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Published in:
2015 | OriginalPaper | Chapter
Introduction to Partial Differential Equations
Author : Ivan G. Avramidi
Published in: Heat Kernel Method and its Applications
Publisher: Springer International Publishing
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In this chapter we present an introduction to some methods for the solution of partial differential equations. After a short review of the first-order equations we discuss the classification of second-order equations and introduce the fundamental tools such as the resolvent and the heat kernel. We also show how to solve exactly partial differential equations in some simple cases, such as equations with constant coefficients and homogeneous equations.