Chapter 1: Introduction to Differential EquationsSection 1.1:
Definitions and Terminology
Section 1.2:
Initial-Value Problems
Section 1.3:
Differential Equations as Mathematical Models
Page 30:
Chapter in Review
Page 31:
Chapter in Review
Page 32:
Chapter in Review
Page 11:
Exercises
Page 12:
Exercises
Page 13:
Exercises
Page 14:
Exercises
Chapter 2: First-Order Differential EquationsSection 2.1:
Solution Curves Without a Solution
Section 2.2:
Separable Equations
Section 2.3:
Linear Equations
Section 2.4:
Exact Equations
Section 2.5:
Solutions by Substitutions
Section 2.6:
A Numerical Method
Section 2.7:
Linear Models
Section 2.8:
Nonlinear Models
Section 2.9:
Modeling with Systems of First-Order DEs
Page 104:
Chapter in Review
Page 105:
Chapter in Review
Page 106:
Chapter in Review
Page 107:
Chapter in Review
Page 108:
Chapter in Review
Page 109:
Chapter in Review
Page 41:
Exercises
Page 42:
Exercises
Page 43:
Exercises
Page 44:
Exercises
Chapter 3: Higher-Order Differential EquationsSection 3.1:
Theory of Linear Equations
Section 3.2:
Reduction of Order
Section 3.3:
Linear Equations with Constant Coefficients
Section 3.4:
Undetermined Coefficients
Section 3.5:
Variation of Parameters
Section 3.6:
Cauchy-Euler Equations
Section 3.7:
Nonlinear Equations
Section 3.8:
Linear Models: Initial-Value Problems
Section 3.9:
Linear Models: Boundary-Value Problems
Section 3.10:
Green's Functions
Section 3.11:
Nonlinear Models
Section 3.12:
Solving Systems of Linear DEs
Page 208:
Chapter in Review
Page 209:
Chapter in Review
Page 210:
Chapter in Review
Page 211:
Chapter in Review
Page 212:
Chapter in ReviewPage 120:
Exercises
Page 121:
Exercises
Page 122:
Exercises
Chapter 4: The Laplace TransformSection 4.1:
Definition of the Laplace Transform
Section 4.2:
Inverse Transforms and Transforms of Derivatives
Section 4.3:
Translation Theorems
Section 4.4:
Additional Operational Properties
Section 4.5:
Dirac Delta Function
Section 4.6:
Systems of Linear Differential Equations
Page 266:
Chapter in Review
Page 267:
Chapter in Review
Page 268:
Chapter in Review
Page 223:
Exercises
Page 224:
Exercises
Chapter 5: Series Solutions of Linear EquationsSection 5.1:
Solutions about Ordinary Points
Section 5.2:
Solutions about Singular Points
Section 5.3:
Special Functions
Page 304:
Chapter in Review
Page 305:
Chapter in Review
Page 280:
Exercises
Page 281:
Exercises
Chapter 6: Numerical Solutions of Ordinary Differential EquationsSection 6.1:
Euler Methods and Error Analysis
Section 6.2:
Runge-Kutta Methods
Section 6.3:
Multistep Methods
Section 6.4:
Higher-Order Equations and Systems
Section 6.5:
Second-Order Boundary-Value Problems
Page 326:
Chapter in Review
Page 310:
Exercises
Page 311:
Exercises
Section 7.1:
Vectors in 2-Space
Section 7.2:
Vectors in 3-Space
Section 7.3:
Dot Product
Section 7.4:
Cross Product
Section 7.5:
Lines and Planes in 3-Space
Section 7.6:
Vector Spaces
Section 7.7:
Gram-Schmidt Orthogonalization Process
Page 371:
Chapter in Review
Page 372:
Chapter in Review
Page 332:
Exercises
Page 333:
Exercises
Page 334:
Exercises
Section 8.1:
Matrix Algebra
Section 8.2:
Systems of Linear Equations
Section 8.3:
Rank of a Matrix
Section 8.4:
Determinants
Section 8.5:
Properties of Determinants
Section 8.6:
Inverse of a Matrix
Section 8.7:
Cramer's Rule
Section 8.8:
Eigenvalue Problem
Section 8.9:
Powers of Matrices
Section 8.10:
Orthogonal Matrices
Section 8.11:
Approximation of Eigenvalues
Section 8.12:
Diagonalization
Section 8.13:
LU-Factorization
Section 8.14:
Cryptography
Section 8.15:
Error-Correcting Code
Section 8.16:
Method of Least Squares
Section 8.17:
Discrete Compartmental Models
Page 483:
Chapter in Review
Page 484:
Chapter in Review
Page 381:
Exercises
Page 382:
Exercises
Page 383:
Exercises
Chapter 9: Vector CalculusSection 9.1:
Vector Functions
Section 9.2:
Motion on a Curve
Section 9.3:
Curvature
Section 9.4:
Partial Derivatives
Section 9.5:
Directional Derivative
Section 9.6:
Tangent Planes and Normal Lines
Section 9.7:
Curl and Divergence
Section 9.8:
Line Integrals
Section 9.9:
Independence of Path
Section 9.10:
Double Integrals
Section 9.11:
Double Integrals in Polar Coordinates
Section 9.12:
Green's Theorem
Section 9.13:
Surface Integrals
Section 9.14:
Stokes' Theorem
Section 9.15:
Triple Integrals
Section 9.16:
Divergence Theorem
Section 9.17:
Change of Variables in Multiple Integrals
Page 593:
Chapter in Review
Page 594:
Chapter in Review
Page 595:
Chapter in Review
Chapter 10: Systems of Linear Differential EquationsSection 10.1:
Theory of Linear Systems
Section 10.2:
Homogeneous Linear Systems
Section 10.3:
Solution by Diagonalization
Section 10.4:
Nonhomogeneous Linear Systems
Section 10.5:
Matrix Exponential
Page 635:
Chapter in Review
Page 636:
Chapter in Review
Page 606:
Exercises
Page 607:
Exercises
Chapter 11: Systems of Nonlinear Differential EquationsSection 11.1:
Autonomous Systems
Section 11.2:
Stability of Linear Systems
Section 11.3:
Linearization and Local Stability
Section 11.4:
Autonomous Systems as Mathematical Models
Section 11.5:
Periodic Solutions, Limit Cycles, and Global Stability
Page 676:
Chapter in Review
Page 677:
Chapter in Review
Chapter 12: Fourier SeriesSection 12.1:
Orthogonal Functions
Section 12.2:
Fourier Series
Section 12.3:
Fourier Cosine and Sine Series
Section 12.4:
Complex Fourier Series
Section 12.5:
Sturm-Liouville Problem
Section 12.6:
Bessel and Legendre Series
Page 713:
Chapter in Review
Page 714:
Chapter in Review
Chapter 13: Boundary-Value Problems in Rectangular CoordinatesSection 13.1:
Separable Partial Differential Equations
Section 13.2:
Classical PDEs and Boundary-Value Problems
Section 13.3:
Heat Equation
Section 13.4:
Wave Equation
Section 13.5:
Laplace's Equation
Section 13.6:
Nonhomogeneous Boundary-Value Problems
Section 13.7:
Orthogonal Series Expansions
Section 13.8:
Higher-Dimensional Problems
Page 754:
Chapter in Review
Page 755:
Chapter in Review
Chapter 14: Boundary-Value Problems in Other Coordinate SystemsSection 14.1:
Polar Coordinates
Section 14.2:
Cylindrical Coordinates
Section 14.3:
Spherical Coordinates
Page 772:
Chapter in Review
Page 773:
Chapter in Review
Page 774:
Chapter in Review
Page 760:
Exercises
Page 761:
Exercises
Page 762:
Exercises
Chapter 15: Integral TransformsSection 15.1:
Error Function
Section 15.2:
Laplace Transform
Section 15.3:
Fourier Integral
Section 15.4:
Fourier Transforms
Section 15.5:
Finite Fourier Transforms
Section 15.6:
Fast Fourier Transform
Page 811:
Exercises
Page 812:
Exercises
Chapter 16: Numerical Solutions of Partial Differential EquationsSection 16.1:
Laplace's Equation
Section 16.2:
Heat Equation
Section 16.3:
Wave Equation
Page 828:
Chapter in Review
Page 819:
Exercises
Page 820:
Exercises
Chapter 17: Functions of a Complex VariableSection 17.1:
Complex Numbers
Section 17.2:
Powers and Roots
Section 17.3:
Sets in the Complex Plane
Section 17.4:
Functions of a Complex Variable
Section 17.5:
Cauchy-Riemann Equations
Section 17.6:
Exponential and Logarithmic Functions
Section 17.7:
Trigonometric and Hyperbolic Functions
Section 17.8:
Inverse Trigonometric and Hyperbolic Functions
Page 862:
Chapter in Review
Chapter 18: Integration in the Complex PlaneSection 18.1:
Contour Integrals
Section 18.2:
Cauchy-Goursat Theorem
Section 18.3:
Independence of Path
Section 18.4:
Cauchy's Integral Formulas
Page 885:
Chapter in Review
Page 886:
Chapter in Review
Page 869:
Exercises
Page 870:
Exercises
Chapter 19: Series and ResiduesSection 19.1:
Sequences and Series
Section 19.2:
Taylor Series
Section 19.3:
Laurent Series
Section 19.4:
Zeros and Poles
Section 19.5:
Residue Theorem
Section 19.6:
Evaluation of Real Integrals
Page 919:
Chapter in Review
Page 920:
Chapter in Review
Chapter 20: Conformal MappingsSection 20.1:
Complex Functions as Mappings
Section 20.2:
Conformal Mappings
Section 20.3:
Linear Fractional Transformations
Section 20.4:
Schwarz-Christoffel Transformations
Section 20.5:
Poisson Integral Formulas
Section 20.6:
Applications
Page 953:
Chapter in Review
Page 954:
Chapter in Review
Chapter A: Appendix A: Integral-Defined FunctionsPage APP8:
Exercises
Page APP9:
ExercisesExercise 16
Exercise 17
Exercise 18
Exercise 19
Exercise 20
Exercise 21
Exercise 22
Exercise 23
Exercise 24
Exercise 25
Exercise 26
Exercise 27
Exercise 28
Exercise 29
Exercise 30
Exercise 31
Exercise 32
Exercise 33
Exercise 34
Exercise 35
Exercise 36
Exercise 37
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