Applied Mathematics

ISBN-10: 0471746622

ISBN-13: 9780471746621

Edition: 3rd 2006 (Revised)

Authors: J. David Logan

List price: $159.00
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This updated edition of its popular predecessor strikes a balance between the mathematical aspects of the subject and its origin in empirics. Applied Mathematics offers, at an elementary level, some of the current topics in applied mathematics such as singular perturbation, nonlinear waves, bifurcation, and the numerical solution of partial differential equations. New material includes a discussion on discrete models, more references to mathematical biology in the text and exercises, and a new chapter on stochastic models including sections on probability, stochastic processes, and stochastic differential equations and difference equations.
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Book details

List price: $159.00
Edition: 3rd
Copyright year: 2006
Publisher: John Wiley & Sons, Incorporated
Publication date: 4/14/2006
Binding: Hardcover
Pages: 552
Size: 6.25" wide x 9.25" long x 1.00" tall
Weight: 1.892
Language: English

Dimensional Analysis, Scaling, and Differential Equations
Dimensional Analysis
The Program of Applied Mathematics
Dimensional Methods
The Pi Theorem
Proof of the Pi Theorem
Characteristic Scales
A Chemical Reactor Problem
The Projectile Problem
Differential Equations
Review of Elementary Methods
Stability and Bifurcation
Two-Dimensional Problems
Phase Plane Phenomena
Linear Systems
Nonlinear Systems
Perturbation Methods
Regular Perturbation
Motion in a Resistive Medium
Nonlinear Oscillations
The Poincare-Lindstedt Method
Asymptotic Analysis
Singular Perturbation
Algebraic Equations
Differential Equations
Boundary Layers
Boundary Layer Analysis
Inner and Outer Approximations
Uniform Approximations
General Procedures
Initial Layers
Damped Spring-Mass System
Chemical Reaction Kinetics
The WKB Approximation
The Non-oscillatory Case
The Oscillatory Case
Asymptotic Expansion of Integrals
Laplace Integrals
Integration by Parts
Other Integrals
Calculus of Variations
Variational Problems
Necessary Conditions for Extrema
Normed Linear Spaces
Derivatives of Functionals
Necessary Conditions
The Simplest Problem
The Euler Equation
Solved Examples
First Integrals
Higher Derivatives
Several Functions
Natural Boundary Conditions
The Canonical Formalism
Hamilton's Principle
Hamilton's Equations
The Inverse Problem
Isoperimetric Problems
Eigenvalue Problems, Integral Equations, and Green's Functions
Orthogonal Expansions
Classical Fourier Series
Sturm-Liouville Problems
Integral Equations
Volterra Equations
Fredholm Equations with Degenerate Kernels
Symmetric Kernels
Green's Functions
Inverses of Differential Operators
Physical Interpretation
Green's Function via Eigenfunctions
Test Functions
Distribution Solutions to Differential Equations
Discrete Models
One-Dimensional Models
Linear and Nonlinear Models
Equilibria, Stability, and Chaos
Systems of Difference Equations
Linear Models
Nonlinear Interactions
Stochastic Models
Elementary Probability
Stochastic Processes
Environmental and Demographic Models
Probability-Based Models
Markov Processes
Random Walks
The Poisson Process
Partial Differential Equations
Basic Concepts
Linearity and Superposition
Conservation Laws
One Dimension
Several Dimensions
Constitutive Relations
Probability and Diffusion
Boundary Conditions
Equilibrium Equations
Laplace's Equation
Basic Properties
Eigenfunction Expansions
Spectrum of the Laplacian
Evolution Problems
Integral Transforms
Laplace Transforms
Fourier Transforms
Stability of Solutions
Reaction-Diffusion Equations
Pattern Formation
Elliptic Problems
Tempered Distributions
Diffusion Problems
Wave Phenomena
Wave Propagation
The Advection Equation
Nonlinear Waves
Nonlinear Advection
Traveling Wave Solutions
Conservation Laws
Quasi-linear Equations
Age-Structured Populations
The Wave Equation
The Acoustic Approximation
Solutions to the Wave Equation
Scattering and Inverse Problems
Mathematical Models of Continua
Mass Conservation
Momentum Conservation
Thermodynamics and Energy Conservation
Stress Waves in Solids
Gas Dynamics
Riemann's Method
The Rankine-Hugoniot Conditions
Fluid Motions in R[superscript 3]
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