of equations, and finite-difference approximation to a two-points boundary value problem. This is an introductory course and will be a mix of mathematics and computing.

Tentative Syllabus:

1. Computer Number Systems and Floating Point Arithmetic Conversion from base 10 to base 2,  conversion from base 2 to base 10, floating point systems and round-off errors.

2. Solutions of Equations in One Variable:
Bisection method, fixed-point iteration, Newton's method, the secant method and their error analysis.

3. Direct Methods for Solving Linear Systems:
Gaussian elimination with backward substitution, pivoting strategies, LU-factorization and forward substitution., Crout factorization.

4. Interpolation and polynomial approximation:
Interpolation and the Lagrange polynomial, errors in polynomial interpolation, divided differences, Cubic spline interpolation, curve fitting.

5. Numerical differentiation and integration:
Numerical differentiation, numerical integration, composite numerical integration, Gaussian quadratures, multiple integrals.

6. Numerical Solutions of Ordinary Differential Equations (ODEs):
Euler's Method, higher-order Taylor methods, Runge'Kutta methods, multi-step methods and its stability, stiff differential equations, two-points boundary value problem.