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Advanced Engineering Mathematics

Dennis G. Zill, Michael R. Cullen

1038 pages, parution le 01/01/2000 (2^eme édition)

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Résumé

Advanced Engineering Mathematics is a compendium of many mathematical topics, all of which are loosely related by the expedient of either being needed or useful in courses and subsequent careers in science and engineering. Consequently, this book represents the most accurate list of what constitutes "engineering mathematics." For flexibility in topic selection, the text is divided into five major sections that illustrate the backbone of science/engineering related mathematics. The first eight chapters of this book constitute a complete short course in ordinary differential equations.

New to this Edition! The five major sections of the text open with an essay by an acknowledged expert in the field of engineering, this helps to provide students with real-life context to the course material.
Real-world applications, current examples, and a many illustrations help students visualize important concepts and apply the material to everyday life.
A complete Solutions Manual is available for the instructor, and a Student Solutions Manual that provides the answers to every third problem.
Text includes boxed definitions and boxed theorems for easy reference.
Zill devotes an entire section to Fast Fourier Transforms (FFT), and provides problems using the FFT. Mathematical Models for differential equations are also given special attention.
Zill has provided Remark sections throughout the text that alert students to certain discussions that require special attention.

Contents

Part I: Ordinary Differential Equations

Chapter 1. Introduction to Differential Equations

Definitions and Terminology
Initial-Value Problems
Differential Equations as Mathematical Models

Chapter 2. First-Order Differential Equations

Solution Curves Without the Solution
Separable Variables
Linear Equations
Exact Equations
Solutions by Substitutions
A Numerical Solutions
Linear Models
Nonlinear
Systems: Linear and Nonlinear Models

Chapter 3. Higher-Order Differential Equations

Preliminary Theory: Linear and Nonlinear Models
Reduction of Order
Homogenous Linear Equations with Constant Coefficients
Undetermined
Variations of Parameters
Cauchy-Euler Equation
Nonlinear Equations
Linear Models: Initial-Value Problems
Linear Models: Boundary-Value Problems
Nonlinear Models
Solving Systems of Linear Models

Chapter 4. The Laplace Transform

Definition of the Laplace Transform
The Inverse Transform and Transforms of Derivations
Translation Theorems
Additional Operational Properties
Dirac Delta Function
Solving Systems of Linear Equations

Chapter 5. Series Solutions of Linear Equations

Solutions about Ordinary Points
Solutions about Singular Points
Two Special Equations

Chapter 6. Numerical Solutions of Ordinary Differential Equations

Euler Methods and Error Analysis
Runge-Kutta Methods
Methods
Higher-Order Equations and Systems
Second-Order Boundary-Value Problems

Part II: Vectors, Matrices, and Vector Calculus

Chapter 7. Vectors

Vectors in 2-Space
Vectors in 3-Space
The Dot Product
The Cross Product
Lines and Planes in 3-Space
Vector Spaces

Chapter 8. Matrices

Matrix Algebra
Systems of Linear Algebraic Equations
Rank of a Matrix
Determinants
Properties of Determinants
Inverse of a Matrix
Cramer's Rule
The Eigenvalue Problem
Power of Matrices
Orthogonal Matrices
Approximation of Eigenvalues
Diagonalization
Cryptography
An Error-Correcting Code
Method of Least Squares
Discrete Compartmental Models

Chapter 9. Vector Calculus

Vector Functions
Motion on a Curve
Curvature and Components of Acceleration
Functions of Several Variables
The Directional Derivative
Planes and Normal Lines
Divergence and Curl
Line Integrals
Line Integrals Independent of the Path
Review of Double Integrals
Double Integrals in Polar Coordinates
Green's Theorem
Surface Integrals
Strokes' Theorem
Review of Triple Integrals
Divergence Theorem
Change of Variables in Multiple Integrals

Part III: Systems of Differential Equations

Chapter 10. System of Linear Differential Equations

Preliminary
Homogeneous Linear Systems
Solution by Diagonalization
Nonhomogenous Linear Systems
Matrix Exponential

Chapter 11. Systems of Nonlinear Differential Equations

Autonomous Systems, Critical Points, and Periodic Solutions
Stability of Linear Systems
Linearization and Local Stability
Modeling Using Autonomous Systems
Periodic Solutions, Limit Cycles, and Global Stability

Part IV: Fourier Series and Partial Differential Equations

Chapter 12. Orthogonal Functions and Fourier Series

Orthogonal Functions
Fourier Series
Fourier Cosine and Sine Series
Complex Fourier Series and Frequency Spectrum
Sturm-Liouville Problem
Bessel and Legendre Series

Chapter 13. Boundary-Value Problems in Rectangular Coordinates

Separable Partial Differential Equations
Classical Equations and Boundary-Value Problems
Heat Equation
Wave Equation
Laplace's Equation
Nonhomogeneous Equations and Boundary Conditions
Orthogonal Series Expansions
Fourier Series in Two Variable

Chapter 14. Boundary-Value Problems in Other Coordinate Systems

Problems Involving Laplace's Equation in Polar Coordinates
Problems in Polar and Cylindrical Coordinates: Bessel Functions
Problems in Spherical Coordinates: Legendre Polynomials

Chapter 15. Integral Transform Method

Error Function
Applications of the Laplace Transform
Fourier Integral
Fourier Transforms
Fast Fourier Transform

Chapter 16. Numerical Solutions to Partial Differential Equations

Elliptic Equations
Parabolic Equations
Hyperbolic Equations

Part V: Complex Analysis

Chapter 17. Functions of a Complex Variable

Complex Numbers
Form of Complex Numbers; Power and Roots
Sets of Points in the Complex Plane
Functions of a Complex Variable; Analyticity
Cauchy-Reimann Equations
Exponential and Logarithmic Functions
Trigonometric and Hyperbolic Functions
Inverse Trigonometric and Hyperbolic Functions

Chapter 18. Integration in the Complex Plane

Contour Integrals
Cauchy-Goursat Theorem
Independence of Path
Cauchy's Integral Formula

Chapter 19. Series and Residues

Sequences and Series
Taylor Series
Laurent Series
Zeros and Poles
Residues and Residue Theorem
Evaluation of Real Integrals

Chapter 20. Conformal Mappings and Applications

Complex Functions as Mappings
Conformal Mapping and the Dirichlet Problem
Linear Fractional Transformations
Schwarz-Christoffel Transformations
Poisson Integral Formulas
Applications

Appendix I Some Derivative and Integral Formulas
Appendix II Gamma Function; Exercises
Appendix III Table of Laplace Transforms
Appendix IV Conformal Mappings
Appendix V Some BASIC Programs for Numerical Methods
Selected Answers for Odd-Numbered Problems

L'auteur - Dennis G. Zill

Loyola Marymount University
Ph.D. in applied mathematics from Iowa State University. Currently professor of mathematics and former chair of the math dept at Loyola Marymount University in Los Angeles. Dennis Zill's research interests include Applied Mathematics, Special Functions, and Integral Transforms.

L'auteur - Michael R. Cullen

Michael R. Cullen, of Loyola Marymount University

Caractéristiques techniques

	PAPIER
Éditeur(s)	Jones and Bartlett Computer Science
Auteur(s)	Dennis G. Zill, Michael R. Cullen
Parution	01/01/2000
Édition	2^eme édition
Nb. de pages	1038
Format	20,5 x 25,4
Couverture	Broché
Poids	1842g
Intérieur	2 couleurs
EAN13	9780763713577