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: The Laplace Transform and Some Elementary Applications
- Section 10.1: Definition of the Laplace Transform
- Section 10.2: The Existence of the Laplace Transform and the Inverse Transform
- Section 10.3: Periodic Functions and the Laplace Transform
- Section 10.4: The Transform of Derivatives and Solution of Initial-Value Problems
- Section 10.5: The First Shifting Theorem
- Section 10.6: The Unit Step Function
- Section 10.7: The Second Shifting Theorem
- Section 10.8: Impulsive Driving Terms: The Dirac Delta Function
- Section 10.9: The Convolution Integral
- Chapter 11: Series Solutions to Linear Differential Equations
- Section 11.1: A Review of Power Series
- Section 11.2: Series Solutions about an Ordinary Point
- Section 11.3: The Legendre Equation
- Section 11.4: Series Solutions about a Regular Singular Point
- Section 11.5: Frobenius Theory
- Section 11.6: Bessel's Equation of Order p
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