COURSE SYLLABUS Course Number: MATH6060 Course Title: ELEMENTARY PARTIAL DIFFERENTIAL EQUATIONS Credit Hours: 3 Prerequisites: MATH2650 Corequisite: Objectives: To present the fundamentals of partial differential equations and to develop student understanding and problem solving skills in the subject, as necessary for its applications in the sciences and engineering. Course Content: Heat conduction and diffusion processes, mechanical vibrations and wave propagation, electromagnetism and potentials, and other examples of linear partial differential equations (physical principles, equations and boundary conditions in rectangular and curvilinear coordinates) [6 days] Linear partial differential operators, the superposition principle, separation of variables, formal solution of simple boundary and initial-boundary value problems via Fourier series [9 days] Classification of second-order linear partial differential equations (elliptic, parabolic, hyperbolic equations), qualitative features (characteristics, energy dissipation/conservation and causality, smoothing and propagation of singularities, maximum rinciples), well-posedness of boundary and initial-boundary value problems [9 days] Eigenvalues and eigenfunctions of elliptic operators, Hilbert space, orthogonality and completeness, Sturm-Liouville problems and special functions, solution of elliptic, parabolic, and hyperbolic problems via eigenfunction expansions [9 days] Fundamental solutions and Green's functions, integral transform methods [6 days] Possible Textbooks: W.A. Strauss, Partial Differential Equations --- An Introduction, Wiley, New York, 1992 D.W. Trim, Applied Partial Differential Equations, PWS--Kent, Boston, 1990 Grading and Evaluation Procedures: Tests, midterm exam, final exam, homework projects. Other methods of evaluation are used at the discretion of the instructor. Statement Related to Policies on Unannounced Quizzes and Class Attendance and Participation: Individual instructors have different policies concerning pop quizzes, homework grades, class attendance and participation, which are announced at the beginning of the semester.