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APPLIED ANALYSIS
Mathematical Methods in Natural Science
by Takasi Senba (Miyazaki University, Japan) & Takashi Suzuki (Osaka University, Japan)
This book provides a general introduction to applied analysis; vector analysis with physical motivation, calculus of variation, Fourier analysis, eigenfunction expansion, distribution, and so forth, including a catalogue of mathematical theories, such as basic analysis, topological spaces, complex function theory, real analysis, and abstract analysis. This book also gives fundamental ideas of applied mathematics to discuss recent developments in nonlinear science, such as mathematical modeling of reinforced random motion of particles, semi-conductor device equation in applied physics, and chemotaxis in biology. Several tools in linear PDE theory, such as fundamental solutions, Perron's method, layer potentials, iteration scheme, are described, as well as systematic descriptions on the recent study of blowup of the solution.
Contents:
- Geometric Objects
- Calculus of Variation
- Infinite-Dimensional
Analysis
- Random Motion of Particles
- Linear PDE Theory
- Nonlinear PDE Theory
- System of Chemotaxis
Readership: Mathematics undergraduates.
“One good feature of the book is the rather large bibliography of mostly research papers that pertain to the applications mentioned in the textual material. This feature should be a huge help in understanding the ideas and concepts presented and soften some of the abstractions ... most topics are covered in an introductory way and serve to tie together this body of mathematical methods that can serve the natural sciences.”
| 392pp |
Pub. date: Apr 2004 |
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