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Advanced Engineering Mathematics

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ISBN-10: 0534400779

ISBN-13: 9780534400774

Edition: 5th 2003

Authors: Peter V. O'Neil

List price: $245.95
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Through four editions, Peter O'Neil has made rigorous engineering mathematics topics accessible to thousands of students by emphasizing visuals, numerous examples, and interesting mathematical models. ADVANCED ENGINEERING MATHEMATICS featuries a greater number of examples and problems and is fine-tuned throughout to improve the clear flow of ideas. The computer plays a more prominent role than ever in generating computer graphics used to display concepts. And problem sets incorporate the use of such leading software packages as MAPLE. Computational assistance, exercises and projects have been included to encourage students to make use of these computational tools. The content is organized…    
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Book details

List price: $245.95
Edition: 5th
Copyright year: 2003
Publisher: Course Technology
Publication date: 7/9/2002
Binding: Hardcover
Pages: 1194
Size: 8.25" wide x 10.00" long x 1.75" tall
Weight: 5.148
Language: English

Ordinary Differential Equations
First-Order Differential Equations
Preliminary Concepts
Separable Equations
Linear Differential Equations
Exact Differential Equations
Integrating Factors
Homogeneous, Bernoulli, and Riccati Equations
Applications to Mechanics, Electrical Circuits, and Orthogonal Trajectories
Existence and Uniqueness for Solutions of Initial Value Problems
Second-Order Differential Equations
Preliminary Concepts
Theory of Solutions y" + p(x)y' + q(x)y = f(x)
Reduction of Order
The Constant Coefficient Homogeneous Linear Equation
Euler's Equation
The Nonhomogeneous Equation y" + p(x)y' + q(x)y = f(x)
Application of Second-Order Differential Equations to a Mechanical System
The Laplace Transform
Definition and Basic Properties
Solution of Initial Value Problems Using the Laplace Transform
Shifting Theorems and the Heaviside Function
Convolution
Unit Impulses and the Dirac Delta Function
Laplace Transform Solution of Systems
Differential Equations with Polynomial Coefficients
Series Solutions
Power Series Solutions of Initial Value Problems
Power Series Solutions Using Recurrence Relations
Singular Points and the Method of Frobenius
Second Solutions and Logarithm Factors
Appendix on Power Series
Vectors and Linear Algebra
Vectors and Vector Spaces
The Algebra and Geometry of Vectors
The Dot Product
The Cross Product
The Vector Space R[superscript n]
Linear Independence, Spanning Sets, and Dimension in R[superscript n]
Abstract Vector Spaces
Matrices and Systems of Linear Equations
Matrices
Elementary Row Operations and Elementary Matrices
The Row Echelon Form of a Matrix
The Row and Column Spaces of a Matrix and Rank of a Matrix
Solution of Homogeneous Systems of Linear Equations
The Solution Space of AX = O
Nonhomogeneous Systems of Linear Equations
Summary for Linear Systems
Matrix Inverses
Determinants
Permutations
Definition of the Determinant
Properties of Determinants
Evaluation of Determinants by Elementary Row and Column Operations
Cofactor Expansions
Determinants of Triangular Matrices
A Determinant Formula for a Matrix Inverse
Cramer's Rule
The Matrix Tree Theorem
Eigenvalues, Diagonalization, and Special Matrices
Eigenvalues and Eigenvectors
Diagonalization of Matrices
Orthogonal and Symmetric Matrices
Quadratic Forms
Unitary, Hermitian, and Skew-Hermitian Matrices
Systems of Differential Equations and Qualitative Methods
Systems of Linear Differential Equations
Theory of Systems of Linear First-Order Differential Equations
Solution of X' = AX When A Is Constant
Solution of X' = AX + G
Qualitative Methods and Systems of Nonlinear Differential Equations
Nonlinear Systems and Existence of Solutions
The Phase Plane, Phase Portraits, and Direction Fields
Phase Portraits of Linear Systems
Critical Points and Stability
Almost Linear Systems
Predator/Prey Population Models
Competing Species Models
Lyapunov's Stability Criteria
Limit Cycles and Periodic Solutions
Vector Analysis
Vector Differential Calculus
Vector Functions of One Variable
Velocity, Acceleration, Curvature, and Torsion
Vector Fields and Streamlines
The Gradient Field and Directional Derivatives
Divergence and Curl
Vector Integral Calculus
Line Integrals
Green's Theorem
Independence of Path and Potential Theory in the Plane
Surfaces in 3-Space and Surface Integrals
Applications of Surface Integrals
Preparation for the Integral Theorems of Gauss and Stokes
The Divergence Theorem of Gauss
The Integral Theorem of Stokes
Fourier Analysis, Orthogonal Expansions, and Wavelets
Fourier Series
Why Fourier Series?
The Fourier Series of a Function
Convergence of Fourier Series
Fourier Cosine and Sine Series
Integration and Differentiation of Fourier Series
The Phase Angle Form of a Fourier Series
Complex Fourier Series and the Frequency Spectrum
The Fourier Integral and Fourier Transforms
The Fourier Integral
Fourier Cosine and Sine Integrals
The Complex Fourier Integral and the Fourier Transform
Additional Properties and Applications of the Fourier Transform
The Fourier Cosine and Sine Transforms
The Finite Fourier Cosine and Sine Transforms
The Discrete Fourier Transform
Sampled Fourier Series
The Fast Fourier Transform
Special Functions, Orthogonal Expansions, and Wavelets
Legendre Polynomials
Bessel Functions
Sturm-Liouville Theory and Eigenfunction Expansions
Orthogonal Polynomials
Wavelets
Partial Differential Equations
The Wave Equation
The Wave Equation and Initial and Boundary Conditions
Fourier Series Solutions of the Wave Equation
Wave Motion Along Infinite and Semi-infinite Strings
Characteristics and d'Alembert's Solution
Normal Modes of Vibration of a Circular Elastic Membrane
Vibrations of a Circular Elastic Membrane, Revisited
Vibrations of a Rectangular Membrane
The Heat Equation
The Heat Equation and Initial and Boundary Conditions
Fourier Series Solutions of the Heat Equation
Heat Conduction in Infinite Media
Heat Conduction in an Infinite Cylinder
Heat Conduction in a Rectangular Plate
The Potential Equation
Harmonic Functions and the Dirichlet Problem
Dirichlet Problem for a Rectangle
Dirichlet Problem for a Disk
Poisson's Integral Formula for the Disk
Dirichlet Problems in Unbounded Regions
A Dirichlet Problem for a Cube
The Steady-State Heat Equation for a Solid Sphere
The Neumann Problem
Canonical Forms, Existence and Uniqueness of Solutions, and Well-Posed Problems
Canonical Forms
Existence and Uniqueness of Solutions
Well-Posed Problems
Complex Analysis
Geometry and Arithmetic of Complex Numbers
Complex Numbers
Loci and Sets of Points in the Complex Plane
Complex Functions
Limits, Continuity, and Derivatives
Power Series
The Exponential and Trigonometric Functions
The Complex Logarithm
Powers
Complex Integration
Curves in the Plane
The Integral of a Complex Function
Cauchy's Theorem
Consequences of Cauchy's Theorem
Series Representations of Functions
Power Series Representations
The Laurent Expansion
Singularities and the Residue Theorem
Singularities
The Residue Theorem
Some Applications of the Residue Theorem
Conformal Mappings
Functions as Mappings
Conformal Mappings
Construction of Conformal Mappings Between Domains
Harmonic Functions and the Dirichlet Problem
Complex Function Models of Plane Fluid Flow
Historical Notes
Development of Areas of Mathematics
Ordinary Differential Equations
Matrices and Determinants
Vector Analysis
Fourier Analysis
Partial Differential Equations
Complex Function Theory
Biographical Sketches
Galileo Galilei (1564-1642)
Isaac Newton (1642-1727)
Gottfried Wilhelm Leibniz (1646-1716)
The Bernoulli Family
Leonhard Euler (1707-1783)
Carl Friedrich Gauss (1777-1855)
Joseph-Louis Lagrange (1736-1813)
Pierre-Simon de Laplace (1749-1827)
Augustin-Louis Cauchy (1789-1857)
Joseph Fourier (1768-1830)
Henri Poincare (1854-1912)
Answers and Solutions to Selected Odd-Numbered Problems
Index