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Combining both the classical theory and numerical techniques for
partial differential equations, this thoroughly modern approach
shows the significance of computations in PDEs and illustrates the
strong interaction between mathematical theory and the development
of numerical methods. Great care has been taken throughout the book
to seek a sound balance between these techniques. The authors
present the material at an easy pace and exercises ranging from the
straightforward to the challenging have been included. In addition
there are some "projects" suggested, either to refresh the students
memory of results needed in this course, or to extend the theories
developed in the text. Suitable for undergraduate and graduate
students in mathematics and engineering.
This book teaches basic methods of partial differential
equations and introduces related important ideas associated with
the analysis of numerical methods for those partial differential
equations. Coverage details such topics as separation of variables,
Fourier analysis, maximum principles, and energy estimates. The
book introduces numerical methods in parallel to the classical
theory and also includes many engaging exercises.
This book teaches basic methods of partial differential
equations and introduces related important ideas associated with
the analysis of numerical methods for those partial differential
equations. Coverage details such topics as separation of variables,
Fourier analysis, maximum principles, and energy estimates. The
book introduces numerical methods in parallel to the classical
theory and also includes many engaging exercises.
In diesem Buch werden die Grundlagen partieller
Differentialgleichungen sowie mit der Untersuchung numerischer
Methoden fur diese partiellen Differentialgleichungen in
Zusammenhang stehende wichtige Uberlegungen vorgestellt.
Standardthemen wie Trennung der Variablen, Fourier Analysis,
Maximumprinzipien und Energieabschatzungen werden behandelt.
Numerische Verfahren werden parallel zur klassischen Theorie
vorgestellt. Die Eigenschaften von Differentialgleichungen werden
anhand numerischer Experimente veranschaulicht, und die Theorie der
finiten Differentialapproximationen wird entwickelt. Numerische
Verfahren werden eingefuhrt, um die Bedeutung des Rechnens bei
partiellen Differentialgleichungen zu zeigen und die starke
Interaktion zwischen mathematischer Theorie und der Entwicklung
numerischer Verfahren zu illustrieren. Besonderer Wert wurde im
gesamten Buch auf eine moglichst gleichgewichtige Darstellung der
analytischen und der numerischen Verfahren gelegt."
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