Numerical Applied Mathematics

Posted on August 30, 2021 (Cupples I / 113)

Description: Math449

Categories: teaching;

Syllabus: Math 449, Fall 2021

Course Title

Numerical Applied Mathematics

Summary

This course is intended to serve as a first introduction of numerical methods. The course will cover basic numerical methods for solving various problems that arise in mathematics, science and engineering: linear and nonlinear equations, eigenvalue problems, ordinary differential equations (ODEs). We will introduce methods that perform numerical differentiation and integration, polynomial interpolation and analyze them.

Prerequisites are first courses in calculus, linear algebra and ordinary differential equations. Basic programming proficiency will be helpful but is not required.

• Instructor: Donsub Rim (rim@wustl.edu)
• Lectures: MWF 3:00-3:50, Cupples I / 113 (in-person)
• Office Hours: TTh 3:00-3:50, Cupples I / 206

Textbook

Endre Süli and David Mayers
An Introduction to Numerical Analysis
Cambridge University Press
(ISBN-10: 0521007941)

Course Outline

The course will cover following topics, following the textbook.
(The item number will roughly correspond to the week of the semester).

1. Iterative methods for solution of nonlinear equations (Ch 1)
2. Solution of systems of linear equations (Ch 2)
3. Simultaneous nonlinear equations (Ch 4)
4. Eigenvalues and eigenvectors (Ch 5)
5. Polynomial interpolation (Ch 6)
6. Numerical interpolation I (Ch 7)
7. Midterm Exam
8. Polynomial approximation in the inf-norm (Ch 8)
9. Approximation in the 2-norm (Ch 9)
10. Numerical integration II (Ch 10)
11. Piecewise polynomial approximation (Ch 11)
12. Initial value problems for ODEs (Ch 12)
13. Further topics as time allows

Online Discussions and Software

• Further course information will be available on Canvas.
• Piazza boards will be used for discussion.
• The programming portion of the course will use Python with NumPy and SciPy libraries.
  Anaconda Python is recommended.

Assignments, Exams, Grading

There will be weekly assignments during the semester which will consist of 30% of the total grade. The assignments will include both a written part and a a programming part. Late homeworks will not be accepted and lowest assignment grade will be dropped.

There will be a midterm and a final exam. The midterm exam will be 30% and the final exam 40% of the final grade.

Academic Integrity

Students are encouraged to collaborate on problems together, however the submitted write-up should be entirely their own. Students are expected to adhere to the university academic integrity policy.

COVID-19 Health and Safety Protocols

While on campus, it is imperative that students follow all public health guidelines established to reduce the risk of COVID-19 transmission within our community. Review the University protocols.