# Advanced Engineering Mathematics 10E

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The tenth edition of this bestselling text includes examples in more detail and more applied exercises; both changes are aimed at making the material more relevant and accessible to readers. Kreyszig introduces engineers and computer scientists to advanced math topics as they relate to practical problems. It goes into the following topics at great depth differential equations, partial differential equations, Fourier analysis, vector analysis, complex analysis, and linear algebra/differential equations.

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## Product details

- Hardback | 1280 pages
- 214 x 258 x 48mm | 2,240.73g
- 16 Aug 2011
- John Wiley and Sons Ltd
- John Wiley & Sons Ltd
- Chichester, United Kingdom
- English
- 10th Revised ed.
- 0470458364
- 9780470458365
- 1,484,478

## Table of contents

PART A Ordinary Differential Equations (ODEs) CHAPTER 1 First-Order ODEs 1.1 Basic Concepts. Modeling 1.2 Geometric Meaning of y' = f(x, y). Direction Fields 1.3 Separable ODEs. Modeling 1.4 Exact ODEs. Integrating Factors 1.5 Linear ODEs. Bernoulli Equation. Population Dynamics 1.6 Orthogonal Trajectories. Optional 1.7 Existence and Uniqueness of Solutions Chapter 1 Review Questions and Problems Summary of Chapter 1 CHAPTER 2 Second-Order Linear ODEs 2.1 Homogeneous Linear ODEs of Second Order 2.2 Homogeneous Linear ODEs with Constant Coefficients 2.3 Differential Operators. Optional 2.4 Modeling: Free Oscillations. (Mass-Spring System) 2.5 Euler-Cauchy Equations 2.6 Existence and Uniqueness of Solutions. Wronskian 2.7 Nonhomogeneous ODEs 2.8 Modeling: Forced Oscillations. Resonance 2.9 Modeling: Electric Circuits 2.10 Solution by Variation of Parameters Chapter 2 Review Questions and Problems Summary of Chapter 2 CHAPTER 3 Higher Order Linear ODEs 3.1 Homogeneous Linear ODEs 3.2 Homogeneous Linear ODEs with Constant Coefficients 3.3 Nonhomogeneous Linear ODEs Chapter 3 Review Questions and Problems Summary of Chapter 3 CHAPTER 4 Systems of ODEs. Phase Plane. Qualitative Methods 4.0 Basics of Matrices and Vectors 4.1 Systems of ODEs as Models 4.2 Basic Theory of Systems of ODEs 4.3 Constant-Coefficient Systems. Phase Plane Method 4.4 Criteria for Critical Points. Stability 4.5 Qualitative Methods for Nonlinear Systems 4.6 Nonhomogeneous Linear Systems of ODEs Chapter 4 Review Questions and Problems Summary of Chapter 4 CHAPTER 5 Series Solutions of ODEs. Special Functions 5.1 Power Series Method 5.2 Legendre's Equation. Legendre Polynomials Pn(x) 5.3 Frobenius Method 5.4 Bessel's Equation. Bessel Functions Jv(x) 5.5 Bessel Functions of the Second Kind Yv(x) Chapter 5 Review Questions and Problems Summary of Chapter 5 CHAPTER 6 Laplace Transforms 6.1 Laplace Transform. Inverse Transform. Linearity. ^-Shifting 6.2 Transforms of Derivatives and Integrals. ODEs 6.3 Unit Step Function. f-Shifting 6.4 Short Impulses. Dirac's Delta Function. Partial Fractions 6.5 Convolution. Integral Equations 6.6 Differentiation and Integration of Transforms. 6.7 Systems of ODEs 6.8 Laplace Transform: General Formulas 6.9 Table of Laplace Transforms Chapter 6 Review Questions and Problems Summary of Chapter 6 PART B Linear Algebra. Vector Calculus CHAPTER 7 Linear Algebra: Matrices, Vectors, Determinants. Linear Systems 7.1 Matrices, Vectors: Addition and Scalar Multiplication 7.2 Matrix Multiplication 7.3 Linear Systems of Equations. Gauss Elimination 7.4 Linear Independence. Rank of a Matrix. Vector Space 7.5 Solutions of Linear Systems: Existence, Uniqueness 7.6 For Reference: Second- and Third-Order Determinants 7.7 Determinants. Cramer's Rule 7.8 Inverse of a Matrix. Gauss-Jordan Elimination 7.9 Vector Spaces, Inner Product Spaces. Linear Transformations Optional Chapter 7 Review Questions and Problems Summary of Chapter 7 CHAPTER 8 Linear Algebra: Matrix Eigenvalue Problems 8.1 Eigenvalues, Eigenvectors 8.2 Some Applications of Eigenvalue Problems 8.3 Symmetric, Skew-Symmetric, and Orthogonal Matrices 8.4 Eigenbases. Diagonalization. Quadratic Forms 8.5 Complex Matrices and Forms. Optional Chapter 8 Review Questions and Problems Summary of Chapter 8 CHAPTER 9 Vector Differential Calculus. Grad, Div, Curl 9.1 Vectors in 2-Space and 3-Space 9.2 Inner Product (Dot Product) 9.3 Vector Product (Cross Product) 9.4 Vector and Scalar Functions and Fields. Derivatives 9.5 Curves. Arc Length. Curvature. Torsion 9.6 Calculus Review: Functions of Several Variables. Optional 9.7 Gradient of a Scalar Field. Directional Derivative 9.8 Divergence of a Vector Field 9.9 Curl of a Vector Field Chapter 9 Review Questions and Problems Summary of Chapter 9 CHAPTER 10 Vector Integral Calculus. Integral Theorems 10.1 Line Integrals 10.2 Path Independence of Line Integrals 10.3 Calculus Review: Double Integrals. Optional 10.4 Green's Theorem in the Plane 10.5 Surfaces for Surface Integrals 10.6 Surface Integrals 10.7 Triple Integrals. Divergence Theorem of Gauss 10.8 Further Applications of the Divergence Theorem 10.9 Stokes's Theorem Chapter 10 Review Questions and Problems Summary of Chapter 10 PART C Fourier Analysis. Partial Differential Equations (PDEs) CHAPTER 11 Fourier Series, Integrals, and Transforms 11.1 Fourier Series 11.2 Functions of Any Period p = 2L. Even and Odd Functions. Half-Range Expansions 11.3 Forced Oscillations 11.4 Approximation by Trigonometric Polynomials 11.5 Sturm-Liouville Problems. Orthogonal Functions 11.6 Orthogonal Eigenfunction Expansions 11.7 Fourier Integral 11.8 Fourier Cosine and Sine Transforms 11.9 Fourier Transform. Discrete and Fast Fourier Transforms 11.10 Tables of Transforms Chapter 11 Review Questions and Problems Summary of Chapter 11 CHAPTER 12 Partial Differential Equations (PDEs) 12.1 Basic Concepts 12.2 Modeling: Vibrating String, Wave Equation 12.3 Solution by Separating Variables. Use of Fourier Series 12.4 D'Alembert's Solution of the Wave Equation. Characteristics 12.5 Introduction to the Heat Equation 12.6 Heat Equation: Solution by Fourier Series 12.7 Heat Equation: Solution by Fourier Integrals and Transforms 12.8 Modeling: Membrane, Two-Dimensional Wave Equation 12.9 Rectangular Membrane. Double Fourier Series 12.10 Laplacian in Polar Coordinates. Circular Membrane. Fourier-Bessel Series 12.11 Laplace's Equation in Cylindrical and Spherical Coordinates. Potential 12.12 Solution of PDEs by Laplace Transforms Chapter 12 Review Questions and Problems Summary of Chapter 12 PART D Complex Analysis CHAPTER 13 Complex Numbers and Functions 13.1 Complex Numbers. Complex Plane 13.2 Polar Form of Complex Numbers. Powers and Roots 13.3 Derivative. Analytic Function 13.4 Cauchy-Riemann Equations. Laplace's Equation 13.5 Exponential Function 13.6 Trigonometric and Hyperbolic Functions 13.7 Logarithm. General Power Chapter 13 Review Questions and Problems Summary of Chapter 13 CHAPTER 14 Complex Integration 14.1 Line Integral in the Complex Plane 14.2 Cauchy's Integral Theorem 14.3 Cauchy's Integral Formula 14.4 Derivatives of Analytic Functions Chapter 14 Review Questions and Problems Summary of Chapter 14 CHAPTER 15 Power Series, Taylor Series 15.1 Sequences, Series, Convergence Tests 15.2 Power Series 15.3 Functions Given by Power Series 15.4 Taylor and Maclaurin Series 15.5 Uniform Convergence. Optional Chapter 15 Review Questions and Problems Summary of Chapter 15 CHAPTER 16 Laurent Series. Residue Integration 16.1 Laurent Series 16.2 Singularities and Zeros. Infinity 16.3 Residue Integration Method 16.4 Residue Integration of Real Integrals Chapter 16 Review Questions and Problems Summary of Chapter 16 CHAPTER 17 Conformal Mapping 17.1 Geometry of Analytic Functions: Conformal Mapping 17.2 Linear Fractional Transformations 17.3 Special Linear Fractional Transformations 17.4 Conformal Mapping by Other Functions 17.5 Riemann Surfaces. Optional Chapter 17 Review Questions and Problems Summary of Chapter 17 CHAPTER 18 Complex Analysis and Potential Theory 18.1 Electrostatic Fields 18.2 Use of Conformal Mapping. Modeling 18.3 Heat Problems 18.4 Fluid Flow 18.5 Poisson's Integral Formula for Potentials 18.6 General Properties of Harmonic Functions Chapter 18 Review Questions and Problems Summary of Chapter 18 PART E Numeric Analysis Software CHAPTER 19 Numerics in General 19.1 Introduction 19.2 Solution of Equations by Iteration 19.3 Interpolation 19.4 Spline Interpolation 19.5 Numeric Integration and Differentiation Chapter 19 Review Questions and Problems Summary of Chapter 19 CHAPTER 20 Numeric Linear Algebra 20.1 Linear Systems: Gauss Elimination 20.2 Linear Systems: LU-Factorization, Matrix Inversion 20.3 Linear Systems: Solution by Iteration 20.4 Linear Systems: Ill-Conditioning, Norms 20.5 Least Squares Method 20.6 Matrix Eigenvalue Problems: Introduction 20.7 Inclusion of Matrix Eigenvalues 20.8 Power Method for Eigenvalues 20.9 Tridiagonalization and QR-Factorization Chapter 20 Review Questions and Problems Summary of Chapter 20 CHAPTER 21 Numerics for ODEs and PDEs 21.1 Methods for First-Order ODEs 21.2 Multistep Methods 21.3 Methods for Systems and Higher Order ODEs 21.4 Methods for Elliptic PDEs 21.5 Neumann and Mixed Problems. Irregular Boundary 21.6 Methods for Parabolic PDEs 21.7 Method for Hyperbolic PDEs Chapter 21 Review Questions and Problems Summary of Chapter 21 PART F Optimization, Graphs CHAPTER 22 Unconstrained Optimization. Linear Programming 22.1 Basic Concepts. Unconstrained Optimization 22.2 Linear Programming 22.3 Simplex Method 22.4 Simplex Method: Difficulties Chapter 22 Review Questions and Problems Summary of Chapter 22 CHAPTER 23 Graphs. Combinatorial Optimization 23.1 Graphs and Digraphs 23.2 Shortest Path Problems. Complexity 23.3 Bellman's Principle. Dijkstra's Algorithm 23.4 Shortest Spanning Trees: Greedy Algorithm 23.5 Shortest Spanning Trees: Prim's Algorithm 23.6 Flows in Networks 23.7 Maximum Flow: Ford-Fulkerson Algorithm 23.8 Bipartite Graphs. Assignment Problems Chapter 23 Review Questions and Problems Summary of Chapter 23 PART G Probability, Statistics CHAPTER 24 Data Analysis. Probability Theory 24.1 Data Representation. Average. Spread 24.2 Experiments, Outcomes, Events 24.3 Probability 24.4 Permutations and Combinations 24.5 Random Variables. Probability Distributions 24.6 Mean and Variance of a Distribution 24.7 Binomial, Poisson, and Hypergeometric Distributions 24.8 Normal Distribution 24.9 Distributions of Several Random Variables Chapter 24 Review Questions and Problems Summary of Chapter 24 CHAPTER 25 Mathematical Statistics 25.1 Introduction. Random Sampling 25.2 Point Estimation of Parameters 25.3 Confidence Intervals 25.4 Testing Hypotheses. Decisions 25.5 Quality Control 25.6 Acceptance Sampling 25.7 Goodness of Fit. 2-Test 25.8 Nonparametric Tests 25.9 Regression. Fitting Straight Lines. Correlation Chapter 25 Review Questions and Problems Summary of Chapter 25

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