Applied analysis : mathematical methods in natural science
著者
書誌事項
Applied analysis : mathematical methods in natural science
Imperial College Press, c2004
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注記
Includes bibliographical references (p. 363-367) and index
内容説明・目次
内容説明
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 uses fundamental ideas of applied mathematics to discuss recent developments in nonlinear science, such as mathematical modeling of reinforced random motion of particles, semiconductor device equation in applied physics, and chemotaxis in biology. Several tools in linear PDE theory, such as fundamental solutions, Perron's method, layer potentials, and iteration scheme, are described, as well as systematic descriptions on the recent study of the blowup of the solution.
目次
- Geometric Objects
- Calculus of Variation
- Infinite-Dimensional Analysis
- Random Motion of Particles
- Linear PDE Theory
- Nonlinear PDE Theory
- Systems of Chemotaxis
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