عنوان
پدید آورنده
موضوع
رده
QA377
QA377
کتابخانه
محل استقرار
3319124927
3319124935
9783319124926
9783319124933
9783319124926
b623864
Applied partial differential equations /
[Book]
J. David Logan.
Third edition.
1 online resource (x, 289 pages) :
illustrations
Undergraduate texts in mathematics
Includes bibliographical references and index.
Intro; Contents; Preface to the Third Edition; To Students; 1 The Physical Origins of Partial Differential Equations; 1.1 PDE Models; 1.2 Conservation Laws; 1.3 Diffusion; 1.4 Diffusion and Randomness; 1.5 Vibrations and Acoustics; 1.6 Quantum Mechanics*; 1.7 Heat Conduction in Higher Dimensions; 1.8 Laplace's Equation; 1.9 Classification of PDEs; 2 Partial Differential Equations on Unbounded Domains; 2.1 Cauchy Problem for the Heat Equation; 2.2 Cauchy Problem for the Wave Equation; 2.3 Well-Posed Problems; 2.4 Semi-Infinite Domains; 2.5 Sources and Duhamel's Principle
2.6 Laplace Transforms2.7 Fourier Transforms; 3 Orthogonal Expansions; 3.1 The Fourier Method; 3.2 Orthogonal Expansions; 3.3 Classical Fourier Series; 4 Partial Differential Equations on Bounded Domains; 4.1 Overview of Separation of Variables; 4.2 Sturm-Liouville Problems; 4.3 Generalization and Singular Problems; 4.4 Laplace's Equation; 4.5 Cooling of a Sphere; 4.6 Diffusion in a Disk; 4.7 Sources on Bounded Domains; 4.8 Poisson's Equation*; 5 Applications in the Life Sciences; 5.1 Age-Structured Models; 5.2 Traveling Waves Fronts; 5.3 Equilibria and Stability
6 Numerical Computation of Solutions6.1 Finite Difference Approximations; 6.2 Explicit Scheme for the Heat Equation; 6.3 Laplace's Equation; 6.4 Implicit Scheme for the Heat Equation; A Differential Equations; References; Index
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... Reading this book and solving the problems, the students will have a solid base for a course in partial differential equations ... ." -Tibor Krisztin, Acta Scientiarum Mathematicarum, Vol.
150 (4), 2007 "This is a unique book in the sense that it provides a coverage of the main topics of the subject in a concise style which is accessible to science and engineering students.
74, 2008.
A brief appendix reviews techniques from ordinary differential equations.
A student who reads this book and works many of the exercises will have a sound knowledge for a second course in partial differential equations or for courses in advanced engineering and science.
Emphasis is placed on motivation, concepts, methods, and interpretation, rather than on formal theory.
From the reviews of the second edition: "This second edition of the short undergraduate text provides a fist course in PDE aimed at students in mathematics, engineering and the sciences.
In this third edition, text remains intimately tied to applications in heat transfer, wave motion, biological systems, and a variety other topics in pure and applied science.
Many exercises and worked examples have been added to this edition.
Methods include eigenfunction expansions, integral transforms, and characteristics.
Prerequisites include calculus and ordinary differential equations.
Steinbauer, Monatshefte für Mathematik, Vol.
The concise treatment of the subject is maintained in this third edition covering all the major ideas: the wave equation, the diffusion equation, the Laplace equation, and the advection equation on bounded and unbounded domains.
The exposition is presented in a friendly, easy-to-read, style, with mathematical ideas motivated from physical problems.
The material is standard ... Strong emphasis is put on modeling and applications throughout; the main text is supplied with many examples and exercises." -R.
The text offers flexibility to instructors who, for example, may wish to insert topics from biology or numerical methods at any time in the course.
This text presents the standard material usually covered in a one-semester, undergraduate course on boundary value problems and PDEs.
Two additional chapters include short introductions to applications of PDEs in biology and a new chapter to the computation of solutions.
Differential equations, Partial.
Mathematics.
Differential equations, Partial.
515/
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353
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QA377
Logan, J. David, (John David)
20201221082949.0
pn
مطالعه متن کتاب [Book]
270410
Y
