Problems 1.1.1 -

- Chapter 1: Introduction to Differential Equations
- Section 1.1: Definitions and Terminology
- Section 1.2: Initial-Value Problems
- Section 1.3: Differential Equations as Mathematical Models

- Chapter 2: First-Order Differential Equations
- Section 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

- Chapter 3: Modeling with First-Order Differential Equations
- Section 3.1: Linear Models
- Section 3.2: Nonlinear Models
- Section 3.3: Modeling with Systems of First-Order DEs

- Chapter 4: Higher-Order Differential Equations
- Section 4.1: Preliminary Theory---Linear Equations
- Section 4.2: Reduction of Order
- Section 4.3: Homogeneous Linear Equations with Constant Coefficients
- Section 4.4: Undetermined Coefficients---Superposition Approach
- Section 4.5: Undetermined Coefficients---Annihilator Approach
- Section 4.6: Variation of Parameters
- Section 4.7: Cauchy-Euler Equations
- Section 4.8: Green's Functions
- Section 4.9: Solving Systems of Linear DEs by Elimination
- Section 4.10: Nonlinear Differential Equations

- Chapter 5: Modeling with Higher-Order Differential Equations
- Section 5.1: Linear Models: Initial-Value Problems
- Section 5.2: Linear Models: Boundary-Value Problems
- Section 5.3: Nonlinear Models

- Chapter 6: Series Solutions of Linear Equations
- Section 6.1: Review of Power Series
- Section 6.2: Solutions About Ordinary Points
- Section 6.3: Solutions About Singular Points
- Section 6.4: Special Functions

- Chapter 7: The Laplace Transform
- Section 7.1: Definition of the Laplace Transform
- Section 7.2: Inverse Transforms and Transforms of Derivatives
- Section 7.3: Operational Properties I
- Section 7.4: Operational Properties II
- Section 7.5: The Dirac Delta Function
- Section 7.6: Systems of Linear Differential Equations

- Chapter 8: Systems of Linear First-Order Differential Equations
- Section 8.1: Preliminary Theory---Linear Systems
- Section 8.2: Homogeneous Linear Systems
- Section 8.3: Nonhomogeneous Linear Systems
- Section 8.4: Matrix Exponential

- Chapter 9: Numerical Solutions of Ordinary Differential Equations
- Section 9.1: Euler Methods and Error Analysis
- Section 9.2: Runge-Kutta Methods
- Section 9.3: Multistep Methods
- Section 9.4: Higher-Order Equations and Systems
- Section 9.5: Second-Order Boundary-Value Problems

- Chapter 10: Systems of Nonlinear First-Order Differential Equations
- Section 10.1: Autonomous Systems
- Section 10.2: Stability of Linear Systems
- Section 10.3: Linearization and Local Stability
- Section 10.4: Autonomous Systems as Mathematical Models

- Chapter 11: Fourier Series
- Section 11.1: Orthogonal Functions
- Section 11.2: Fourier Series
- Section 11.3: Fourier Cosine and Sine Series
- Section 11.4: Sturm-Liouville Problem
- Section 11.5: Bessel and Legendre Series

- Chapter 12: Boundary-Value Problems in Rectangular Coordinates
- Section 12.1: Separable Partial Differential Equations
- Section 12.2: Classical PDEs and Boundary-Value Problems
- Section 12.3: Heat Equation
- Section 12.4: Wave Equation
- Section 12.5: Laplace's Equation
- Section 12.6: Nonhomogeneous Boundary-Value Problems
- Section 12.7: Orthogonal Series Expansions
- Section 12.8: Higher-Dimensional Problems

- Chapter 13: Boundary-Value Problems in Other Coordinate Systems
- Section 13.1: Polar Coordinates
- Section 13.2: Polar and Cylindrical Coordinates
- Section 13.3: Spherical Coordinates

- Chapter 14: Integral Transforms
- Section 14.1: Error Function
- Section 14.2: Laplace Transform
- Section 14.3: Fourier Integral
- Section 14.4: Fourier Transforms

- Chapter 15: Numerical Solutions of Partial Differential Equations
- Section 15.1: Laplace's Equation
- Section 15.2: Heat Equation
- Section 15.3: Wave Equation