Book description
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.
Table of contents
 Cover
 Title Page
 Copyright
 Preface
 Contents

PART A Ordinary Differential Equations (ODEs)

CHAPTER 1: FirstOrder ODEs
 1.1 Basic Concepts. Modeling
 1.2 Geometric Meaning of y′ = f(x, y). Direction Fields, Euler's Method
 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 for Initial Value Problems
 CHAPTER 1 Review Questions and Problems
 Summary of Chapter 1

CHAPTER 2: SecondOrder 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 of Free Oscillations of a 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

CHAPTER 4: Systems of ODEs. Phase Plane. Qualitative Methods
 4.0 For Reference: Basics of Matrices and Vectors
 4.1 Systems of ODEs as Models in Engineering Applications
 4.2 Basic Theory of Systems of ODEs. Wronskian
 4.3 ConstantCoefficient 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

CHAPTER 6: Laplace Transforms
 6.1 Laplace Transform. Linearity. First Shifting Theorem (sShifting)
 6.2 Transforms of Derivatives and Integrals. ODEs
 6.3 Unit Step Function (Heaviside Function). Second Shifting Theorem (tShifting)
 6.4 Short Impulses. Dirac's Delta Function. Partial Fractions
 6.5 Convolution. Integral Equations
 6.6 Differentiation and Integration of Transforms. ODEs with Variable Coefficients
 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

CHAPTER 1: FirstOrder ODEs

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 ThirdOrder 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 The Matrix Eigenvalue Problem. Determining Eigenvalues and Eigenvectors
 8.2 Some Applications of Eigenvalue Problems
 8.3 Symmetric, SkewSymmetric, 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 2Space and 3Space
 9.2 Inner Product (Dot Product)
 9.3 Vector Product (Cross Product)
 9.4 Vector and Scalar Functions and Their Fields. Vector Calculus: 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

CHAPTER 7: Linear Algebra: Matrices, Vectors, Determinants. Linear Systems

PART C Fourier Analysis. Partial Differential Equations (PDEs)

CHAPTER 11: Fourier Analysis
 11.1 Fourier Series
 11.2 Arbitrary Period. Even and Odd Functions. HalfRange Expansions
 11.3 Forced Oscillations
 11.4 Approximation by Trigonometric Polynomials
 11.5 Sturm–Liouville Problems. Orthogonal Functions
 11.6 Orthogonal Series. Generalized Fourier Series
 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 of PDEs
 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 Modeling: Heat Flow from a Body in Space. Heat Equation
 12.6 Heat Equation: Solution by Fourier Series. Steady TwoDimensional Heat Problems. Dirichlet Problem
 12.7 Heat Equation: Modeling Very Long Bars. Solution by Fourier Integrals and Transforms
 12.8 Modeling: Membrane, TwoDimensional 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

CHAPTER 11: Fourier Analysis

PART D Complex Analysis

CHAPTER 13: Complex Numbers and Functions. Complex Differentiation
 13.1 Complex Numbers and Their Geometric Representation
 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. Euler's Formula
 13.7 Logarithm. General Power. Principal Value
 CHAPTER 13 Review Questions and Problems
 Summary of Chapter 13
 CHAPTER 14: Complex Integration
 CHAPTER 15: Power Series, Taylor Series
 CHAPTER 16: Laurent Series. Residue Integration

CHAPTER 17: Conformal Mapping
 17.1 Geometry of Analytic Functions: Conformal Mapping
 17.2 Linear Fractional Transformations (Möbius 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. Uniqueness Theorem for the Dirichlet Problem
 CHAPTER 18 Review Questions and Problems
 Summary of Chapter 18

CHAPTER 13: Complex Numbers and Functions. Complex Differentiation

PART E Numeric Analysis
 CHAPTER 19: Numerics in General

CHAPTER 20: Numeric Linear Algebra
 20.1 Linear Systems: Gauss Elimination
 20.2 Linear Systems: LUFactorization, Matrix Inversion
 20.3 Linear Systems: Solution by Iteration
 20.4 Linear Systems: IllConditioning, 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 QRFactorization
 CHAPTER 20 Review Questions and Problems
 Summary of Chapter 20

CHAPTER 21: Numerics for ODEs and PDEs
 21.1 Methods for FirstOrder 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

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. Χ2Test
 25.8 Nonparametric Tests
 25.9 Regression. Fitting Straight Lines. Correlation
 CHAPTER 25 Review Questions and Problems
 Summary of Chapter 25

CHAPTER 24: Data Analysis. Probability Theory
 APPENDIX 1 References
 APPENDIX 2 Answers to OddNumbered Problems
 APPENDIX 3 Auxiliary Material
 APPENDIX 4 Additional Proofs
 APPENDIX 5 Tables
 INDEX
 PHOTO CREDITS
Product information
 Title: Advanced Engineering Mathematics, 10th Edition
 Author(s):
 Release date: December 2010
 Publisher(s): Wiley
 ISBN: 9780470458365
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