Introduction to Partial Differential Equation

This self-contained textbook offers an elementary introduction to partial differential equations (PDEs), primarily focusing on linear equations, but also providing a perspective on nonlinear equations, through Hamilton–Jacobi equations, elliptic equations with measurable coefficients and DeGiorgi classes. The exposition is complemented by examples, problems, and solutions that enhance understanding and explore related directions.

This second edition of a highly successful graduate text presents a complete introduction to partial differential equations and numerical analysis.

The Introduction to Navier-Stokes Equation and Oceanography corresponds to a graduate course in mathematics, taught at Carnegie Mellon University in the spring of 1999. Comments were added to the lecture notes distributed to the students, as well as short biographical information for all scientists mentioned in the text, the purpose being to show that the creation of scientific knowledge is an international enterprise, and who contributed to it, from where, and when.