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 and COSC 1410 or equivalent.

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.

CSD Accommodations:

Accommodation Forms: Students seeking academic adjustments/auxiliary aids must, in a timely manner (usually at the beginning of the semester), provide their instructor with a current Student Accommodation Form (SAF) (paper copy or online version, as appropriate) from the CSD office before an approved accommodation can be implemented.

Details of this policy, and the corresponding responsibilities of the student are outlined in The Student Academic Adjustments/Auxiliary Aids Policy (01.D.09) document under [STEP 4: Student Submission (5.4.1 & 5.4.2), Page 6]. For more information please visit the Center for Students with Disabilities Student Resources page.

Additionally, if a student is requesting a (CSD approved) testing accommodation, then the student will also complete a Request for Individualized Testing Accommodations (RITA) paper form to arrange for tests to be administered at the CSD office. CSD suggests that the student meet with their instructor during office hours and/or make an appointment to complete the RITA form to ensure confidentiality.

*Note: RITA forms must be completed at least 48 hours in advance of the original test date. Please consult your counselor ahead of time to ensure that your tests are scheduled in a timely manner. Please keep in mind that if you run over the agreed upon time limit for your exam, you will be penalized in proportion to the amount of extra time taken.

UH CAPS

Counseling and Psychological Services (CAPS) can help students who are having difficulties managing stress, adjusting to college, or feeling sad and hopeless. You can reach (CAPS) by calling 713-743-5454 during and after business hours for routine appointments or if you or someone you know is in crisis. No appointment is necessary for the "Let's Talk" program, a drop-in consultation service at convenient locations and hours around campus.