# Mathematics 434

MATH 434
Numerical Analysis I

1. Catalog Entry

MATH 434
Numerical Analysis I

Credit hours (3)
Prerequisites: MATH 252, MATH 260, and ITEC 109 or 120; or permission of instructor.

Introduction to scientific programming, numerical solutions nonlinear equations and problems from linear algebra, interpolation, numerical integration, and numerical methods for differential equations.

2. Detailed Description of Course

The first part of this course typically covers:
1) Programming using MATLAB, MAPLE or other programming environments.
2) Floating point arithmetic.
3) Solution of non-linear equations, Newton's method, secant method, and other iterative schemes.
4) Linear systems of equations, matrix factorizations.
5) Interpolation.
6) Least squares approximation.
7) Eigenvalue computation.

The second part typically covers:
1) Numerical differentiation.
2) Numerical integration, including Newton-Cotes formulas, adaptive quadrature, and Gaussian quadrature
3) Numerical methods for differential equations, including Euler's method, Runge-Kutta methods, boundary value problems, and methods for partial
differential equations.
4) Selected additional topics, such as fast Fourier transform, numerical optimization, random number generators, and stochastic differential
equations.

3. Detailed Description of Conduct of Course

This course will contain an introduction to scientific computing; the particular software used will vary among instructors.  Most instructors will use the lecture method, with some classes being taught in the computer lab.

4. Goals and Objectives of the Course

Acquire a working knowledge of algorithms and modern computer software for approximating solutions of scientific computing problems.

5. Assessment Measures

The assessment measures will vary among instructors and may include in-class examinations, homework assignments, computer projects, and performance in class and in laboratory activities.

6. Other Course Information

Students who plan to work in an applied science need exposure to and hands-on experience with methods and computer software that is applicable to many of the general problems they will encounter.  Math 434:435 is intended to be the sequence that provides this exposure and experience.

Review and Approval

September 2001

March 2009