## Typical Syllabus for Math 321: Numerical Analysis## at Lycoming CollegeNote: This is a typical syllabus for this course. Each semester in which Numerical Analysis is taught, a semester-specific syllabus will be distributed, which will spell out --in addition to the topics-- other administrative details, such as information about grading, homework, tests, labs, etc. As early as in the time of Archimedes, Numerical Analysis arose as the study of obtaining numerical approximations. In recent times, the emphasis in numerical analysis has been to use computers to such an extent that its definition has narrowed to specify the computer as the exclusive tool. The course, as taught recently at Lycoming, treads a middle path: to illustrate the use of computer programming and software to apply the principles of numerical analysis to classic problems of solving equations and approximating functions, as well as the use of paper-and-pencil (and a four-function calculator) to find approximations that are readily available with more sophisticated scientific or graphing calculators. The following topics form the traditional core of the course - Solving equations using the Bisection Method and related methods, as well as Newton's Method and the Secant Method;
- Polynomial Interpolation, and its application to problems of approximation, numerical differentiation and numerical integration;
- Ordinary Differential Equations and their numerical solution using a variety of methods;
- Computational Linear Algebra, both direct methods and iterative methods;
- Cubic spline interpolation, and possibly the mathematics of parametric curve interpolation.
If time allows, elliptic partial differential equations are presented at an elementary level. Additional topics may be the Fast Fourier Transform and its uses. Extensive use is made of Microsoft Excel, Java, and C++. |