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About this book :-
Introduction to Partial Differential Equations written by Peter J. Olver .
This textbook is designed for a one-year course covering the fundamentals of partial differential equations, geared towards advanced undergraduates and beginning graduate students in mathematics, science, and engineering. No previous experience with the subject is assumed, while the mathematical prerequisites for embarking on this course of study will be listed below. For many years, I have been teaching such a course to students from mathematics, physics, engineering, statistics, chemistry, and, more recently, biology, finance, economics, and elsewhere. Over time, I realized that there is a genuine need for a well-written, systematic, modern introduction to the basic theory, solution techniques, qualitative properties, and numerical approximation schemes for the principal varieties of partial differential equations that one encounters in both mathematics and applications. It is my hope that this book will fill this need, and thus help to educate and inspire the next generation of students, researchers, and practitioners.
While the classical topics of separation of variables, Fourier analysis, Green’s functions, and special functions continue to form the core of an introductory course, the inclusion of nonlinear equations, shock wave dynamics, dispersion, symmetry and similarity methods, the Maximum Principle, Huygens’ Principle, quantum mechanics and the Schr¨odinger equation, and mathematical finance makes this book more in tune with recent developments and trends. Numerical approximation schemes should also play an essential role in an introductory course, and this text covers the two most basic approaches: finite differences and finite elements.
(Peter J. Olver)
Book Detail :-
Title: Introduction to Partial Differential Equations
Author(s): Peter J. Olver
Publisher: Springer International Publishing
Series: Undergraduate Texts in Mathematics
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About Author :-
The author Peter J. Olver is an American mathematician whose primary research interests involve the applications of symmetry and Lie groups to differential equations. He has been a full professor at the University of Minnesota since 1985 and is currently head of their mathematics department. In 2003, Olver was one of the top 234 most cited mathematicians in the world.
In 2014, Olver became a fellow of the Society for Industrial and Applied Mathematics for "developing new geometric methods for differential equations leading to applications in fluid mechanics, elasticity, quantum mechanics, and image processing.". In addition, Olver is an elected fellow of the Institute of Physics and a fellow of the American Mathematical Society.
Olver is a prolific author, having written over 200 academic papers as of 2015. Of these, 137 have appeared or will appear in major refereed journals, 46 have appeared in conference proceedings and seven have appeared as appendices and chapters in books.
All Famous Books of this Author :-
Here is list all books, text books, editions, versions or solution manuals avaliable of this author, We recomended you to download all.
• Download PDF Applied Linear Algebra by Peter J. Olver, Chehrzad Shakiban
• Download PDF Applied Linear Algebra (Solution Manual) by Peter J. Olver, Chehrzad Shakiban
• Download PDF Applications of Lie Groups to Differential Equations by Peter J. Olver
• Download PDF Introduction to Partial Differential Equations by Peter J. Olver
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Book Contents :-
Introduction to Partial Differential Equations written by Peter J. Olver cover the following topics. '
1. What Are Partial Differential Equations?
2. Linear and Nonlinear Waves
3. Fourier Series
4. Separation of Variables
5. Finite Differences
6. Generalized Functions and Green’s Functions
7. Fourier Transforms
8. Linear and Nonlinear Evolution Equations
9. A General Framework for Linear Partial Differential Equations
10. Finite Elements and Weak Solutions
11. Dynamics of Planar Media
12. Partial Differential Equations in Space
Appendix Complex Numbers, Linear Algebra
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