Advanced Engineering Mathematics

ISBN-10: 076374591X

ISBN-13: 9780763745912

Edition: 3rd 2006 (Revised)

Authors: Dennis G. Zill, Michael R. Cullen

List price: $303.95
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Thoroughly updated, Zill's Advanced Engineering Mathematics, Third Edition is a compendium of many mathematical topics for students planning a career in engineering or the sciences. A key strength of this text is Zill's emphasis on differential equations as mathematical models, discussing the constructs and pitfalls of each. The Third Edition is comprehensive, yet flexible, to meet the unique needs of various course offerings ranging from ordinary differential equations to vector calculus. Numerous new projects contributed by esteemed mathematicians have been added.
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Book details

List price: $303.95
Edition: 3rd
Copyright year: 2006
Publisher: Jones & Bartlett Learning, LLC
Publication date: 2/17/2006
Binding: Hardcover
Pages: 1020
Size: 8.75" wide x 11.00" long x 1.75" tall
Weight: 5.236
Language: English

About the Cover
Project for Section 3.7 Road Mirages
Project for Section 3.10 The Ballistic Pendulum
Project for Section 8.1 Two-Ports in Electrical Circuits
Project for Section 8.2 Traffic Flow
Project for Section 8.15 Temperature Dependence of Resistivity
Project for Section 9.16 Minimal Surfaces
Project for Section 14.3 The Hydrogen Atom
Project for Section 15.4 The Uncertainty Inequality in Signal Processing
Project for Section 15.4 Fraunhofer Diffraction by a Circular Aperture
Project for Section 16.2 Instabilities of Numerical Methods
Ordinary Differential Equations
Introduction to Differential Equations
Definitions and Terminology
Initial-Value Problems
Differential Equations as Mathematical Models
Review Exercises
First-Order Differential Equations
Solution Curves Without a Solution
Direction Fields
Autonomous First-Order DEs
Separable Variables
Linear Equations
Exact Equations
Solutions by Substitutions
A Numerical Method
Linear Models
Nonlinear Models
Modeling with Systems of First-Order DEs
Review Exercises
Higher-Order Differential Equations
Preliminary Theory: Linear Equations
Initial-Value and Boundary-Value Problems
Homogeneous Equations
Nonhomogeneous Equations
Reduction of Order
Homogeneous Linear Equations with Constant Coefficients
Undetermined Coefficients
Variation of Parameters
Cauchy-Euler Equation
Nonlinear Equations
Linear Models: Initial-Value Problems
Spring/Mass Systems: Free Undamped Motion
Spring/Mass Systems: Free Damped Motion
Spring/Mass Systems: Driven Motion
Series Circuit Analogue
Linear Models: Boundary-Value Problems
Nonlinear Models
Solving Systems of Linear Equations
Review Exercises
The Laplace Transform
Definition of the Laplace Transform
The Inverse Transform and Transforms of Derivatives
Inverse Transforms
Transforms of Derivatives
Translation Theorems
Translation on the s-axis
Translation on the t-axis
Additional Operational Properties
Derivatives of Transforms
Transforms of Integrals
Transform of a Periodic Function
The Dirac Delta Function
Systems of Linear Differential Equations
Review Exercises
Series Solutions of Linear Differential Equations
Solutions about Ordinary Points
Review of Power Series
Power Series Solutions
Solutions about Singular Points
Special Functions
Bessel Functions
Legendre Functions
Review Exercises
Numerical Solutions of Ordinary Differential Equations
Euler Methods and Error Analysis
Runge-Kutta Methods
Multistep Methods
Higher-Order Equations and Systems
Second-Order Boundary-Value Problems
Review Exercises
Vectors, Matrices, and Vector Calculus
Vectors in 2-Space
Vectors in 3-Space
Dot Product
Cross Product
Lines and Planes in 3-Space
Vector Spaces
Gram-Schmidt Orthogonalization Process
Review Exercises
Matrix Algebra
Systems of Linear Algebraic Equations
Rank of a Matrix
Properties of Determinants
Inverse of a Matrix
Finding the Inverse
Using the Inverse to Solve Systems
Cramer's Rule
The Eigenvalue Problem
Powers of Matrices
Orthogonal Matrices
Approximation of Eigenvalues
An Error-Correcting Code
Method of Least Squares
Discrete Compartmental Models
Review Exercises
Vector Calculus
Vector Functions
Motion on a Curve
Curvature and Components of Acceleration
Partial Derivatives
Directional Derivatives
Tangent Planes and Normal Lines
Divergence and Curl
Line Integrals
Independence of Path
Double Integrals
Double Integrals in Polar Coordinates
Green's Theorem
Surface Integrals
Stokes' Theorem
Triple Integrals
Divergence Theorem
Change of Variables in Multiple Integrals
Review Exercises
Systems of Differential Equations
Systems of Linear Differential Equations
Preliminary Theory
Homogeneous Linear Systems
Distinct Real Eigenvalues
Repeated Eigenvalues
Complex Eigenvalues
Solution by Diagonalization
Nonhomogeneous Linear Systems
Undetermined Coefficients
Variation of Parameters
Matrix Exponential
Review Exercises
Systems of Nonlinear Differential Equations
Autonomous Systems
Stability of Linear Systems
Linearization and Local Stability
Autonomous Systems as Mathematical Models
Periodic Solutions, Limit Cycles, and Global Stability
Review Exercises
Fourier Series and Partial Differential Equations
Orthogonal Functions and Fourier Series
Orthogonal Functions
Fourier Series
Fourier Cosine and Sine Series
Complex Fourier Series
Sturm-Liouville Problem
Bessel and Legendre Series
Fourier-Bessel Series
Fourier-Legendre Series
Review Exercises
Boundary-Value Problems in Rectangular Coordinates
Separable Partial Differential Equations
Classical Equations and Boundary-Value Problems
Heat Equation
Wave Equation
Laplace's Equation
Nonhomogeneous BVPs
Orthogonal Series Expansions
Fourier Series in Two Variables
Review Exercises
Boundary-Value Problems in Other Coordinate Systems
Problems in Polar Coordinates
Problems in Cylindrical Coordinates
Problems in Spherical Coordinates
Review Exercises
Integral Transform Method
Error Function
Applications of the Laplace Transform
Fourier Integral
Fourier Transforms
Fast Fourier Transform
Review Exercises
Numerical Solutions of Partial Differential Equations
Laplace's Equation
The Heat Equation
The Wave Equation
Review Exercises
Complex Analysis
Functions of a Complex Variable
Complex Numbers
Powers and Roots
Sets in the Complex Plane
Functions of a Complex Variable
Cauchy-Riemann Equations
Exponential and Logarithmic Functions
Trigonometric and Hyperbolic Functions
Inverse Trigonometric and Hyperbolic Functions
Review Exercises
Integration in the Complex Plane
Contour Integrals
Cauchy-Goursat Theorem
Independence of Path
Cauchy's Integral Formulas
Review Exercises
Series and Residues
Sequences and Series
Taylor Series
Laurent Series
Zeros and Poles
Residues and Residue Theorem
Evaluation of Real Integrals
Review Exercises
Conformal Mappings
Complex Functions as Mappings
Conformal Mappings
Linear Fractional Transformations
Schwarz-Christoffel Transformations
Poisson Integral Formulas
Review Exercises
Some Derivative and Integral Formulas
Gamma Function
Table of Laplace Transforms
Conformal Mappings
Answers for Selected Odd-Numbered Problems
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