Northeastern State University
College of Mathematics, Science and Nursing
Department of Mathematics
Syllabus for Math 4123 Partial Differential Equations
PREREQUISITES: Math 2633 Calculus III and Math 4113 Differential Equations.
CATALOG DESCRIPTION OF COURSE: Series solution of ordinary equations, Fourier series, classical second order partial differential equations, heat
equation, wave equation, and Laplace's equation. Boundary-value problems and Sturm-Liouville theory.
COURSE PURPOSE: The purpose of this course is to introduce the advanced undergraduate mathematics and/or physics major to the theory and applications
of classical elementary partial differential equations. This course will provide the necessary background, expertise, and experience that is required to solve
elementary classical partial differential equations in 2 and 3 dimensions.
EXPECTED COURSE OUTCOMES: The student will be expected to achieve the following objectives:
1. Communicate with appropriate mathematical symbols.
2. Understand and be able to use the method of separation of variables to solve linear partial differential equations.
3. Understand and be able to use Fourier Series for the solution of linear partial differential equations.
4. Understand and solve Sturm-Liouville eigenvalue problems.
5. Understand and use the methods of infinite series solutions of ordinary differential equations and how they apply to Bessel's equation and other differential equations that arise from separation of variables.
6. Understand and apply all of the above to the solution of the heat equation, the wave equation, and Laplace's equation.
INSTRUCTIONAL MATERIALS: (Required Textbook) Elementary Applied Partial Differential Equations, Third Edition, Haberman, Prentice-Hall, 1998
INSTRUCTIONAL PROCEDURES: The expected course outcomes will be realized through a variety of instructional strategies to aid the students in
construction of cognitive schemas . Those strategies include, but are not limited to, the following: expository-discussion, demonstration, inquiry, and group
activities.
Partial Differential Equations
I. Heat Equation
Derivation of the Conduction of Heat in a One-Dimensional Rod, Boundary Conditions, Equilibrium Temperature Distribution, Derivation of the Heat Equation
in 2 or 3 Dimensions.
II. Method of Separation of Variables
Linearity, Heat Equation with Zero Temperatures at Finite Ends, separation of variables, principle of superposition, Examples using different boundary
conditions, Examples of separation of variables using Laplace's equation.
III. Fourier Series
Convergence Theorems, Fourier Cosine and Sine Series, term by term integration and differentiation of Fourier Series.
IV. The 1-dimensional wave equation
The vibrating string problem, its derivation and solution.
V. Sturm-Liouville Eigenvalue Problems
Regular Sturm-Liouville Problems, Examples, Self-Adjoint Operators, Examples.
VI. Three Dimensional Problems
Vibrating Circular membrane, Bessel's Equation, Infinite Series Methods of solving ordinary differential equations, singular points, Bessel Functions, Laplace's
equation on a cylinder and on a sphere, Legendre polynomials.
ADA COMPLIANCE: If any member of the class feels that he/she has a disability and needs special accommodations of any nature, whatsoever, the instructor
will work with you and the University's Office of Student Affairs to provide reasonable accommodations to ensure that you have a fair opportunity to perform in
this class. Please advise the instructor of such disability and the desired accommodations at the first class attended.
INCLEMENT WEATHER / DISASTER POLICY: The following are basic premises for the inclement weather policy at Northeastern State University:
1. Class will be held if at all possible.
2. It is the student's responsibility to receive the information when weather is questionable.
3. Neither students nor faculty are expected to risk life or limb.
4. Faculty members are obligated to hold classes if the University is not closed, unless the faculty member is unable to get to campus.
Policy: During times of inclement weather, decisions concerning day classes will be made by 6:00 a.m. in order for the media to be notified and for students to
receive the announcement before they leave home. Decisions concerning night classes will be made by 3:00 p.m.
The following media will be notified regarding closing of the campus:
Radio Stations: Television Stations:
KRMG 740 AM Tulsa KJRH Channel 2 Tulsa
KAYI 107 FM Tulsa KOTV Channel 6 Tulsa
KTLQ 1350 AM Tahlequah KTUL Channel 8 Tulsa
KEOK 102 FM Tahlequah KFSM Channel 5 Fort Smith
KBIX 1490 AM Muskogee Cable Channel 96 Tahlequah
KMMY 97 FM Muskogee
KVOO 1170 AM Tulsa
The automated attendant message on 918-456-5511 will be modified to include information concerning campus operations during inclement weather.