Students should know all relevant definitions, correct statements of the major theorems (including their hypotheses and limitations), and examples and non-examples of the various concepts. The students should be able to demonstrate their mastery by solving non-trivial problems related to these concepts, and by proving simple (but non-trivial) theorems about the concepts below, related to, but not identical to, statements proven by the text or instructor.
This course is designed to prepare students to solve mathematical models represented by initial or boundary value problems involving partial differential equations that cannot be solved directly using standard mathematical techniques but are amenable to a computational approach. Numerical solution of partial differential equations has important applications in many application areas. Students are introduced to the discretization methodologies, with particular emphasis on the finite difference method, that allows the construction of accurate and stable numerical schemes. In-depth discussion of theoretical aspects such as stability analysis and convergence will be used to enhance the students' understanding of the numerical methods. Students will also be required to perform some programming and computation so as to gain experience in implementing the schemes and to be able to observe the numerical performance of the various numerical methods. For more detailed information visit the Math 511 Wiki page