# Advanced Engineering Mathematics 10th edition

Erwin Kreyszig
Publisher: John Wiley & Sons

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• Chapter 1: First-Order ODEs
• 1.1: Basic Concepts. Modeling
• 1.2: Geometric Meaning 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
• 1.7: Existence and Uniqueness of Solutions for Initial Value Problems
• 1: Review Questions and Problems

• 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
• 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
• 2: Review Questions and Problems

• Chapter 3: Higher Order Linear ODEs
• 3.1: Homogeneous Linear ODEs
• 3.2: Homogeneous Linear ODEs with Constant Coefficients
• 3.3: Nonhomogeneous Linear ODEs
• 3: Review Questions and Problems

• 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 (3)
• 4.2: Basic Theory of Systems of ODEs. Wronskian
• 4.3: Constant-Coefficient Systems. Phase Plane Method (3)
• 4.4: Criteria for Critical Points. Stability (4)
• 4.5: Qualitative Methods for Nonlinear Systems (3)
• 4.6: Nonhomogeneous Linear Systems of ODEs (2)
• 4: Review Questions and Problems

• Chapter 5: Series Solutions of ODEs. Special Functions
• 5.1: Power Series Method
• 5.2: Legendre's Equation. Legendre Polynomials Pn(x)
• 5.3: Extended Power Series Method: Frobenius Method
• 5.4: Bessel's Equation. Bessel Functions Jv(x) (5)
• 5.5: Bessel Functions of the Yv(x). General Solutions (5)
• 5: Review Questions and Problems

• Chapter 6: Laplace Transforms
• 6.1: Laplace Transform. Linearity. First Shifting Theorem (s-Shifting) (8)
• 6.2: Transforms of Derivatives and Integrals. ODEs (5)
• 6.3: Unit Step Function (Heaviside Functions). Second Shifting Theorem (t-Shifting) (6)
• 6.4: Short Impulses. Dirac's Delta Function. Partial Fractions (3)
• 6.5: Convolution. Integral Equations (3)
• 6.6: Differentiation and Integration of Transforms. ODEs with Variable Coefficients (4)
• 6.7: Systems of ODEs (2)
• 6.8: Laplace Transform: General Formulas
• 6.9: Table of Laplace Transforms
• 6: Review Questions and Problems

• Chapter 7: Linear Algebra: Matrices, Vectors, Determinants. Linear Systems
• 7.1: Matrices, Vectors: Addition and Scalar Multiplication (3)
• 7.2: Matrix Multiplication (4)
• 7.3: Linear Systems of Equations. Gauss Elimination (3)
• 7.4: Linear Independence. Rank of a Matrix. Vector Space (11)
• 7.5: Solutions of Linear Systems: Existence, Uniqueness
• 7.6: For Reference: Second- and Third-Order Determinants
• 7.7: Determinants. Cramer's Rule (4)
• 7.8: Inverse of a Matrix. Gauss–Jordan Elimination (3)
• 7.9: Vector Spaces, Inner Product Spaces. Linear Transformations (6)
• 7: Review Questions and Problems

• Chapter 8: Linear Algebra: Matrix Eigenvalue Problems
• 8.1: The Matrix Eigenvalue Problem. Determining Eigenvalues and Eigenvectors (4)
• 8.2: Some Applications of Eigenvalue Problems
• 8.3: Symmetric, Skew-Symmetric, and Orthogonal Matrices (3)
• 8.4: Eigenbases. Diagonalization. Quadratic Forms (5)
• 8.5: Complex Matrices and Forms (4)
• 8: Review Questions and Problems

• 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
• 9.7: Gradient of a Scalar Field. Directional Derivative (6)
• 9.8: Divergence of a Vector Field (4)
• 9.9: Curl of a Vector Field (3)
• 9: Review Questions and Problems

• Chapter 10: Vector Integral Calculus. Integral Theorems
• 10.1: Line Integrals (5)
• 10.2: Path Independence of Line Integrals (4)
• 10.3: Calculus Review: Double Integrals (4)
• 10.4: Green's Theorem in the Plane (5)
• 10.5: Surfaces for Surface Integrals (7)
• 10.6: Surface Integrals (5)
• 10.7: Triple Integrals. Divergence Theorem of Gauss (4)
• 10.8: Further Applications of the Divergence Theorem (4)
• 10.9: Stokes's Theorem (5)
• 10: Review Questions and Problems

• Chapter 11: Fourier Analysis
• 11.1: Fourier Series (3)
• 11.2: Arbitrary Period. Even and Odd Functions. Half-Range Expansions (4)
• 11.3: Forced Oscillations (2)
• 11.4: Approximation by Trigonometric Polynomials (3)
• 11.5: Sturm–Liouville Problems. Orthogonal Functions (3)
• 11.6: Orthogonal Series. Generalized Fourier Series (3)
• 11.7: Fourier Integral (3)
• 11.8: Fourier Cosine and Sine Transforms (4)
• 11.9: Fourier Transform. Discrete and Fast Fourier Transforms (3)
• 11.10: Tables of Transforms
• 11: Review Questions and Problems

• Chapter 12: Partial Differential Equations (PDEs)
• 12.1: Basic Concepts of PDEs (5)
• 12.2: Modeling: Vibrating String, Wave Equation
• 12.3: Solution by Separating Variables. Use of Fourier Series (3)
• 12.4: D'Alembert's Solution of the Wave Equation. Characteristics (2)
• 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 (5)
• 12.7: Heat Equation: Modeling Very Long Bars. Solution by Fourier Integrals and Transforms (4)
• 12.8: Modeling: Membrane, Two-Dimensional Wave Equation
• 12.9: Rectangular Membrane. Double Fourier Series (4)
• 12.10: Laplacian in Polar Coordinates. Circular Membrane. Fourier–Bessel Series (1)
• 12.11: Laplace's Equation in Cylindrical and Spherical Coordinates. Potential
• 12.12: Solution of PDEs by Laplace Transforms (1)
• 12: Review Questions and Problems

• Chapter 13: Complex Numbers and Functions. Complex Differentiation
• 13.1: Complex Numbers and Their Geometric Representation (6)
• 13.2: Polar Form of Complex Numbers. Powers and Roots (8)
• 13.3: Derivative. Analytic Function (6)
• 13.4: Cauchy–Riemann Equations. Laplace's Equation (6)
• 13.5: Exponential Function (5)
• 13.6: Trigonometric and Hyperbolic Functions. Euler's Formula (5)
• 13.7: Logarithm. General Power. Principal Value (6)
• 13: Review Questions and Problems

• Chapter 14: Complex Integration
• 14.1: Line Integral in the Complex Plane (6)
• 14.2: Cauchy's Integral Theorem (6)
• 14.3: Cauchy's Integral Formula (5)
• 14.4: Derivatives of Analytic Functions (4)
• 14: Review Questions and Problems

• Chapter 15: Power Series, Taylor Series
• 15.1: Sequences, Series, Convergence Tests (9)
• 15.2: Power Series (5)
• 15.3: Functions Given by Power Series (5)
• 15.4: Taylor and Maclaurin Series (5)
• 15.5: Uniform Convergence
• 15: Review Questions and Problems

• Chapter 16: Laurent Series. Residue Integration
• 16.1: Laurent Series (7)
• 16.2: Singularities and Zeros. Infinity (10)
• 16.3: Residue Integration Method (9)
• 16.4: Residue Integration of Real Integrals (9)
• 16: Review Questions and Problems

• Chapter 17: Conformal Mapping
• 17.1: Geometry of Analytic Functions: Conformal Mapping (5)
• 17.2: Linear Fractional Transformations (Möbius Transformations) (4)
• 17.3: Special Linear Fractional Transformations (2)
• 17.4: Conformal Mapping by Other Functions (8)
• 17.5: Riemann Surfaces
• 17: Review Questions and Problems

• Chapter 18: Complex Analysis and Potential Theory
• 18.1: Electrostatic Fields (3)
• 18.2: Use of Conformal Mapping. Modeling (2)
• 18.3: Heat Problems (3)
• 18.4: Fluid Flow (2)
• 18.5: Poisson's Integral Formula for Potentials
• 18.6: General Properties of Harmonic Functions. Uniqueness Theorem for the Dirichlet Problem
• 18: Review Questions and Problems

• 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
• 19: Review Questions and Problems

• 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
• 20: Review Questions and Problems

• 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
• 21: Review Questions and Problems

• Chapter 22: Unconstrained Optimization. Linear Programming
• 22.1: Basic Concepts. Unconstrained Optimization: Method of Steepest Descent
• 22.2: Linear Programming
• 22.3: Simplex Method
• 22.4: Simplex Method: Difficulties
• 22: Review Questions and Problems

• 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
• 23: Review Questions and Problems

• 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
• 24: Review Questions and Problems

• 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. Χ 2-Test
• 25.8: Nonparametric Tests
• 25.9: Regression. Fitting Straight Lines. Correlation
• 25: Review Questions and Problems

Advanced Engineering Mathematics, 10th Edition by Edwin Kreyszig is known for its comprehensive coverage, careful and correct mathematics, outstanding exercises, and self-contained subject matter parts for maximum flexibility. This edition provides instructors and students with a comprehensive and up-to-date resource for teaching and learning engineering mathematics, that is, applied mathematics for engineers and physicists, mathematicians and computer scientists, as well as members of other disciplines. The WebAssign component for this text includes links to the full eBook and instant student feedback on randomized online questions.

## Questions Available within WebAssign

Most questions from this textbook are available in WebAssign. The online questions are identical to the textbook questions except for minor wording changes necessary for Web use. Whenever possible, variables, numbers, or words have been randomized so that each student receives a unique version of the question. This list is updated nightly.

##### Question Availability Color Key
BLACK questions are available now
GRAY questions are under development

Group Quantity Questions
Chapter 1: First-Order ODEs
1 0
Chapter 2: Second-Order Linear ODEs
2 0
Chapter 3: Higher Order Linear ODEs
3 0
Chapter 4: Systems of ODEs. Phase Plane. Qualitative Methods
4.1 3 005 007 012
4.3 3 003 013 018
4.4 4 003 005 007 011
4.5 3 004 007 011
4.6 2 003 011
Chapter 5: Series Solutions of ODEs. Special Functions
5.4 5 002 006 008 010 024
5.5 5 001 002 004 006 008
Chapter 6: Laplace Transforms
6.1 8 001 002 005 013 014 023 030 032
6.2 5 004 005 017 019 026
6.3 6 006 010 013 016 025 039
6.4 3 003 010 014
6.5 3 007 008 023
6.6 4 003 008 010 016
6.7 2 003 012
Chapter 7: Linear Algebra: Matrices, Vectors, Determinants. Linear Systems
7.1 3 009 012 013
7.2 4 012 014 017 029
7.3 3 003 009 018
7.4 11 001 002 005 007 009 012 014 015 017 032 034
7.7 4 004 007 012 022
7.8 3 002 005 020
7.9 6 003 004 006 009 012 022
Chapter 8: Linear Algebra: Matrix Eigenvalue Problems
8.1 4 004 011 012 024
8.3 3 003 006 008
8.4 5 001 009 010 024 025
8.5 4 001 002 005 013
Chapter 9: Vector Differential Calculus. Grad, Div, Curl
9.7 6 003 008 012 015 021 026
9.8 4 003 005 009 017
9.9 3 004 009 014
Chapter 10: Vector Integral Calculus. Integral Theorems
10.1 5 002 003 005 006 010
10.2 4 003 005 013 016
10.3 4 005 010 012 017
10.4 5 003 007 015 016 019
10.5 7 002 003 005 007 014 015 018
10.6 5 003 005 007 013 015
10.7 4 011 013 017 022
10.8 4 001 003 005 007
10.9 5 003 005 013 015 019
Chapter 11: Fourier Analysis
11.1 3 012 014 018
11.2 4 011 020 024 029
11.3 2 002 006
11.4 3 008 011 012
11.5 3 005 007 013
11.6 3 001 003 005
11.7 3 001 011 018
11.8 4 001 002 003 005
11.9 3 003 004 007
Chapter 12: Partial Differential Equations (PDEs)
12.1 5 002 004 008 010 019
12.3 3 011 015 016
12.4 2 008 019
12.6 5 007 010 011 018 021
12.7 4 002 003 004 005
12.9 4 004 005 007 018
12.10 1 004
12.12 1 005
Chapter 13: Complex Numbers and Functions. Complex Differentiation
13.1 6 001 009 011 013 017 019
13.2 8 001 005 011 013 016 021 023 028
13.3 6 001 003 005 007 011 023
13.4 6 003 005 007 013 017 023
13.5 5 003 009 015 017 019
13.6 5 001 003 007 013 016
13.7 6 005 007 008 015 019 023
Chapter 14: Complex Integration
14.1 6 001 011 019 021 025 029
14.2 6 009 011 013 018 022 024
14.3 5 003 011 012 013 015
14.4 4 001 003 006 011
Chapter 15: Power Series, Taylor Series
15.1 9 016 017 018 019 020 021 022 023 024
15.2 5 007 009 013 015 017
15.3 5 005 007 009 011 013
15.4 5 003 016 019 021 023
Chapter 16: Laurent Series. Residue Integration
16.1 7 001 003 005 008 013 022 023
16.2 10 001 003 005 007 009 013 015 017 019 021
16.3 9 003 005 007 009 011 015 017 019 021
16.4 9 001 007 009 011 015 017 019 021 025
Chapter 17: Conformal Mapping
17.1 5 011 013 015 017 019
17.2 4 007 013 015 019
17.3 2 009 011
17.4 8 001 003 005 007 011 013 019 021
Chapter 18: Complex Analysis and Potential Theory
18.1 3 003 006 009
18.2 2 007 009
18.3 3 005 007 009
18.4 2 009 013
Chapter 19: Numerics in General
19 0
Chapter 20: Numeric Linear Algebra
20 0
Chapter 21: Numerics for ODEs and PDEs
21 0
Chapter 22: Unconstrained Optimization. Linear Programming
22 0
Chapter 23: Graphs. Combinatorial Optimization
23 0
Chapter 24: Data Analysis. Probability Theory
24 0
Chapter 25: Mathematical Statistics
25 0
Total 366