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Advanced Engineering Mathematics

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ISBN-10: 0534552080

ISBN-13: 9780534552084

Edition: 6th 2007

Authors: Lawrence Turyn, Peter V. O'Neil

List price: $341.95
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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. Advanced Engineering Mathematics features 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, incorporating the use of leading software packages. Computational assistance, exercises and projects have been included to encourage students to make use of these computational tools. The content is organized into eight…    
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Book details

List price: $341.95
Edition: 6th
Copyright year: 2007
Publisher: Course Technology
Publication date: 3/7/2006
Binding: Hardcover
Pages: 1400
Size: 8.50" wide x 10.25" long x 1.75" tall
Weight: 4.950
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 of y"+p(x)y'+q(x)y=f(x)
Reduction of Order
The Constant CoefficientHomogeneous Linear Equation
The Nonhomogeneous Equation y"+p(x)y'+q(x)y=f(x)
Application of Second-OrderDifferential 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
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
Numerical Approximation of Solutions
One-Step Methods
Multistep Methods
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]
Matrices and Systems of Linear Equations
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
Matrix Inverses
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
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-OrderDifferential 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
Lyapunov'sStability 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
Partial Differential Equations
The Wave Equation
The Wave Equation and Initial and Boundary Conditions
Fourier Series Solutions of the Wave Equation
WaveMotion Along Infinite and Semi-InfiniteStrings
Characteristics and d'Alembert'sSolution
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-StateHeat Equation for a Solid Sphere
The Neumann Problem
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
Complex Integration
Curves in the Plane
The Integral of a Complex Function
Consequences of Cauchy'sTheorem
Series Representations of Functions
Power Series Representations
The Laurent Expansion
Singularities and the Residue Theorem
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
Probability and Statistics
Counting and Probability
The Multiplication Principle
Choosing r Objects from n Objects
Events and Sample Spaces
The Probability of an Event
Complementary Events
Conditional Probability
Independent Events
Tree Diagrams in Computing Probabilities
Bayes' Theorem
Expected Value
Measures of Center and Variation
Random Variables and Probability Distributions
The Binomial and Poisson Distributions
A Coin Tossing Experiment, Normally Distributed Data, and the Bell Curve
Sampling Distributions and the Central Limit Theorem
Confidence Intervals and Estimating Population Proportion
Estimating Population Mean and the Student t Distribution
Correlation and Regression
Answers and Solutions to Selected Problems