Math 8141 (old 561), Fall 2009

MATH 8141 (old 561)
Fall 2009 Partial Differential Equations
Course Information

Instructor Cristian E. Gutiérrez
Wachman Hall 432
Phone: 1-7284
email: gutierre@temple.edu

Lectures Tuesdays and Thursdays 9:30 - 10:50 AM, Wachman Hall 617.

Texts Partial Differential Equations, by L. C. Evans, Graduate Texts in Mathematics vol. 19, American Mathematical Society, 1998, ISBN: 0-8218-0772-2.
Elliptic Partial Differential Equations of Second Order, by D. Gilbarg and N. S. Trudinger, Springer, ISBN: 9783540411604.

Syllabus A partial differential equation (PDE) is an equation involving functions and their partial derivatives, and since many natural laws can be expressed in terms of rates of changes,PDEs appear and have applications in an enormous number of questions. For example,PDEs describe the propagation of sound or heat, the motion of fluids, the description of electric and magnetic fields, and the behavior of financial markets. In the first semester the course will focus in the study of the three basic equations that contain the ideas and the germ of generality to study more general PDEs: the Laplace equation, the heat equation,and the wave equation. The solutions of these equations have different qualitative and quantitative properties and their study is essential to understand elliptic, parabolic and hyperbolic equations. The emphasis will be on ideas and techniques presented in a modern way and that can be use later to deal with more difficult situations such us nonlinear equations. These extensions will be the subject of the second semester.The course will be useful for students in analysis and applied mathematics.

Homework
Preliminaries.
First order pdes (due 9/22/09).
Newton's and Coulomb's laws (due 10/8/09).
Divergence (due 10/22/09).
Differentiability of the Newtonian potential (due 11/5/09).

Notes
Systems of odes and first order pdes.
Second derivatives of the Newtonian potential.

Solutions to Exams

Evaluation The grading will be based on regular homework and take home exams.

MATH 8141 (old 561) Fall 2009	Partial Differential Equations Course Information

Instructor	Cristian E. Gutiérrez Wachman Hall 432 Phone: 1-7284 email: gutierre@temple.edu

Lectures	Tuesdays and Thursdays 9:30 - 10:50 AM, Wachman Hall 617.

Texts	Partial Differential Equations, by L. C. Evans, Graduate Texts in Mathematics vol. 19, American Mathematical Society, 1998, ISBN: 0-8218-0772-2. Elliptic Partial Differential Equations of Second Order, by D. Gilbarg and N. S. Trudinger, Springer, ISBN: 9783540411604.

Syllabus	A partial differential equation (PDE) is an equation involving functions and their partial derivatives, and since many natural laws can be expressed in terms of rates of changes,PDEs appear and have applications in an enormous number of questions. For example,PDEs describe the propagation of sound or heat, the motion of fluids, the description of electric and magnetic fields, and the behavior of financial markets. In the first semester the course will focus in the study of the three basic equations that contain the ideas and the germ of generality to study more general PDEs: the Laplace equation, the heat equation,and the wave equation. The solutions of these equations have different qualitative and quantitative properties and their study is essential to understand elliptic, parabolic and hyperbolic equations. The emphasis will be on ideas and techniques presented in a modern way and that can be use later to deal with more difficult situations such us nonlinear equations. These extensions will be the subject of the second semester.The course will be useful for students in analysis and applied mathematics.

Homework	Preliminaries. First order pdes (due 9/22/09). Newton's and Coulomb's laws (due 10/8/09). Divergence (due 10/22/09). Differentiability of the Newtonian potential (due 11/5/09).

Notes	Systems of odes and first order pdes. Second derivatives of the Newtonian potential.

Solutions to Exams

Evaluation	The grading will be based on regular homework and take home exams.