Skip Navigation
search: People Opens New Window | Departments Opens New Window | Penn State Opens New Window | Web Opens New Window
Penn State mark
Penn State mark
University Bulletin
Undergraduate Degree Programs

These course descriptions are not being updated as of August 1, 2016. Current course descriptions are maintained in LionPATH.

Mathematics (MATH)

MATH 412 Fourier Series and Partial Differential Equations (3) Orthogonal systems and Fourier series; derivation and classification of partial differential equations; eigenvalue function method and its applications; additional topics.

MATH 412 Fourier Series and Partial Differential Equations (3)

(BA) This course meets the Bachelor of Arts degree requirements.

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.


General Education: None
Diversity: None
Bachelor of Arts: Quantification
Effective: Spring 2009
Prerequisite: MATH 230;MATH 250 orMATH 251

Note : Class size, frequency of offering, and evaluation methods will vary by location and instructor. For these details check the specific course syllabus.

Search
CourseInfo

Look up course abbreviations

Course descriptions are stored in LionPATH, the University-wide student information system. Please visit the LionPATH Course Catalog to access current course descriptions. At that point, you will be leaving the University Bulletin website.



Skip Popular Searches
  1. Bachelor of Arts Degree Requirements
  2. General Education: United States Cultures and International Cultures
  3. Course Index
  4. Graduate Degree Programs Bulletin
  5. General Education: Arts
  6. General Education: Humanities
  7. General Education: Health and Physical Activity
  8. General Education: Natural Sciences
  9. General Education: Social and Behavioral Sciences
  10. General Education: Writing/Speaking