The required text is Advanced Engineering Mathematics, 2nd edition, by Michael D. Greenberg (published by Prentice Hall, Upper Saddle River, New Jersey). The course will cover parts of Chapters 4 and 15-20, and some other material. The following is a listing of most of the subject matter to be covered, not necessarily in this order:
 

Power series. Radius of convergence. The power series and Frobenius methods of solving differential equations. Legendre's equation; Legendre polynomials; Bessel's equation and properties of Bessel functions. Sturm-Liouville problems. Orthogonal functions. Eigenvalues and eigenfunctions.

Contour, surface, and volume integrals. Differential forms. Computation of areas, moments,circulation, flux. The Generalized Fundamental Theorem of Calculus, including Green's Theorem and the Divergence Theorem. Applications to fluid flows. Laplace's Equation in Cartesian, cylindrical, and polar coordinates.

Classification of PDEs as elliptical, parabolic, or hyperbolic; solutions by change of variables. D'Alembert's approach to the wave equation. Separation of variables and Fourier series techniques for one- and two-dimensional wave equations, including forced vibrations. One-dimensional heat equation: bar with insulated ends, and with adiabatic boundary conditions, and with radiation. Two- dimensional steady-state heat equation, isotherms, lines of heat flow. Vibrations of rectangular and circular membranes; nodal lines Legendre's equation in spherical coordinates.
 

Requirements: There will be three one-hour tests and a two-hour final exam. The test dates are followed by 3 dots in the calendar above. There will be three problem sets; each due date is followed by one dot in the calendar. Each problem set will be marked and returned, along with a partial key, by the next date that is followed by two dots. A part of the score on every problem set will be based on whether it is easily legible, neat, organized, clear, and well-written. Your solutions to problems and test questions may be reproduced and distributed to the class.

I expect you to attend class faithfully and to keep up with assigned work. When you are absent, or if you are late to class, or if you leave class early, please let me know why. If you have difficulties of any kind that affect your work, I will be glad for you to tell me about them. Whenever there is some way you think I can help, please ask. It will be best for you not to miss scheduled tests; but if you find that you are unable to take a test (or even the final exam) at the appointed time due to illness or other personal difficulty, please discuss it with me as soon as possible. Once you have taken the final, or any other test, a re-take is not allowed. When a test is graded and handed back to you, you should look it over carefully, and if you have any question or complaint about the grading, you should discuss it with me. It never hurts to ask.

Let T be the average grade on the three hour tests, P the average grade on the problem sets, and E the grade on the final exam. Your overall grade in the course will be no lower than