book

Advanced Engineering Mathematics, 10th Edition

by Erwin Kreyszig, Herbert Kreyszig, Edward J. Norminton

December 2010

Intermediate to advanced

1276 pages

41h 42m

English

Wiley

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1.1 Basic Concepts. Modeling1.2 Geometric Meaning of y′ = f(x, y). Direction Fields, Euler's Method1.3 Separable ODEs. Modeling1.4 Exact ODEs. Integrating Factors1.5 Linear ODEs. Bernoulli Equation. Population Dynamics1.6 Orthogonal Trajectories. Optional1.7 Existence and Uniqueness of Solutions for Initial Value ProblemsCHAPTER 1 Review Questions and ProblemsSummary of Chapter 1
2.1 Homogeneous Linear ODEs of Second Order2.2 Homogeneous Linear ODEs with Constant Coefficients2.3 Differential Operators. Optional2.4 Modeling of Free Oscillations of a Mass–Spring System2.5 Euler–Cauchy Equations2.6 Existence and Uniqueness of Solutions. Wronskian2.7 Nonhomogeneous ODEs2.8 Modeling: Forced Oscillations. Resonance2.9 Modeling: Electric Circuits2.10 Solution by Variation of ParametersCHAPTER 2 Review Questions and ProblemsSummary of Chapter 2
3.1 Homogeneous Linear ODEs3.2 Homogeneous Linear ODEs with Constant Coefficients3.3 Nonhomogeneous Linear ODEsCHAPTER 3 Review Questions and ProblemsSummary of Chapter 3
4.0 For Reference: Basics of Matrices and Vectors4.1 Systems of ODEs as Models in Engineering Applications4.2 Basic Theory of Systems of ODEs. Wronskian4.3 Constant-Coefficient Systems. Phase Plane Method4.4 Criteria for Critical Points. Stability4.5 Qualitative Methods for Nonlinear Systems4.6 Nonhomogeneous Linear Systems of ODEsCHAPTER 4 Review Questions and ProblemsSummary of Chapter 4

5.1 Power Series Method5.2 Legendre's Equation. Legendre Polynomials Pn(x)5.3 Extended Power Series Method: Frobenius Method5.4 Bessel's Equation. Bessel Functions Jν(x)5.5 Bessel Functions of the Yν(x). General SolutionCHAPTER 5 Review Questions and ProblemsSummary of Chapter 5
6.1 Laplace Transform. Linearity. First Shifting Theorem (s-Shifting)6.2 Transforms of Derivatives and Integrals. ODEs6.3 Unit Step Function (Heaviside Function). Second Shifting Theorem (t-Shifting)6.4 Short Impulses. Dirac's Delta Function. Partial Fractions6.5 Convolution. Integral Equations6.6 Differentiation and Integration of Transforms. ODEs with Variable Coefficients6.7 Systems of ODEs6.8 Laplace Transform: General Formulas6.9 Table of Laplace TransformsCHAPTER 6 Review Questions and ProblemsSummary of Chapter 6
7.1 Matrices, Vectors: Addition and Scalar Multiplication7.2 Matrix Multiplication7.3 Linear Systems of Equations. Gauss Elimination7.4 Linear Independence. Rank of a Matrix. Vector Space7.5 Solutions of Linear Systems: Existence, Uniqueness7.6 For Reference: Second- and Third-Order Determinants7.7 Determinants. Cramer's Rule7.8 Inverse of a Matrix. Gauss–Jordan Elimination7.9 Vector Spaces, Inner Product Spaces. Linear Transformations. OptionalCHAPTER 7 Review Questions and ProblemsSummary of Chapter 7
8.1 The Matrix Eigenvalue Problem. Determining Eigenvalues and Eigenvectors8.2 Some Applications of Eigenvalue Problems8.3 Symmetric, Skew-Symmetric, and Orthogonal Matrices8.4 Eigenbases. Diagonalization. Quadratic Forms8.5 Complex Matrices and Forms. OptionalCHAPTER 8 Review Questions and ProblemsSummary of Chapter 8
9.1 Vectors in 2-Space and 3-Space9.2 Inner Product (Dot Product)9.3 Vector Product (Cross Product)9.4 Vector and Scalar Functions and Their Fields. Vector Calculus: Derivatives9.5 Curves. Arc Length. Curvature. Torsion9.6 Calculus Review: Functions of Several Variables. Optional9.7 Gradient of a Scalar Field. Directional Derivative9.8 Divergence of a Vector Field9.9 Curl of a Vector FieldCHAPTER 9 Review Questions and ProblemsSummary of Chapter 9
10.1 Line Integrals10.2 Path Independence of Line Integrals10.3 Calculus Review: Double Integrals. Optional10.4 Green's Theorem in the Plane10.5 Surfaces for Surface Integrals10.6 Surface Integrals10.7 Triple Integrals. Divergence Theorem of Gauss10.8 Further Applications of the Divergence Theorem10.9 Stokes's TheoremCHAPTER 10 Review Questions and ProblemsSummary of Chapter 10
11.1 Fourier Series11.2 Arbitrary Period. Even and Odd Functions. Half-Range Expansions11.3 Forced Oscillations11.4 Approximation by Trigonometric Polynomials11.5 Sturm–Liouville Problems. Orthogonal Functions11.6 Orthogonal Series. Generalized Fourier Series11.7 Fourier Integral11.8 Fourier Cosine and Sine Transforms11.9 Fourier Transform. Discrete and Fast Fourier Transforms11.10 Tables of TransformsCHAPTER 11 Review Questions and ProblemsSummary of Chapter 11
12.1 Basic Concepts of PDEs12.2 Modeling: Vibrating String, Wave Equation12.3 Solution by Separating Variables. Use of Fourier Series12.4 D'Alembert's Solution of the Wave Equation. Characteristics12.5 Modeling: Heat Flow from a Body in Space. Heat Equation12.6 Heat Equation: Solution by Fourier Series. Steady Two-Dimensional Heat Problems. Dirichlet Problem12.7 Heat Equation: Modeling Very Long Bars. Solution by Fourier Integrals and Transforms12.8 Modeling: Membrane, Two-Dimensional Wave Equation12.9 Rectangular Membrane. Double Fourier Series12.10 Laplacian in Polar Coordinates. Circular Membrane. Fourier–Bessel Series12.11 Laplace's Equation in Cylindrical and Spherical Coordinates. Potential12.12 Solution of PDEs by Laplace TransformsCHAPTER 12 Review Questions and ProblemsSummary of Chapter 12
13.1 Complex Numbers and Their Geometric Representation13.2 Polar Form of Complex Numbers. Powers and Roots13.3 Derivative. Analytic Function13.4 Cauchy–Riemann Equations. Laplace's Equation13.5 Exponential Function13.6 Trigonometric and Hyperbolic Functions. Euler's Formula13.7 Logarithm. General Power. Principal ValueCHAPTER 13 Review Questions and ProblemsSummary of Chapter 13
14.1 Line Integral in the Complex Plane14.2 Cauchy's Integral Theorem14.3 Cauchy's Integral Formula14.4 Derivatives of Analytic FunctionsCHAPTER 14 Review Questions and ProblemsSummary of Chapter 14
15.1 Sequences, Series, Convergence Tests15.2 Power Series15.3 Functions Given by Power Series15.4 Taylor and Maclaurin Series15.5 Uniform Convergence. OptionalCHAPTER 15 Review Questions and ProblemsSummary of Chapter 15
16.1 Laurent Series16.2 Singularities and Zeros. Infinity16.3 Residue Integration Method16.4 Residue Integration of Real IntegralsCHAPTER 16 Review Questions and ProblemsSummary of Chapter 16
17.1 Geometry of Analytic Functions: Conformal Mapping17.2 Linear Fractional Transformations (Möbius Transformations)17.3 Special Linear Fractional Transformations17.4 Conformal Mapping by Other Functions17.5 Riemann Surfaces. OptionalCHAPTER 17 Review Questions and ProblemsSummary of Chapter 17
18.1 Electrostatic Fields18.2 Use of Conformal Mapping. Modeling18.3 Heat Problems18.4 Fluid Flow18.5 Poisson's Integral Formula for Potentials18.6 General Properties of Harmonic Functions. Uniqueness Theorem for the Dirichlet ProblemCHAPTER 18 Review Questions and ProblemsSummary of Chapter 18
19.1 Introduction19.2 Solution of Equations by Iteration19.3 Interpolation19.4 Spline Interpolation19.5 Numeric Integration and DifferentiationCHAPTER 19 Review Questions and ProblemsSummary of Chapter 19
20.1 Linear Systems: Gauss Elimination20.2 Linear Systems: LU-Factorization, Matrix Inversion20.3 Linear Systems: Solution by Iteration20.4 Linear Systems: Ill-Conditioning, Norms20.5 Least Squares Method20.6 Matrix Eigenvalue Problems: Introduction20.7 Inclusion of Matrix Eigenvalues20.8 Power Method for Eigenvalues20.9 Tridiagonalization and QR-FactorizationCHAPTER 20 Review Questions and ProblemsSummary of Chapter 20
21.1 Methods for First-Order ODEs21.2 Multistep Methods21.3 Methods for Systems and Higher Order ODEs21.4 Methods for Elliptic PDEs21.5 Neumann and Mixed Problems. Irregular Boundary21.6 Methods for Parabolic PDEs21.7 Method for Hyperbolic PDEsCHAPTER 21 Review Questions and ProblemsSummary of Chapter 21
22.1 Basic Concepts. Unconstrained Optimization: Method of Steepest Descent22.2 Linear Programming22.3 Simplex Method22.4 Simplex Method: DifficultiesCHAPTER 22 Review Questions and ProblemsSummary of Chapter 22
23.1 Graphs and Digraphs23.2 Shortest Path Problems. Complexity23.3 Bellman's Principle. Dijkstra's Algorithm23.4 Shortest Spanning Trees: Greedy Algorithm23.5 Shortest Spanning Trees: Prim's Algorithm23.6 Flows in Networks23.7 Maximum Flow: Ford–Fulkerson Algorithm23.8 Bipartite Graphs. Assignment ProblemsCHAPTER 23 Review Questions and ProblemsSummary of Chapter 23
24.1 Data Representation. Average. Spread24.2 Experiments, Outcomes, Events24.3 Probability24.4 Permutations and Combinations24.5 Random Variables. Probability Distributions24.6 Mean and Variance of a Distribution24.7 Binomial, Poisson, and Hypergeometric Distributions24.8 Normal Distribution24.9 Distributions of Several Random VariablesCHAPTER 24 Review Questions and ProblemsSummary of Chapter 24
25.1 Introduction. Random Sampling25.2 Point Estimation of Parameters25.3 Confidence Intervals25.4 Testing Hypotheses. Decisions25.5 Quality Control25.6 Acceptance Sampling25.7 Goodness of Fit. Χ2-Test25.8 Nonparametric Tests25.9 Regression. Fitting Straight Lines. CorrelationCHAPTER 25 Review Questions and ProblemsSummary of Chapter 25
A3.1 Formulas for Special FunctionsA3.2 Partial DerivativesA3.3 Sequences and SeriesA3.4 Grad, Div, Curl, 2 in Curvilinear Coordinates

Overview

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.