Elements of Advanced Engineering Mathematics

ISBN-10: 0495668184

ISBN-13: 9780495668183

Edition: 2010

Authors: Peter V. O'Neil

List price: $165.95
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Book details

List price: $165.95
Copyright year: 2010
Publisher: Course Technology
Publication date: 9/11/2009
Binding: Hardcover
Pages: 496
Size: 8.00" wide x 10.25" long x 0.75" tall
Weight: 2.376
Language: English

Ordinary Differential Equations
First-Order Differential Equations Terminology and Separable Equations
Linear Equations
Exact Equations
Additional Applications
Existence and Uniqueness Questions
Direction Fields
Numerical Approximation of Solutions
Linear Second-Order Equations
Theory of the Linear Second-Order Equation
The Constant Coefficient Homogeneous Equation
Solutions of the Nonhomogeneous Equation
Spring Motion
The Laplace Transform Definition and Notation
Solution of Initial Value Problems
Shifting and the Heaviside Function
Convolution
Impulses and the Dirac Delta Function
Appendix on Partial Fractions Decompositions
Series Solutions Power Series Solutions
Frobenius Solutions
Vectors, Linear Algebra, and Systems of Linear Differential Equations
Algebra and Geometry of Vectors Vectors in the Plane and 3-Space
The Dot Product
The Cross Product
The Vector Space Rn
Matrices and Systems of Linear Equations Matrices
Linear Homogeneous Systems
Nonhomogeneous Systems of Linear Equations
Matrix Inverses
Determinants Definition of the Determinant
Evaluation of Determinants
Evaluationof Determinants
A Determinant Formula for A-1
Cramer's Rule
Eigenvalues and Diagonalization Eigenvalues and Eigenvectors
Diagonalization
Some Special Matrices
Systems of Linear Differential Equations Systems of Linear Differential Equations
Solution of X_ = AX when a Is Constant
Solution of X_ = AX + G
Vector Analysis
Vector Differential Calculus Vector Functions of One Variable
Velocity and Curvature
Vector Fields and Streamlines
The Gradient Field
Divergence and Curl
Vector Integral Calculus
Line Integrals
Green's Theorem
An Extension of Green's Theorem
Potential Theory
Surface Integrals
Applications of Surface Integrals
The Divergence Theorem of Gauss
Stokes's Theorem
Fourier Analysis and Eigenfunction Expansions
Fourier Series the Fourier Series of a Function
Sine and Cosine Series
Derivatives and Integrals of Fourier Series
Complex Fourier Series
The Fourier Integral and Transforms
The Fourier Integral
Fourier Cosine and Sine Integrals
The Fourier Transform
Fourier Cosine and Sine Transforms
Eigenfunction Expansions General Eigenfunction Expansions
Fourier-Legendre Expansions
Fourier-Bessel Expansions
Partial Differential Equations
The Wave Equation Derivation of the Equation
Wave Motion on an Interval
Wave Motion in an Infinite Medium
Wave Motion in a Semi-Infinite Medium. d'Alembert's Solution
Vibrations in a Circular Membrane
Vibrations in a Rectangular Membrane
The Heat Equation Initial and Boundary Conditions
The Heat Equation on [0, L]
Solutions in an Infinite Medium
Heat Conduction in an Infinite Cylinder
Heat Conduction in a Rectangular Plate
The Potential Equation Laplace's Equation
Dirichlet Problem for a Rectangle
Dirichlet Problem for a Disk
Poisson's Integral Formula
Dirichlet Problem for Unbounded Regions
A Dirichlet Problem for a Cube
Steady-State Heat Equation for a Sphere
Appendix a Guide to Notation
Appendix B a MAPLE Primer
Answers to Selected Problems
Index
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