Logan Applied Mathematics

4. Auflage 2013
ISBN: 978-1-118-50170-2
Verlag: John Wiley & Sons
Format: EPUB
Kopierschutz: Adobe DRM (»Systemvoraussetzungen)

E-Book, Englisch, 688 Seiten, E-Book

Praise for the Third Edition
"Future mathematicians, scientists, and engineers shouldfind the book to be an excellent introductory text for courseworkor self-study as well as worth its shelf space forreference."
--MAA Reviews
Applied Mathematics, Fourth Edition is a thoroughly updated andrevised edition on the applications of modeling and analyzingnatural, social, and technological processes. The book covers awide range of key topics in mathematical methods and modeling andhighlights the connections between mathematics and the applied andnatural sciences.
The Fourth Edition covers both standard and moderntopics, including scaling and dimensional analysis; regular andsingular perturbation; calculus of variations; Green'sfunctions and integral equations; nonlinear wave propagation; andstability and bifurcation. The book provides extended coverage ofmathematical biology, including biochemical kinetics, epidemiology,viral dynamics, and parasitic disease. In addition, the new editionfeatures:
* Expanded coverage on orthogonality, boundary value problems,and distributions, all of which are motivated by solvability andeigenvalue problems in elementary linear algebra
* Additional MATLAB® applications for computer algebrasystem calculations
* Over 300 exercises and 100 illustrations that demonstrateimportant concepts
* New examples of dimensional analysis and scaling along with newtables of dimensions and units for easy reference
* Review material, theory, and examples of ordinary differentialequations
* New material on applications to quantum mechanics, chemicalkinetics, and modeling diseases and viruses
Written at an accessible level for readers in a wide range ofscientific fields, Applied Mathematics, Fourth Edition is anideal text for introducing modern and advanced techniques ofapplied mathematics to upper-undergraduate and graduate-levelstudents in mathematics, science, and engineering. The book is alsoa valuable reference for engineers and scientists in government andindustry.

Autoren/Hrsg.

Logan, J. David

Inhaltsverzeichnis

Preface xiii
1. Dimensional Analysis and One-Dimensional Dynamics1
1.1 Dimensional Analysis 2
1.2 Scaling 30
1.3 Differential Equations 46
2. Two-Dimensional Dynamical Systems 77
2.1 Phase Plane Phenomena. 77
2.2 Linear Systems 87
2.3 Nonlinear Systems 94
2.4 Bifurcations 103
2.5 Reaction Kinetics112
2.6 Pathogens 126
3. Perturbation Methods and Asymptotic Expansions 149
3.1 Regular Perturbation 150
3.2 Singular Perturbation 170
3.3 Boundary Layer Analysis. 179
3.4 Initial Layers 191
3.5 The WKB Approximation202
3.6 Asymptotic Expansion of Integrals 210
4. Calculus of Variations221
4.1 Variational Problems221
4.2 Necessary Conditions for Extrema 227
4.3 The Simplest Problem 236
4.4 Generalizations 245
4.5 Hamilton's Principle253
4.6 Isoperimetric Problems 266
5. Eigenvalue Problems, Integral Equations, and Green'sFunctions 275
5.1 Boundary-Value Problems277
5.2 Sturm-Liouville Problems284
5.3 Classical Fourier Series 310
5.4 Integral Equations 317
5.5 Green's Functions 339
5.6 Distributions 352
6. Partial Differential Equations 365
6.1 Basic Concepts 365
6.2 Conservation Laws 375
6.3 Equilibrium Equations 397
6.4 Eigenfunction Expansions404
6.5 Integral Transforms 415
6.7 Distributions 443
7. Wave Phenomena 457
7.1 Waves 457
7.2 Nonlinear Waves470
7.3 Quasi-linear Equations 488
7.4 The Wave Equation497
8. Mathematical Models of Continua 523
8.1 Kinematics and Mass Conservation 524
8.2 Momentum and Energy 534
8.3 Gas Dynamics 551
8.4 Fluid Motions in R3 560
9. Discrete Models 587
9.1 One-Dimensional Models. 588
9.2 Systems of Difference Equations 601
9.3 Stochastic Models 621
9.4 Probability-Based Models 639
Index 655

Über Autor(innen)

J. DAVID LOGAN, PhD, is Willa Cather Professor of Mathematics at the University of Nebraska, Lincoln. He is also the author of An Introduction to Nonlinear Partial Differential Equations, Second Edition and Mathematical Methods in Biology, both published by Wiley. Dr. Logan has served on the faculties at the University of Arizona, Kansas State University, and Rensselaer Polytechnic Institute, and he has been affiliated with Los Alamos Scientific Laboratory, Lawrence Livermore National Laboratory, and the Aerospace Research Laboratory.