# MATH 331: Partial Differential Equations Spring 2015.

## Presentation on theme: "MATH 331: Partial Differential Equations Spring 2015."— Presentation transcript:

MATH 331: Partial Differential Equations Spring 2015

Course Topics Review of ordinary differential equations (Sections 0.1 - 0.2) Boundary value problems for ODE (Sections 0.3 - 0.4) Fourier series; Fourier integral; convergence (Chapter 1) Heat equation; the product method (Sections 2.1 - 2.6) Sturm-Liouville problems; eigenfunctions series (Sections 2.7 - 2.13) Wave equation: product method solution; D’Alembert’s solution (Chapter 3) Potential equation; harmonic functions (Chapter 4) Higher dimensions, other coordinates, applications (selected sections of Chapter 5) Laplace and Fourier transform methods (Chapter 6 and handouts) Numerical methods; Monte-Carlo method (selected sections of Chapter 7) The tentative schedule of the course has been posted on my website; see http://home.sandiego.edu/~pruski/m331s15schedule.html

Course Learning Outcomes Upon successful completion of this course, the student will: 1. Demonstrate a working knowledge of the theory of second-order linear partial differential equations, including the knowledge of theorems with assumptions. 2. Be able to: –solve simple boundary value problems for ordinary differential equations, –determine Fourier series and Fourier integral of simple functions, –apply the product method to solve standard initial-boundary value problems for heat, wave, and potential equations. 3. Demonstrate the ability to: –solve problems in the topics listed above, including applications from the field of physics and engineering, –use a computer environment, such as MATLAB, to solve differential equations and visualize and interpret the solutions, –understand simple proofs and write elementary proofs, –communicate mathematical ideas clearly.

Office Hours and Contact Office hours (Dr. Lukasz Pruski, Serra 149, x. 4035): Monday3:30 – 5 Tuesday2:30 – 4 Wednesday12:30 – 1:30 Friday10:10 – 11:10 and at other times, by appointment. (I am usually less available on Thursdays.) Contact: The best way to contact me is by using e-mail (pruski@sandiego.edu or lukaszpruski@gmail.com). I read e-mail many times a day. I have voice mail (x. 4035), but I often forget to check it. If for some reason you are unable to contact me, try calling our departmental Executive Assistant, Tina Manabat, at extension 4706.pruski@sandiego.edu

Assignments, Quizzes, Project Homework Assignments will be assigned and collected with frequency yet to be determined (decision by class vote). For many of the assigned exercises, a BOB (back of the book) answer will be available. The total homework assignment score will count for 25% of the course grade. Late assignments will not be accepted unless you have a valid reason and you arrange it with me in advance. Pop-quizzes (not announced in advance). There will be 8 - 10 of them. Quiz questions will refer to the recently covered material and to the new material you were supposed to read. Two or three lowest quiz scores will be dropped, and the remaining scores will count for 20% of the course grade. Quizzes cannot be made up unless you have a valid reason for not taking the quiz and you notify me in advance of your absence. Research project requiring team research will be assigned in April to be completed by May 8. Each project requires a write-up; volunteers will be solicited to present their projects in class. The project counts for 5% of the course grade.