Math 401/501: Partial Differential Equations I.
Math 691: Engineering Analysis I.

Time:
Tuesdays and Thursdays, 7:10pm-8:25pm, Aug. 23 - Dec. 5, 2008
Place:
Room 0128 @ Edu. BLDG
Office Hours:
Tuesdays and Thursdays, 3:30pm-4:30pm, Room 2109 @ E&ES BLDG
Textbook:
Applied Partial Differential Equations (4th Ed.) by Richard Haberman
Prerequisites:
A grade of C or better in MATH 307 and 312.

Final exam schedule: 7:00-10:00pm, Tuesday, December 9th, 2008

The exam is open book.

Final exam will cover the following equations:

  • The heat equation;
  • The wave equation;
  • Laplace's equation;
  • Helmholtz equation;
  • Bessel's equation;
    • with or without
  • non-homogeneous boundary conditions
  • non-honogeneous source
    • in 1D and 2D, with Cartesian and polar coordinates, on a finite or infinite domain, by using the following techniques:
  • Separation of variables;
  • Fourier series;
  • Eigenfunction expansion;
  • Fourier transform.

    • Midterm exam schedule: 7:10-8:25pm, Thursday, October 16th, 2008

    The midterm exam is closed-book.

    Midterm exam covers Chapters I and II. Specifically, the heat equation and Laplace's equation, in various coordinate systems (Cartesian, polar, cylindrical, and spherical), will be included the exam. One should know very well, for instance, how to use method of separation of variables and Fourier expansion to solve various initial value and boundary value problems.

    Students taking Math 401 will be given TWO problems in the midterm exam, and those talking Math 501 and 691 will be given one additional problem.

    Grading: Homework 50%, mid-term exam 20%, final exam 30%.

    Grading scales:
    A: 92-100%, A-: 90-91.9%
    B+: 88-89.9%, B: 82-87.9%, B-: 80--81.9%
    C+: 78-79.9%, C: 72-77.9%, C-: 70-71.9%
    D+: 68-69.9%, D: 62-67.9%, D-: 60-61.9%
    F: 0-59.9%

    Synopsis:
    The goal of this course to provide an introduction to partial differential equations and their applications to physics and engineering. The content of the course will include:
  • Separation of variable techniques;
  • Sturm-Liouville systems;
  • Generalized Fourier series;
  • Orthogonal functions of the trigonometric, Legendre and Bessel type;
  • Boundary value problems associated with the wave equation and the heat conduction equation in various coordinate systems.

    • The materials in the textbook to be covered are:

  • Chapter 1: Sec. 1.1 - 1.5;
  • Chapter 2: Sec. 2.1 - 2.5;
  • Chapter 3: Sec. 3.1 - 3.6;
  • Chapter 4: Sec. 4.1 - 4.5;
  • Chapter 5: Sec. 5.1 - 5.8;
  • Chapter 7: Sec. 7.1 - 7.7;
  • Chapter 8: Sec. 8.1 - 8.3;
  • Chapter 10: Sec. 10.1 - 10.6

    • Homework:

  • Assignment #1 (due Thursday, Sept. 18, 2008):
    Problems in Chpt 1: 1.4.1(a) and (f), 1.4.3, 1.4.7(a), .5.2, 1.5.9(a), 1.5.13.
    Problems in Chpt 2: 2.3.1(a) and (b), 2.3.2(a) and (d), 2.3.3(b), 2.3.5, 2.3.8, 2.4.2, 2.4.3, 2.4.7, 2.5.1(a), 2.5.5(a), 2.5.15(a).
  • Assignment #2 (due Tuesday, Oct. 7, 2008):
    Problems in Chpt 3: 3.3.1(a) and (e), 3.3.4, 3.3.5(c), 3.3.10, 3.4.9, 3.4.10.
    Problems in Chpt 4: 4.4.2, 4.4.3, 4.4.7, 4.4.8, 4.4.9.
  • Assignment #3 (due Tuesday, Oct. 28, 2008):
    Problems in Chpt 5: 5.3.4(a) and (b), 5.4.1, 5.4.2, 5.4.6, 5.5.1(a) and (b), 5.8.5, 5.8.6, 5.8.8, 5.8.10, 5.8.11.
  • Assignment #4 (due Tuesday, Nov. 4, 2008):
    Problems in Chpt 7: 7.3.1(b), 7.3.2(b), 7.3.6, 7.4.1, 7.4.2
  • Assignment #5 (due Tuesday, Nov. 18, 2008):
    Problems in Chpt 8: 8.2.1(a), (b) and (d), 8.2.2(a) and (b), 8.3.1(a) and (b).
  • Assignment #6 (due Tuesday, Dec. 2, 2008):
    Problems in Chpt 10: 10.3.1, 10.3.5, 10.5.1, 10.5.2, 10.6.1(a), 10.6.2(b), 10.6.4(a).