MTH 415/515

COURSE INFORMATION

SPRING 2008

Catalog Description:  Partial Differential Equations.  3 hrs.  Elementary partial differential equations.  Heat Equation, Lapaces's Equation, separation of variables, Fourier series, vibrating strings, eigenvalue problems, finite differences, Bessel functions, Legendre polynomials.  (PR:  MTH 331 and MTH 335)

Course Objectives: 

Required Materials:  Haberman, Richard.  Applied Partial Differential Equations, With Fourier Series and Boundary Value Problems.  Fourth Edition.  Pearson/Prentice Hall.  2004.  ISBN 0-13-065243-1.

Instructor:  Dr. J. Silver

Office:  SH 717

Telephone:  696-3044

Email:  silver@marshall.edu

Website:  http://users.marshall.edu/~silver

Office Hours:  2:00-3:00 p.m. MWF; 10:00 - 11:00 a.m.  TR 

Grading Policy:  Grades will be figured on a percentage basis. There will be three chapter exams. The homework average will be counted as a chapter exam. Homework is due no later than 4 PM on the day it is due (usually two class days after assignment). The lowest six homework grades will be dropped. No excuses are accepted for late homework.

90 - 100% = A 80 - 89% = B 70 - 79% = C 60 - 69% = D 0 - 59% = F

Attendance Policy:  Attendance will be taken daily by collecting homework. Borderline grades will be determined by class attendance.

Exams:  Tests will be given as scheduled in the syllabus. If it is necessary to change the date of an exam, two class day's notification will be given. If you are unable to take an exam due to unavoidable circumstances (e.g. illness, death in the family, accidents), you must contact me prior to the exam time and furnish written verification of the excuse in order to take a make-up test.
 

MTH 415/515, Partial Differential Equations

Daily Schedule, Spring 2008

 

JAN 15   1.1 & 1.2 Heat in a One-Dimensional Rod
JAN 17   1.3 Boundary Conditions; 1.4 Equilibrium Temperature Distribution
JAN 22   1.5 Derivation of the Heat Equation; 2.1 Separation of Variables
JAN 24   2.2 Linearity; 2.3 Heat Equation, Zero Temperatures
   
JAN 29   2.3 cont.
JAN 31   2.4 Examples with the Heat Equation
FEB 5   2.5 Laplace's Equation
FEB 7   3.1, 3.2 Convergence Theorems
FEB 12   3.3 Fourier Cosine and Sine Series
FEB 14   Exam 1
FEB 19   3.4 Differentiation of Fourier Series
FEB 21   3.5 Integration; 4.1 & 4.2 Vertically Vibrating String
FEB 26   4.3 Boundary Conditions on a String; 4.4 Vibrating String with Fixed Ends
FEB 28   4.4 Vibrating Membrane; 5.1 Sturm Liouville Problems
MAR 4   5.2 Heat Flow Examples; 5.3 Eigenvalue Problems
MAR 6   5.4 Nonuniform Rod; 5.5 Self-Adjoint Operators
MAR 11   5.6 Rayleigh Quotient; 5.6 Nonuniform String
MAR 13   5.7 Boundary Conditions of the Third Kind
MAR 18   5.9 Asymptotic Behavior; 6.1 Finite Differences
MAR 20   Exam 2
MAR 22-24   Spring Vacation
APR 1   6.2 Truncated Taylor Series; 6.3 Partial Differences
APR 3   6.3 Fourier-von Neumann, Nonhomogeneity
APR 8   6.4 2D Heat Equation; 6.5 Wave Equation
APR 10   6.6 Finite Differences & Laplace's Equation; 6.7 Finite Element Method
APR 15   7.1 & 7.2 Separation of Variables in 3D
APR 17   7.3 Vibrating Rectangular Membrane; 7.4 Eigenvalue Theorems
APR 22   7.5 Multidimensions; 7.6 Rayleigh Quotient in 3D
APR 24   7.7 Vibrating Circular Membrane
APR 29   7.8 Bessel Functions; 7.9 Circular Cylinders
MAY 1   7.10 Spherical Problems, Legendre Polynomials
MAY 8   Final Exam, Thursday, 10:15 - 12:15 AM