Elementary Differential Equations
A first course in ordinary differential equations.
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- Chapter 1 Introduction
- 1.1 Applications Leading to Differential Equations
- 1.2 First Order Equations
- 1.3 Direction Fields for First Order Equations
- Chapter 2 First Order Equations
- 2.1 Linear First Order Equations
- 2.2 Separable Equations
- 2.3 Existence and Uniqueness of Solutions of Nonlinear Equations
- 2.4 Transformation of Nonlinear Equations into Separable Equations
- 2.5 Exact Equations
- 2.6 Integrating Factors
- Chapter 3 Numerical Methods
- 3.1 Euler’s Method
- 3.2 The Improved Euler Method and Related Methods
- 3.3 The Runge-Kutta Method
- Chapter 4 Applications of First Order Equations1em
- 4.1 Growth and Decay
- 4.2 Cooling and Mixing
- 4.3 Elementary Mechanics
- 4.4 Autonomous Second Order Equations
- 4.5 Applications to Curves
- Chapter 5 Linear Second Order Equations
- 5.1 Homogeneous Linear Equations
- 5.2 Constant Coefficient Homogeneous Equations
- 5.3 Nonhomgeneous Linear Equations
- 5.4 The Method of Undetermined Coefficients I
- 5.5 The Method of Undetermined Coefficients II
- 5.6 Reduction of Order
- 5.7 Variation of Parameters
- Chapter 6 Applcations of Linear Second Order Equations
- 6.1 Spring Problems I
- 6.2 Spring Problems II
- 6.3 The RLC Circuit
- 6.4 Motion Under a Central Force
- Chapter 7 Series Solutions of Linear Second Order Equations
- 7.1 Review of Power Series
- 7.2 Series Solutions Near an Ordinary Point I
- 7.3 Series Solutions Near an Ordinary Point II
- 7.4 Regular Singular Points Euler Equations
- 7.5 The Method of Frobenius I
- 7.6 The Method of Frobenius II
- 7.7 The Method of Frobenius III
- Chapter 8 Laplace Transforms
- 8.1 Introduction to the Laplace Transform
- 8.2 The Inverse Laplace Transform
- 8.3 Solution of Initial Value Problems
- 8.4 The Unit Step Function
- 8.5 Constant Coefficient Equations with Piecewise Continuous Forcing Functions
- 8.6 Convolution
- 8.7 Constant Cofficient Equations with Impulses
- 8.8 A Brief Table of Laplace Transforms
- Chapter 9 Linear Higher Order Equations
- 9.1 Introduction to Linear Higher Order Equations
- 9.2 Higher Order Constant Coefficient Homogeneous Equations
- 9.3 Undetermined Coefficients for Higher Order Equations
- 9.4 Variation of Parameters for Higher Order Equations
- Chapter 10 Linear Systems of Differential Equations
- 10.1 Introduction to Systems of Differential Equations
- 10.2 Linear Systems of Differential Equations
- 10.3 Basic Theory of Homogeneous Linear Systems
- 10.4 Constant Coefficient Homogeneous Systems I
- 10.5 Constant Coefficient Homogeneous Systems II
- 10.6 Constant Coefficient Homogeneous Systems II
- 10.7 Variation of Parameters for Nonhomogeneous Linear Systems
Supplements:
- Student Solutions Manual. Worked out solutions for selected exercises
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