Scientific Computing: Continuous Systems

The goal of the course is to provide a bridge between the theoretical and practical aspects of scientific computing, so that you will understand the mathematical ideas behind several numerical algorithms and know how to apply them to solve problems in your major discipline. It is not a cookbook course on how to use algorithms, nor is it a class purely on the theory of algorithms. Within most topics, there will be a progression from basic conceptual material to more practical implementation issues, and homework will reflect this balance, with a mix of theoretical problems and applied “programming” problems. We will spend a portion of most class meetings having you work (potentially in pairs) on Matlab to get started on these applied problems.\ud This course focuses on continuous (as compared to discrete) problems, where ideas from calculus are used in designing algorithms. In many topics, we will begin with one-variable problems, exploring the role of one-variable calculus (especially Taylor expansions), and then move to multivariable problems, where we will introduce a few key ideas from linear algebra to generalize the algorithms. Math 215 (Linear Algebra) is not a prerequisite of the course; we will cover the basic ideas that we need