Analytical techniques for solving nonlinear partial differential equations /
By: Arrigo, Daniel J. (Daniel Joseph) [author.].
Material type:
BookSeries: Synthesis digital library of engineering and computer science: ; Synthesis lectures on mathematics and statistics: #25.Publisher: [San Rafael, California] : Morgan & Claypool, 2019.Description: 1 PDF (xiii, 151 pages) : color illustrations.Content type: text Media type: electronic Carrier type: online resourceISBN: 9781681735344.Subject(s): Differential equations, Partial | Differential equations, Nonlinear | nonlinear partial differential equations | compatibility | differential substitutions | point and contact transformations | first integrals | functional separabilityDDC classification: 515/.353 Online resources: Abstract with links to resource | Abstract with links to full text Also available in print.| Item type | Current location | Call number | Status | Date due | Barcode | Item holds |
|---|---|---|---|---|---|---|
E books
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PK Kelkar Library, IIT Kanpur | Available | EBKE919 |
Mode of access: World Wide Web.
System requirements: Adobe Acrobat Reader.
Part of: Synthesis digital library of engineering and computer science.
Includes bibliographical references.
1. Nonlinear PDEs are everywhere -- 1.1. Exercises -- 1.2. References
2. Compatibility -- 2.1. Charpit's method -- 2.2. Second-order PDEs -- 2.3. Compatibility in (2 + 1) dimensions -- 2.4. Compatibility for systems of PDEs -- 2.5. Exercises -- 2.6. References
3. Differential substitutions -- 3.1. Generalized burgers' equation -- 3.2. KdV-MKdv connection -- 3.3. Generalized Kdv equation -- 3.4. Matrix Hopf-Cole transformation -- 3.5. Darboux transformations -- 3.6. Exercises -- 3.7. References
4. Point and contact transformations -- 4.1. Contact transformations -- 4.2. Contact condition -- 4.3. Plateau problem -- 4.4. Exercises -- 4.5. References
5. First integrals -- 5.1. Quasilinear second-order equations -- 5.2. Monge-Ampere equation -- 5.3. The Martin equation -- 5.4. First integrals and linearization -- 5.5. Exercises -- 5.6. References
6. Functional separability -- 6.1. Exercises -- 6.2. References -- 7. Solutions.
Abstract freely available; full-text restricted to subscribers or individual document purchasers.
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This is an introduction to methods for solving nonlinear partial differential equations (NLPDEs). After the introduction of several PDEs drawn from science and engineering, the reader is introduced to techniques used to obtain exact solutions of NPDEs. The chapters include the following topics: Compatibility, Differential Substitutions, Point and Contact Transformations, First Integrals, and Functional Separability. The reader is guided through these chapters and is provided with several detailed examples. Each chapter ends with a series of exercises illustrating the material presented in each chapter. The book can be used as a textbook for a second course in PDEs (typically found in both science and engineering programs) and has been used at the University of Central Arkansas for more than ten years.
Also available in print.
Title from PDF title page (viewed on June 26, 2019).
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