Differential Equations
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Marian Mureşan
About this book
The book concerns with solving about 650 ordinary and partial differential equations. Each equation has at least one solution and each solution has at least one coloured graph. The coloured graphs reveal different features of the solutions. Some graphs are dynamical as for Clairaut differential equations. Thus, one can study the general and the singular solutions. All the equations are solved by Mathematica. The first chapter contains mathematical notions and results that are used later through the book. Thus, the book is self-contained that is an advantage for the reader. The ordinary differential equations are treated in Chapters 2 to 4, while the partial differential equations are discussed in Chapters 5 to 10. The book is useful for undergraduate and graduate students, for researchers in engineering, physics, chemistry, and others. Chapter 9 treats parabolic partial differential equations while Chapter 10 treats third and higher order nonlinear partial differential equations, both with modern methods. Chapter 10 discusses the Korteweg-de Vries, Dodd-Bullough-Mikhailov, Tzitzeica-Dodd-Bullough, Benjamin, Kadomtsev-Petviashvili, Sawada-Kotera, and Kaup-Kupershmidt equations.
- All the equations are completely solved by Mathematica (analytically, numerically, and/or graphically)
- All solutions are accompanied by full codes
- The equations are gradually introduced according to the degree of difficulty
Author / Editor information
Marian Mureşan, G. DIMA street, 15, ap. 25, Cluj-Napoca, 400335, ROMANIA
E-mail: mmarianus24@yahoo.com, marian.muresan@ubbcluj.ro
Work address:
Faculty of Mathematics and Computer Science, Babeş-Bolyai University
M. Kogălniceanu st. 1, 400084 Cluj-Napoca, ROMANIA
Phone:(+40-)264-405300 ext. 5244, Mobil:(+40-)743-130380
Marian Muresan, Babes-Bolyai University, Cluj-Napoca, Romania.
Topics
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Frontmatter
I -
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Foreword
VII -
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Preface
IX -
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Contents
XIII - Part I: Mathematica and ordinary differential equations
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1 Certain theoretical results
1 -
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2 Elementary ordinary differential equations
39 -
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3 First-order ordinary differential equations
66 -
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4 Higher order and systems of ordinary differential equations
104 - Part II: Mathematica and partial differential equations
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Introduction
169 -
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5 First-order partial differential equations
171 -
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6 Linear hyperbolic partial differential equations
202 -
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7 Nonlinear and higher-order hyperbolic equations
260 -
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8 Elliptic partial differential equations
285 -
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9 Parabolic partial differential equations
323 -
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10 Third- and higher-order nonlinear partial differential equations
393 -
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Bibliography
459 -
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Index
463
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Walter de Gruyter GmbH
Genthiner Straße 13
10785 Berlin
productsafety@degruyterbrill.com
