# Spring 2014, MATH 412, Fourier Series and Partial Differential Equations

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**Review notes:**

- Review notes 1
- Review notes 2
- Review notes 2 - expanded
- Review notes 2 - added: boundary value problems
- Review notes 3
- Notes on Laplace equations: from Evans' textbook
- Final Exam guide - part 1
- Final Exam guide - part 2
- Final Exam guide - part 3

**Exam solutions:**

**HW solutions: **

Lectures:

- Tuesdays and Thursdays: 9:45-11:00am, 219 Hammond Bldg.

Instructor information:

- Instructor: Toan T. Nguyen
- Office: 238 McAllister
- Phone: (814) 863-4123
- Email: This email address is being protected from spambots. You need JavaScript enabled to view it.
- Office hours: Mondays 1:20-2:20pm, Tuesdays 3:00-4:00pm, and Thursdays 8:30-9:30am

Textbook:

- W. Strauss, Partial Differential Equations: An Introduction, Second Edition.

Purpose of the Course:

The purpose of MATH 412 is to introduce students to the origins, theory, and applications of partial differential equations. Several basic physical phenomena are considered - including flows, vibrations, and diffusions - and used to derive the relevant equations. The fundamentals of the mathematical theory of partial differential equations are motivated and developed for the students through the systematic exploration of these classic physical systems and their corresponding equations: the Laplace, wave, and heat equations.

In addition to treating the physical origins of the equations, this course focuses on solving evolution equations as initial value problems on unbounded domains (the Cauchy problem), and also on solving partial differential equations on bounded domains (boundary value problems). There is not one but many techniques for solving these equations, and the course presents some aspect of the expansion in orthogonal functions (including Fourier series), eigenvalue theory, functional analysis, and the use of separation of variables, Fourier transforms, and Laplace transforms to solve PDEs by converting them to ordinary differential equations.

This course currently serves a cross-section of students at the university with interests or the need for this advanced subject mathematics, including students majoring in the engineering program, meteorology, physics, and mathematics. This typically includes the most advanced physics, engineering, and meteorology students, as well as mathematics majors with interests in applied mathematics.

Grading policy: The final grade will be based on

- Weekly homework: 30%
- In-class Midterm 1: 20% on Thursday, Feb 6
- In-class Midterm 2: 20% on Thursday, March 27
- Final exam: 30%. Exact date: TBA

Homework: Homework will be collected weekly at the beginning of each of Thursday classes, with exception of two Thursdays during which the in-class midterms will be taken place. There will be 11 HW assignments. Late homework will not be accepted.

Academic Integrity: All Penn State Policies regarding ethics and honorable behavior apply to this course; for details, see: http://www.psu.edu/ufs/policies/

Students with disabilities: Penn State welcomes students with disabilities into the University's educational programs. Every Penn State campus has an office for students with disabilities. The Office for Disability Services (ODS) Web site provides contact information for every Penn State campus: http://equity.psu.edu/ods/dcl. For further information, please visit the Office for Disability Services Web site: http://equity.psu.edu/ods.