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# Advanced Engineering Mathematics

## Edition: 6th 2007

### Authors: Lawrence Turyn, Peter V. O'Neil

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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 Euler'sEquation 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 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 Numerical Approximation of Solutions Euler'sMethod 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 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 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'sRule 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 Wavelets 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 Powers Complex Integration Curves in the Plane The Integral of a Complex Function Cauchy'sTheorem Consequences of Cauchy'sTheorem 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 Probability and Statistics Counting and Probability The Multiplication Principle Permutations 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 Statistics 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 Index