Numerical and Analytical Methods for Scientists and Engineers Using Mathematica

Name: Numerical and Analytical Methods for Scientists and Engineers Using Mathematica
Price: 112.75 USD
Availability: InStock
ISBN: 9780471266105

ISBN-10: 0471266108

ISBN-13: 9780471266105

Edition: 2003

Authors: Daniel Dubin

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Description:

This work is written from the perspective of a physicist, not a mathematician, emphasising modern practical applications in the physical and engineering sciences. The book itself is essentially software, written in the language of Mathematica, which is widely used in engineering and physics.

Book details

List price: $244.95
Copyright year: 2003
Publisher: John Wiley & Sons, Incorporated
Publication date: 5/5/2003
Binding: Hardcover
Pages: 656
Size: 7.20" wide x 10.30" long x 1.50" tall
Weight: 2.992
Language: English



Preface



Ordinary Differential Equations in the Physical Sciences



Introduction



Definitions


Exercises for Sec. 1.1



Graphical Solution of Initial-Value Problems



Direction Fields; Existence and Uniqueness of Solutions



Direction Fields for Second-Order ODEs: Phase-Space Portraits


Exercises for Sec. 1.2



Analytic Solution of Initial-Value Problems via DSolve



DSolve


Exercises for Sec. 1.3



Numerical Solution of Initial-Value Problems



NDSolve



Error in Chaotic Systems



Euler's Method



The Predictor-Corrector Method of Order 2



Euler's Method for Systems of ODEs



The Numerical N-Body Problem: An Introduction to Molecular Dynamics


Exercises for Sec. 1.4



Boundary-Value Problems



Introduction



Numerical Solution of Boundary-Value Problems: The Shooting Method


Exercises for Sec. 1.5



Linear ODEs



The Principle of Superposition



The General Solution to the Homogeneous Equation



Linear Differential Operators and Linear Algebra



Inhomogeneous Linear ODEs


Exercises for Sec. 1.6


References



Fourier Series and Transforms



Fourier Representation of Periodic Functions



Introduction



Fourier Coefficients and Orthogonality Relations



Triangle Wave



Square Wave



Uniform and Nonuniform Convergence



Gibbs Phenomenon for the Square Wave



Exponential Notation for Fourier Series



Response of a Damped Oscillator to Periodic Forcing



Fourier Analysis, Sound, and Hearing


Exercises for Sec. 2.1



Fourier Representation of Functions Defined on a Finite Interval



Periodic Extension of a Function



Even Periodic Extension



Odd Periodic Extension



Solution of Boundary-Value Problems Using Fourier Series


Exercises for Sec. 2.2



Fourier Transforms



Fourier Representation of Functions on the Real Line



Fourier sine and cosine Transforms



Some Properties of Fourier Transforms



The Dirac [delta]-Function



Fast Fourier Transforms



Response of a Damped Oscillator to General Forcing. Green's Function for the Oscillator


Exercises for Sec. 2.3



Green's Functions



Introduction



Constructing the Green's Function from Homogeneous Solutions



Discretized Green's Function I: Initial-Value Problems by Matrix Inversion



Green's Function for Boundary-Value Problems



Discretized Green's Functions II: Boundary-Value Problems by Matrix Inversion


Exercises for Sec. 2.4


References



Introduction to Linear Partial Differential Equations



Separation of Variables and Fourier Series Methods in Solutions of the Wave and Heat Equations



Derivation of the Wave Equation



Solution of the Wave Equation Using Separation of Variables



Derivation of the Heat Equation



Solution of the Heat Equation Using Separation of Variables


Exercises for Sec. 3.1



Laplace's Equation in Some Separable Geometries



Existence and Uniqueness of the Solution



Rectangular Geometry



2D Cylindrical Geometry



Spherical Geometry



3D Cylindrical Geometry


Exercises for Sec. 3.2


References



Eigenmode Analysis



Generalized Fourier Series



Inner Products and Orthogonal Functions



Series of Orthogonal Functions



Eigenmodes of Hermitian Operators



Eigenmodes of Non-Hermitian Operators


Exercises for Sec. 4.1



Beyond Separation of Variables: The General Solution of the 1D Wave and Heat Equations



Standard Form for the PDE



Generalized Fourier Series Expansion for the Solution


Exercises for Sec. 4.2



Poisson's Equation in Two and Three Dimensions



Introduction. Uniqueness and Standard Form



Green's Function



Expansion of g and 0 in Eigenmodes of the Laplacian Operator



Eigenmodes of [down triangle, open superscript 2] in Separable Geometries


Exercises for Sec. 4.3



The Wave and Heat Equations in Two and Three Dimensions



Oscillations of a Circular Drumhead



Large-Scale Ocean Modes



The Rate of Cooling of the Earth


Exercises for Sec. 4.4


References



Partial Differential Equations in Infinite Domains



Fourier Transform Methods



The Wave Equation in One Dimension



Dispersion; Phase and Group Velocities



Waves in Two and Three Dimensions


Exercises for Sec. 5.1



The WKB Method



WKB Analysis without Dispersion



WKB with Dispersion: Geometrical Optics


Exercises for Sec. 5.2



Wave Action (Electronic Version Only)



The Eikonal Equation



Conservation of Wave Action


Exercises for Sec. 5.3


References



Numerical Solution of Linear Partial Differential Equations



The Galerkin Method



Introduction



Boundary-Value Problems



Time-Dependent Problems


Exercises for Sec. 6.1



Grid Methods



Time-Dependent Problems



Boundary-Value Problems


Exercises for Sec. 6.2



Numerical Eigenmode Methods (Electronic Version Only)



Introduction



Grid-Method Eigenmodes



Galerkin-Method Eigenmodes



WKB Eigenmodes


Exercises for Sec. 6.3


References



Nonlinear Partial Differential Equations



The Method of Characteristics for First-Order PDEs



Characteristics



Linear Cases



Nonlinear Waves


Exercises for Sec. 7.1



The KdV Equation



Shallow-Water Waves with Dispersion



Steady Solutions: Cnoidal Waves and Solitons



Time-Dependent Solutions: The Galerkin Method



Shock Waves: Burgers' Equation


Exercises for Sec. 7.2



The Particle-in-Cell Method (Electronic Version Only)



Galactic Dynamics



Strategy of the PIC Method



Leapfrog Method



Force



Examples


Exercises for Sec. 7.3


References



Introduction to Random Processes



Random Walks



Introduction



The Statistics of Random Walks


Exercises for Sec. 8.1



Thermal Equilibrium



Random Walks with Arbitrary Steps



Simulations



Thermal Equilibrium


Exercises for Sec. 8.2



The Rosenbluth-Teller-Metropolis Monte Carlo Method (Electronic Version Only)



Theory



Simulations


Exercises for Sec. 8.3


References



An Introduction to Mathematica (Electronic Version Only)



Starting Mathematica



Mathematica Calculations



Arithmetic



Exact vs. Approximate Results



Some Intrinsic Functions



Special Numbers



Complex Arithmetic



The Function N and Arbitrary-Precision Numbers


Exercises for Sec. 9.2



The Mathematica Front End and Kernel



Using Previous Results



The % Symbol



Variables



Pallets and Keyboard Equivalents



Lists, Vectors, and Matrices



Defining Lists, Vectors, and Matrices



Vectors and Matrix Operations



Creating Lists, Vectors, and Matrices with the Table Command



Operations on Lists


Exercises for Sec. 9.5



Plotting Results



The Plot Command



The Show Command



Plotting Several Curves on the Same Graph



The ListPlot Function



Parametric Plots



3D Plots



Animations



Add-On Packages


Exercises for Sec. 9.6



Help for Mathematica Users



Computer Algebra



Manipulating Expressions



Replacement



Defining Functions



Applying Functions



Delayed Evaluation of Functions



Putting Conditions on Function Definitions


Exercises for Sec. 9.8



Calculus



Derivatives



Power Series



Integration


Exercises for Sec. 9.9



Analytic Solution of Algebraic Equations



Solve and NSolve


Exercises for Sec. 9.10



Numerical Analysis



Numerical Solution of Algebraic Equations



Numerical Integration



Interpolation



Fitting


Exercises for Sec. 9.11



Summary of Basic Mathematica Commands



Elementary Functions



Using Previous Results; Substitution and Defining Variables



Lists, Tables, Vectors and Matrices



Graphics



Symbolic Mathematics


References



Finite-Differenced Derivatives


Index