Partial Differential Equations (Miersemann)

These lecture notes are intented as a straightforward introduction to partial differential equations which can serve as a textbook for undergraduate and beginning graduate students.

For additional reading we recommend following books: W. I. Smirnov [21], I. G. Petrowski [17], P. R. Garabedian [8], W. A. Strauss [23], F. John [10], L. C. Evans [5] and R. Courant and D. Hilbert[4] and D. Gilbarg and N. S. Trudinger [9]. Some material of these lecture notes was taken from some of these books.

Introduction

Ordinary and partial differential equations occur in many applications. An ordinary differential equation is a special case of a partial differential equation but the behavior of solutions is quite different in general caused by the fact that the functions for which we are looking at are functions of more than one independent variable.

Introduction (Exercises)

These are homework exercises to accompany Miersemann’s “Partial Differential Equations” Textmap. This is a textbook targeted for a one semester first course on differential equations, aimed at engineering students. Partial differential equations are differential equations that contains unknown multivariable functions and their partial derivatives. Prerequisite for the course is the basic calculus sequence.

Equations of First Order

The main tool for studying related problems is the theory of ordinary differential equations, which is quite different for systems of partial differential of first order.

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Equations of First Order (Exercises)

These are homework exercises to accompany Miersemann’s “Partial Differential Equations” Textmap. This is a textbook targeted for a one semester first course on differential equations, aimed at engineering students. Partial differential equations are differential equations that contains unknown multivariable functions and their partial derivatives. Prerequisite for the course is the basic calculus sequence.

Classification (Exercises)

These are homework exercises to accompany Miersemann’s “Partial Differential Equations” Textmap. This is a textbook targeted for a one semester first course on differential equations, aimed at engineering students. Partial differential equations are differential equations that contains unknown multivariable functions and their partial derivatives. Prerequisite for the course is the basic calculus sequence.