This course serves as an introduction to numerical methods as they apply to calculus and differential equations. It is, above all, a mathematics course, not a programming course, so it will center around the mathematical analysis of numerical algorithms, rather than on the development and implementation of such algorithms. An understanding of the effects of estimates and errors involved in the procedures (and in the very nature of computational methods) and how these errors arise and can be minimized will form the core of our studies. A secondary theme will be an analysis of the efficiency of the methods we investigate.
We will develop and analyze methods in the following broad areas:
See the the course outline for more details.
- Solving non-linear equations
- Curve fitting, interpolation and approximation
- Differentiation and Integration
- Solving systems of equations
- Solutions to ordinary differential equations