Office Hours:  MW 11:30 - 12:30  or by appointment

Graded course work: Homework problems, midterm exam, and final exam

Textbook: Fourier Series and Boundary Value Problems,  6th  Edition,  J. W. Ward and R. V. Churchill,McGraw-Hill, 2001

Prerequisites: Advanced Calculus (Math 140) or permission of instructor

Course Outline

• Introduction to PDEs;   classifcation of 2nd order PDEs - ellliptic, parabolic, hyperbolic; Laplace's equation, Poisson's equation, heat equation, wave equation (Chapter 1) .
• Maximum principals for elliptic and parabolic PDEs  (Supplemental)
• (Linear PDEs, superposition principal, separation of variables (Chapter 2)
• Fourier series, orthogonal functions, introduction to normed vector spaces and inner product spaces (L² -spaces), Bessel's inequality, Parseval's equation (Chapter 3) .
•   Convergence of Fourier series, uniform convergence, differentiation and integration of  Fourier series (Chapter 4)
•  More boundary value problems (Chapter 5).
•  Green's functions for 2nd order ordinary differential equations, delta functions (Supplemental).
•  General Sturm-Liouville theory (Chapter 6 + Supplemental).
• Bessel  functions (Chapter 8) .
• Legendre functions (Chapter 9) .
• Fundamential solutions, Potential theory, Dirichlet problems (Supplemental) .

Supplemental References

• H. F. Weinberger,  A First Course in Partial Differential Equations with Complex Variables and Transform Methods,  Wiley,  1965
• Peter V. O'Neil,  Beginning Partial Differential Equations, Wiley, 1999
• E. C. Zachmanoglou and Dale Thoe, Introduction to Partial Differential Equations with Applications,  Williams and Wilkens, 1976
• R. Courant and D. Hilber, Methods of Mathematica Physics I-II, Interscience Publishers, New York, 1962
• P. R. Garabedian, Partial Differential Equations, Wiliey, 1964