Mathematics: Numerical Diff Equations

Numerical solution and analysis of differential equations: initial-value and boundary-value problems; finite difference and finite element methods. Prerequisites: Calculus and linear algebra required in addition to differential equations or numerical analysis.

Open to Degree and PACE students Prereqs: Calculus and equations or numerical analysis (MATH 3230); linear algebra required in addition to differential

The above URL is for the Spring’22 offering of this course. The webpage will be slightly updated in Spring’25.<br>

<br> 1. <br> <strong>Required text: </strong> None. Lecture notes from the website referenced above will be used. <br><br> <strong>Course contents:</strong> The course teaches numerical methods for three types of differential equations (DEs):<br> <ul><li> Evolutionary ordinary DEs (the simplest example: dy/dt = -k*y); </li> <li> Boundary-value problems for ordinary DEs; </li> <li> Evolutionary partial DEs (Heat equation, Wave equation). </li></ul> <br> <strong>Course goals: </strong> <ul><li> Learn why numerical methods work, and what makes a good numerical method. </li> <li> Learn why numerical methods do NOT work sometimes, i.e., what can go wrong. </li> <li> Gain hands-on experience in programming numerical methods into MATLAB codes. </li> </ul> <br> <strong>Assumed background: </strong> Knowledge of linear algebra (Math 2524/2522 or 3201) and elementary knowledge of complex numbers will be required;   Math 5737 and 3230 are recommended, but not required. <br><br> 2. <br> <strong>Class format: </strong> You are expected to read the assigned lecture notes before each class. The class time will be structured as follows: <ul><li> You ask questions about the assigned material, and I answer them; </li> <li>I ask you pre-assigned questions about the material you have read; </li> <li>We discuss your progress in doing the homework; </li> <li> I preview the material to be assigned for the next class. </li> </ul> <br> <strong>Homework </strong> will be assigned after every class. Most homework problems require programming in MATLAB. Prior knowledge of Matlab is <strong>NOT</strong> assumed, but the willingness to learn this computer language <strong>IS</strong> required. For those students who have not used this software before, MATLAB tutorials are posted on the class website. I will provide extra help to such students during the first week or two of the course (and, of course, Matlab assignments at the beginning of the course will be very basic and short). <br> <br> <strong>Tests: </strong>   There will be two take-home tests during the semester and a presentation during the finals' week. The presentation must be on a topic closely related to this course. The topic can be chosen by the student or suggested by the instructor. Both the content and style of the presentation will be graded. A written report of the presentation is to be submitted. <br>

The following policy is approximate. The actual policy will be stated in the syllabus of the course, which will be posted by the beginning of the semester.<br> <ul><li> Homework = 39%, </li> <li> Each of the midterm tests = 24%, </li> <li> Final presentation = 13%. </li> </ul> Note:   <strong> I do NOT drop your lowest grade. </strong> Thus, ALL the grades that you earn during the semester will contribute to your final grade.