Riassunto:
Resoundingly popular in its first edition, Dean Duffy's Advanced Engineering Mathematics has been updated, expanded, and now more than ever provides the solid mathematics background required throughout the engineering disciplines. Melding the author's expertise as a practitioner and his years of teaching engineering mathematics, this text stands clearly apart from the many others available.
Relevant, insightful examples follow nearly every concept introduced and demonstrate its practical application. This edition includes two new chapters on differential equations, another on Hilbert transforms, and many new examples, problems, and projects that help build problem-solving skills. Most importantly, the book now incorporates the use of MATLAB throughout the presentation to reinforce the concepts presented. MATLAB code is included so readers can take an analytic result, fully explore it graphically, and gain valuable experience with this industry-standard software.
Contenuti:
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COMPLEX VARIABLES
Complex Numbers
Finding Roots
The Derivative in the Complex Plane: The Cauchy-Riemann Equations
Line Integrals
Cauchy-Goursat Theorem
Cauchy's Integral Formula
Taylor and Laurent Expansions and Singularities
Theory of Residues
Evaluation of Real Definite Integrals
Cauchy's Principal Value Integral
FIRST-ORDER ORDINARY DIFFERENTIAL EQUATIONS
Classification of Differential Equations
Separation of Variables
Homogeneous Equations
Exact Equations
Linear Equations
Graphical Solutions
Numerical Methods
HIGHER-ORDER ORDINARY DIFFERENTIAL EQUATIONS
Homogeneous Linear Equations with Constant Coefficients
Simple Harmonic Motion
Damped Harmonic Motion
Method of Undetermined Coefficients
Forced Harmonic Motion
Variation of Parameters
Euler-Cauchy Equation
Phase Diagrams
Numerical Methods
FOURIER SERIES
Fourier Series
Properties of Fourier Series
Half-Range Expansions
Fourier Series with Phase Angles
Complex Fourier Series
The Use of Fourier Series in the Solution of Ordinary Differential Equations
Finite Fourier Series
THE FOURIER TRANSFORM
Fourier Transforms
Fourier Transforms Containing the Delta Function
Properties of Fourier Transforms
Inversion of Fourier Transforms
Convolution
Solution of Ordinary Differential Equations by Fourier Transforms
THE LAPLACE TRANSFORM
Definition and Elementary Properties
The Heaviside Step and Dirac Delta Functions
Some Useful Theorems
The Laplace Transform of a Periodic Function
Inversion by Partial Fractions: Heaviside's Expansion Theorem
Convolution
Integral Equations
Solution of Linear Differential Equations with Constant Coefficients
Transfer Functions, Green's Function, and Indicial Admittance
Inversion by Contour Integration
THE Z-TRANSFORM
The Relationship of the Z-Transform to the Laplace Transform
Some Useful Properties
Inverse Z-Transforms
Solution of Difference Equations
Stability of Discrete-Time Systems
THE HILBERT TRANSFORM
Definition
Some Useful Properties
Analytic Signals
Causality: The Kramer-Kronig Relationship
THE STURM-LIOUVILLE PROBLEM
Eigenvalues and Eigenfunctions
Orthogonality of Eigenfunctions
Expansion in Series of Eigenfunctions
A Singular Sturm-Liouville Problem: Legendre's Equation
Another Singular Sturm-Liouville Problem: Bessel's Equation
THE WAVE EQUATION
The Vibrating String
Initial Conditions: Cauchy Problem
Separation of Variables
D'Alembert's Formula
The Laplace Transform Method
Numerical Solution of the Wave Equation
THE HEAT EQUATION
Derivation of the Heat Equation
Initial and Boundary Conditions
Separation of Variables
The Laplace Transform Method
The Fourier Transform Method
The Superposition Integral
Numerical Solution of the Heat Equation
LAPLACE'S EQUATION
Derivation of Laplace's Equation
Boundary Conditions
Separation of Variables
The Solution of Laplace's Equation on the Upper Half-Plane
Poisson's Equation on a Rectangle
The Laplace Transform Method
Numerical Solution of Laplace's Equation
VECTOR CALCULUS
Review
Divergence and Curl
Line Integrals
The Potential Function
Surface Integrals
Green's Lemma
Stokes' Theorem
Divergence Theorem
LINEAR ALGEBRA
Fundamentals of Linear Algebra
Determinants
Cramer's Rule
Row Echelon Form and Gaussian Elimination
Eigenvalues and Eigenvectors
Systems of Linear Differential Equations
ANSWERS TO THE ODD-NUMBERED PROBLEMS
INDEX
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