PHOTO CREDITS
by Edward J. Norminton, Herbert Kreyszig, Erwin Kreyszig
Advanced Engineering Mathematics, 10th Edition
- Cover
- Title Page
- Copyright
- Preface
- 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, 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: 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 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 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
- CHAPTER 6: Laplace Transforms
- 6.1 Laplace Transform. Linearity. First Shifting Theorem (s-Shifting)
- 6.2 Transforms of Derivatives and Integrals. ODEs
- 6.3 Unit Step Function (Heaviside Function). Second Shifting Theorem (t-Shifting)
- 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: First-Order 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 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 The Matrix Eigenvalue Problem. Determining Eigenvalues and 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 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. Half-Range 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 Two-Dimensional Heat Problems. Dirichlet Problem
- 12.7 Heat Equation: Modeling Very Long Bars. 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
- 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: 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
- 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. Χ2-Test
- 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 Odd-Numbered Problems
- APPENDIX 3 Auxiliary Material
- APPENDIX 4 Additional Proofs
- APPENDIX 5 Tables
- INDEX
- PHOTO CREDITS
PHOTO CREDITS
Part A Opener: © Denis Jr. Tangney/iStockphoto
Part B Opener: © Jill Fromer/iStockphoto
Part C Opener: © Science Photo Library/Photo Researchers, Inc
Part D Opener: © Rafa Irusta/iStockphoto
Part E Opener: © Alberto Pomares/iStockphoto
Chapter 19, Figure 437: © Eddie Gerald/Alamy
Part F Opener: © Rainer Plendl/iStockphoto
Part G Opener: © Sean Locke/iStockphoto
Appendix 1 Opener: © Ricardo De Mattos/iStockphoto
Appendix 2 Opener: © joel-t/iStockphoto
Appendix 3 Opener: © Luke Daniek/iStockphoto
Appendix 4 Opener: © Andrey Prokhorov/iStockphoto
Appendix 5 Opener: © Pedro Castellano/iStockphoto
-
No Comment
..................Content has been hidden....................
You can't read the all page of ebook, please click here login for view all page.