Overview

Instructor

Jeffrey Wong ( main site)

Email

jtwong at math dot duke dot edu

Office

Physics 029B

Office Hours

(tentative) Th11-12, F3-4 or by appt.

Lectures

MW 3:05-4:20 (Gross Hall 304B)

Syllabus

Available here.

Textbook(s)

Required: Quarteroni, Sacco and Saleri, Numerical Mathematics, 2nd edition (might be available online)
Secondary texts (purchase not necessary): Ascher and Petzold, Computer Methods for Ordinary Differenial Equations,
Leveque, Finite Difference Methods for Ordinary and Partial Differential Equations, 2007

Course Website

During the semester, we will use Piazza for the course website (not here!) and Sakai for posting grades. Resources will periodically be updated here, but if enrolled, please consult the Piazza site.

Course Description

An introduction to numerical methods for functional approximation, differentiation and integration, ordinary differential equations and related topics. The course will emphasize an understanding of numerical methods and their properties from the perspective of theory and practice and the interplay between the two. First, we briefly cover the essentials of approximation theory. Second, we study numerical analysis of dynamical systems. Last, a selection of more advanced topics will be considered, such as finite difference schemes for partial differential equations and/or stochastic differential equations.

Prerequisites

A solid grasp of undergraduate linear algebra and differential equations (e.g. Math 221 and Math 356) is essential. Experience with programming of some kind is also expected (be comfortable with writing code to implement algorithms). Numerical linear algebra (e.g. Math 561) is suggested, but not necessary (the relevant points will be reviewed as needed).

Homework

• Homework is the primary way you will be assessed for the course. Assignments will be posted (approximately) weekly, involving both theoretical work and computation. Due dates will be listed on the assignment; typically one week after assigned.
• Homework should be turned in by the deadline to ensure full credit. If you miss a deadline, you should still complete the homework and turn it in for feedback (and partial, if not full, credit). The lowest homework score will be dropped.
• Working and studying in groups is strongly encouraged, as well as discussing code (writing code to be read by others is an excellent way to improve computational skills!). However, the final product - solutions and code - should be your own.
• Guidelines for code and computational results are posted to the course website.
• Solutions should be complete arguments. Be thorough, but strive for clarity without extraneous work. Support work with computations when appropriate.
• Typing solutions (in LaTeX) is suggested; if handwritten, make sure solutions are readable. Keep problems in the same order as the assignment, if possible.

Ethics

Students are expected to follow the Duke Community Standard. If a student is found responsible for academic dishonesty through the Office of Student Conduct, the student will receive a core of zero for that assignment. If a student’s admitted academic shonesty is resolved directly through a faculty-student resolution agreement approved by the Office of Student Conduct, the terms of that ent will dictate the grading response to the assignment at issue.