This course addresses the theory and practice of numerical methods as they apply in various areas of mathematics. Possible topics include: numerical solutions of systems of linear and nonlinear equations, interpolation, numerical differentiation and integration, numerical solution of ordinary and partial differential equations.
- Understand the limitations of computer arithmetic as well as methods to mitigate these limitations.
- Understand the theoretical background of numerical algorithms and error estimates.
- Understand, and be able to utilize, numerical algorithms to solve mathematical problems.
- Be able to choose an appropriate mathematical method for a given application.
- Be able to write programs to implement mathematical algorithms on a computer.