UNIVERSITY OF TENNESSEE

SYLLABUS

Math 572 - Numerical Mathematics II

3 Credit Hours

Section 001, CRN 20444

Meetings: TR 12:40p--1:55p Ayres Hall 112.

Spring 2018

**Course Description**: Numerical techniques for initial value problems of ordinary differential equations. Two-point boundary value problems. Finite difference and finite element methods for selected partial differential equations. Fast Poisson solvers.

**Instructor Name**: Abner J. Salgado.

**Office Hours and Location**: Wednesdays 2--3pm in Ayres 214. Office hours can also be arranged by appointment.

**Email**: `asalgad1@utk.edu`

**Course Communications**: You may write to me at `asalgad1@utk.edu` with questions, comments, etc. To avoid confusion, please write the course name (MATH572) in the Subject line. You **must** use your university e-mail account when sending me emails.

**Course web page**: http://www.math.utk.edu/~abnersg/teaching.html

**Goals**: The successful student will be able to derive, apply and analyze elementary numerical algorithms. This course (together with Math 571) is intended to prepare mathematics students for the numerical preliminary examination. Topics in this class include numerical methods for ODEs (linear stability, stiff equations, A-stability, and convergence), and numerical methods for PDEs (stability, von Neumann analysis, convergence, and practical solution).

**Textbook**:
*Required:*

- A First Course in the Numerical Analysis of Differential Equations, A. Iserles, Cambridge University Press, 2nd edition, 2009.

*Supplementary:*

- Introduction to Numerical Analysis, J. Stoer and R. Bulirsch, Springer, 3rd edition, 2002.
- A Theoretical Introduction to Numerical Analysis. V.S. Ryaben'kii and S.V. Tsynkov, Chapman & Hall/CRC, 2007.

**Course Requirements, Assessment and Evaluations**:

- Homeworks will be handed out every other week, or can be downloaded from the class website. While generally homework will not be collected, doing homework will help with the quizzes and exams. In this class it is OK to try to solve the homework in groups. Quizzes and programming assignments, however, must be turn in on an individual basis.
- There will be
**two (2)**programming assignments throughout the semester. You can solve them using Matlab©, or any programming language of your choice. Submission of these will be done online. - There will be a short (10-15 minutes) quiz approximately every other week. They will generally cover the material of the previous lectures.
- There will be one midterm and a
*comprehensive*final exam. A tentative date for the midterm is**March 8**. The official date will be announced*at least*two weeks in advance. The University Calendar sets the final examination date to be**Wednesday, May 2 12:30pm - 2:30pm**. - The midterm is worth
**30**points, the final is worth**35**points, quizzes are worth**20**points and programming assignments**15**points. The cutoffs will be approximately as follows: 90% or higher is an A, 80% - B, 70% - C and 60% - D.

**Makeup Policy**: Late programming assignments will ** NOT** be accepted.
Makeups for the quizzes, midterm and final will be given only if a student can present evidence that
an absence was caused by serious illness, a death in the immediate family, religious observance,
or participation in University activities at the request of University authorities. For an illness,
you must present a signed statement from a doctor that your illness was sufficiently serious to make
you miss class. A note saying only that you visited the doctor or the Health Center will not suffice.

**Course Outline**:
This is a tentative list of topics to be covered in class.

- Review of the theory of initial value problems.
- Euler's method.
- Multistep methods.
- Runge-Kutta methods.
- Stiff equations.
- Finite difference schemes.
- The finite element method for the Poisson problem.
- Spectral methods (time permitting).
- Finite difference schemes for the heat equation.
- Finite difference schemes for the transport equation.

*If the instructor finds it necessary to make informational changes (e.g. office hours, schedule adjustments) due to students' needs or unforeseen circumstances, students will be notified in writing/email of any such changes.*

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Nikos Drakos,
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The translation was initiated by Abner Salgado on 2018-01-03

Abner Salgado 2018-01-03