Applied Mathematics

J. David Logan 지음

Wiley 2013년 06월 18일 출간

작품소개

책소개

Praise for the Third Editionldquo;Future mathematicians, scientists, and engineers should find the book to be an excellent introductory text for coursework or self-study as well as worth its shelf space for reference.rdquo; m-MAA ReviewsApplied Mathematics, Fourth Edition is a thoroughly updated and revised edition on the applications of modeling and analyzing natural, social, and technological processes. The book covers a wide range of key topics in mathematical methods and modeling and highlights the connections between mathematics and the applied and natural sciences.The Fourth Edition covers both standard and modern topics, including scaling and dimensional analysis; regular and singular perturbation; calculus of variations; Green's functions and integral equations; nonlinear wave propagation; and stability and bifurcation. The book provides extended coverage of mathematical biology, including biochemical kinetics, epidemiology, viral dynamics, and parasitic disease. In addition, the new edition features:Expanded coverage on orthogonality, boundary value problems, and distributions, all of which are motivated by solvability and eigenvalue problems in elementary linear algebraAdditional MATLABreg; applications for computer algebra system calculationsOver 300 exercises and 100 illustrations that demonstrate important conceptsNew examples of dimensional analysis and scaling along with new tables of dimensions and units for easy referenceReview material, theory, and examples of ordinary differential equationsNew material on applications to quantum mechanics, chemical kinetics, and modeling diseases and virusesWritten at an accessible level for readers in a wide range of scientific fields,

Preface xiii1. Dimensional Analysis and One-Dimensional Dynamics 11.1 Dimensional Analysis 21.2 Scaling 301.3 Differential Equations 462. Two-Dimensional Dynamical Systems 772.1 Phase Plane Phenomena. 772.2 Linear Systems 872.3 Nonlinear Systems 942.4 Bifurcations 1032.5 Reaction Kinetics1122.6 Pathogens 1263. Perturbation Methods and Asymptotic Expansions 1493.1 Regular Perturbation 1503.2 Singular Perturbation 1703.3 Boundary Layer Analysis. 1793.4 Initial Layers 1913.5 The WKB Approximation2023.6 Asymptotic Expansion of Integrals 2104. Calculus of Variations2214.1 Variational Problems2214.2 Necessary Conditions for Extrema 2274.3 The Simplest Problem 2364.4 Generalizations 2454.5 Hamilton&'s Principle2534.6 Isoperimetric Problems 2665. Eigenvalue Problems, Integral Equations, and Green&'s Functions 275 5.1 Boundary-Value Problems2775.2 Sturm&n-Liouville Problems2845.3 Classical Fourier Series 3105.4 Integral Equations 3175.5 Green&'s Functions 3395.6 Distributions 3526. Partial Differential Equations 3656.1 Basic Concepts 3656.2 Conservation Laws 3756.3 Equilibrium Equations 3976.4 Eigenfunction Expansions4046.5 Integral Transforms 4156.7 Distributions 4437. Wave Phenomena 4577.1 Waves 4577.2 Nonlinear Waves4707.3 Quasi-linear Equations 4887.4 The Wave Equation4978. Mathematical Models of Continua 5238.1 Kinematics and Mass Conservation 5248.2 Momentum and Energy 5348.3 Gas Dynamics 5518.4 Fluid Motions in R3 5609. Discrete Models 5879.1 One-Dimensional Models. 5889.2 Systems of Difference Equations 6019.3 Stochasti

작가정보

저자(글) J. David Logan

저자 :

저자 :

저자 :

저자 :

저자 :
저자 :
저자 :
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.

이 상품의 총서

전체선택