Advanced Engineering Mathematics

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  • Edition: 7th
  • Format: Hardcover
  • Copyright: 2011-01-01
  • Publisher: CL Engineering
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Through previous editions, Peter O'Neil has made rigorous engineering mathematics topics accessible to thousands of students by emphasizing visuals, numerous examples, and interesting mathematical models. Now, ADVANCED ENGINEERING MATHEMATICS features revised examples and problems as well as newly added content that has been 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. In this new edition, computational assistance in the form of a self contained Maple Primer has been included to encourage students to make use of such computational tools. The content has been reorganized into six parts and covers a wide spectrum of topics including Ordinary Differential Equations, Vectors and Linear Algebra, Systems of Differential Equations and Qualitative Methods, Vector Analysis, Fourier Analysis, Orthogonal Expansions, and Wavelets, and much more.

Table of Contents

First-Order Differential Equations
Terminology and Separable Equations
Linear Equations
Exact Equations
Homogeneous, Bernoulli and Riccsti Equations
Additional Applications
Existence and Uniqueness Questions
Linear Second-Order Equations
The Linear Second-Order Equations
The Constant Coefficient Case
The Nonhomogeneous Equation
Spring Motion
Euler's Differential Equation
The Laplace Transform Definition and Notation
Solution of Initial Value Problems
Shifiting and the Heaviside Function
Impulses and the Delta Function
Solution of Systems
Polynomial Coefficients
Appendix on Partial Fractions Decompositions
Series Solutions
Power Series Solutions
Frobenius Solutions
Approximation Of Solutions Direction Fields
Euler's Method
Taylor and Modified Euler Methods
Vectors And Vector Spaces
Vectors in the Plane and 3 - Space
The Dot Product
The Cross Product
The Vector Space Rn
Orthogonal Complements and Projections
The Function Space C[a,b]
Matrices And Linear Systems
Elementary Row Operations
Reduced Row Echelon Form
Row and Column Spaces
Homogeneous Systems
Nonhomogeneous Systems
Matrix Inverses
Least Squares Vectors and Data Fitting
LU - Factorization
Linear Transformations
Definition of the Determinant
Evaluation of Determinants
Evaluationof Determinants
A Determinant Formula for A-1
Cramer's Rule
The Matrix Tree Theorem
Eigenvalues, Diagonalization And Special Matrices
Some Special Types of Matrices
Systems Of Linear Differential Equations
Linear Systems
Solution of X'=AX for Constant A. Solution of X'=AX+G
Exponential Matrix Solutions
Applications and Illustrations of Techniques
Phase Portaits
Vector Differential Calculu.S. Vector Functions of One Variable
Velocity and Curvature
Vector Fields and Streamlines
The Gradient Field
Divergence and Curl
Vector Integral Calculu.S
Line Integrals
Green's Theorem
An Extension of Green's Theorem
Independence of Path and Potential Theory
Surface Integrals
Applications of Surface Integrals
Lifting Green's Theorem to R3
The Divergence Theorem of Gauss
Stokes's Theorem
Curvilinear Coordinates
Fourier Series
Why Fourier Series?
The Fourier Series of a Function
Sine and Cosine Series
Integration and Differentiation of Fourier Series
Phase Angle Form
Complex Fourier Series
Filtering of Signals
The Fourier Integral And Transforms
The Fourier Integral
Fourier Cosine and Sine Integrals
The Fourier Transform
Fourier Cosine and Sine Transforms
The Discrete Fourier Transform
Sampled Fourier Series
DFT Approximation of the Fourier Transform
Special Functions And Eigenfunction Expansions
Eigenfunction Expansions
Legendre Polynomials
Bessel Functions
Part V
The Wave Equation
Derivation of the Wave Equation
Wave Motion on an Interval
Wave Motion in an Infinite Medium
Wave Motion in a Semi-Infinite Medium
Laplace Transform Techniques
Characteristics and d'Alembert's Solution
Vibrations in a Circular Membrane
Vibrationsin 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
Laplace Transform Techniques
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 Equation for a Sphere
The Neumann Problem
Part VI
Complex Numbers And Functions
Geometry and Arithmetic of Complex Numbers
Complex Functions
The Exponential and Trigonometric Functions
The Complex Logarithm
Complex Integration
The Integral of a Complex Function
Cauchy's Theorem
Consequences of Cauchy's Theorem
Series Representations Of Functions
Power Series
The Laurent Expansion
Singularities And The Residue Theorem
The Residue Theorem
Evaluation of Real Integrals
Residues and the Inverse Laplace Transform
Conformal Mappings And Applications
Conformal Mappings
Construction of Conformal Mappings
Conformal Mappings and Solutions of Dirichlet Problems
Models of Plane Fluid Flow
Appendix: A Maple Primer
Answers to Selected Problems
Table of Contents provided by Publisher. All Rights Reserved.

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