
Introductory Differential Equations
Resources
Description
Key Features
- Provides the foundations to assist students in learning how to read and understand the subject, but also helps students in learning how to read technical material in more advanced texts as they progress through their studies
- Exercise sets are particularly comprehensive with a wide range of exercises ranging from straightforward to challenging
- Includes new applications and extended projects made relevant to "everyday life" through the use of examples in a broad range of contexts
- Accessible approach with applied examples and will be good for non-math students, as well as for undergrad classes
Readership
Undergraduates in math, biology, chemistry, economics, environmental sciences, physics, computer science and engineering
Table of Contents
Preface
- Technology
- Applications
- Style
- Features
- Pedagogical Features
- Content
Chapter 1: Introduction to Differential Equations
- Abstract
- 1.1 Introduction to Differential Equations: Vocabulary
- Exercises 1.1
- 1.2 A Graphical Approach to Solutions: Slope Fields and Direction Fields
- Exercises 1.2
- Chapter 1 Summary: Essential Concepts and Formulas
- Chapter 1 Review Exercises
Chapter 2: First-Order Equations
- Abstract
- 2.1 Introduction to First-Order Equations
- Exercises 2.1
- 2.2 Separable Equations
- Exercises 2.2
- 2.3 First-Order Linear Equations
- Exercises 2.3
- 2.4 Exact Differential Equations
- Exercises 2.4
- 2.5 Substitution Methods and Special Equations
- Exercises 2.5
- 2.6 Numerical Methods for First-Order Equations
- Exercises 2.6
- Chapter 2 Summary: Essential Concepts and Formulas
- Chapter 2 Review Exercises
- Differential Equations at Work
Chapter 3: Applications of First-Order Differential Equations
- Abstract
- 3.1 Population Growth and Decay
- Exercises 3.1
- 3.2 Newton’s Law of Cooling and Related Problems
- Exercises 3.2
- 3.3 Free-Falling Bodies
- Exercises 3.3
- Chapter 3 Summary: Essential Concepts and Formulas
- Chapter 3 Review Exercises
- Differential Equations at Work
Chapter 4: Higher Order Equations
- Abstract
- 4.1 Second-Order Equations: An Introduction
- Exercises 4.1
- 4.2 Solutions of Second-Order Linear Homogeneous Equations with Constant Coefficients
- Exercises 4.2
- 4.3 Solving Second-Order Linear Equations: Undetermined Coefficients
- Exercises 4.3
- 4.4 Solving Second-Order Linear Equations: Variation of Parameters
- Exercises 4.4
- 4.5 Solving Higher Order Linear Homogeneous Equations
- Exercises 4.5
- 4.6 Solving Higher Order Linear Equations: Undetermined Coefficients and Variation of Parameters
- Exercises 4.6
- 4.7 Cauchy-Euler Equations
- Exercises 4.7
- 4.8 Power Series Solutions of Ordinary Differential Equations
- Exercises 4.8
- 4.9 Series Solutions of Ordinary Differential Equations
- Exercises 4.9
- Chapter 4 Summary: Essential Concepts and Formulas
- Chapter 4 Review Exercises
- Differential Equations at Work
Chapter 5: Applications of Higher Order Differential Equations
- Abstract
- 5.1 Simple Harmonic Motion
- 5.2 Damped Motion
- 5.3 Forced Motion
- 5.4 Other Applications
- 5.5 The Pendulum Problem
- Chapter 5 Summary: Essential Concepts and Formulas
- Chapter 5 Review Exercises
- Differential Equations at Work
Chapter 6: Systems of Differential Equations
- Abstract
- 6.1 Introduction
- Exercises 6.1
- 6.2 Review of Matrix Algebra and Calculus
- Exercises 6.2
- 6.3 An Introduction to Linear Systems
- Exercises 6.3
- 6.4 First-Order Linear Homogeneous Systems With Constant Coefficients
- Exercises 6.4
- 6.5 First-Order Linear Nonhomogeneous Systems: Undetermined Coefficients and Variation of Parameters
- Exercises 6.5
- 6.6 Phase Portraits
- Exercises 6.6
- 6.7 Nonlinear Systems
- Exercises 6.7
- 6.8 Numerical Methods
- Exercises 6.8
- Chapter 6 Summary: Essential Concepts and Formulas
- Chapter 6 Review Exercises
- Differential Equations at Work
Chapter 7: Applications of Systems of Ordinary Differential Equations
- Abstract
- 7.1 Mechanical and Electrical Problems With First-Order Linear Systems
- Exercises 7.1
- 7.2 Diffusion and Population Problems With First-Order Linear Systems
- Exercises 7.2
- 7.3 Nonlinear Systems of Equations
- Exercises 7.3
- Chapter 7 Summary: Essential Concepts and Formulas
- Chapter 7 Review Exercises
- Differential Equations at Work
Chapter 8: Introduction to the Laplace Transform
- Abstract
- 8.1 The Laplace Transform: Preliminary Definitions and Notation
- Exercises 8.1
- 8.2 The Inverse Laplace Transform
- Exercises 8.2
- 8.3 Solving Initial-Value Problems with the Laplace Transform
- Exercises 8.3
- 8.4 Laplace Transforms Of Several Important Functions
- Exercises 8.4
- 8.5 The Convolution Theorem
- Exercises 8.5
- 8.6 Laplace Transform Methods for Solving Systems
- Exercises 8.6
- 8.7 Some Applications Using Laplace Transforms
- Chapter 8 Review Exercises
- Differential Equations at Work
Answers to Selected Exercises
- Exercises 1.1
- Exercises 1.2
- Chapter 1 Review Exercises
- Exercises 2.1
- Exercises 2.2
- Exercises 2.3
- Exercises 2.4
- Exercises 2.5
- Exercises 2.6
- Chapter 2 Review Exercises
- Exercises 3.1
- Exercises 3.2
- Exercises 3.3
- Chapter 3 Review Exercises
- Exercises 4.1
- Exercises 4.2
- Exercises 4.3
- Exercises 4.4
- Exercises 4.5
- Exercises 4.6
- Exercises 4.7
- Exercises 4.8
- Exercises 4.9
- Chapter 4 Review Exercises
- Exercises 5.1
- Exercises 5.2
- Exercises 5.3
- Exercises 5.4
- Exercises 5.5
- Chapter 5 Review Exercises
- Exercises 6.1
- Exercises 6.2
- Exercises 6.3
- Exercises 6.4
- Exercises 6.5
- Exercises 6.6
- Exercises 6.7
- Exercises 6.8
- Chapter 6 Review Exercises
- Exercises 7.1
- Exercises 7.2
- Exercises 7.3
- Chapter 7 Review Exercises
- Exercises 8.1
- Exercises 8.2
- Exercises 8.3
- Exercises 8.4
- Exercises 8.5
- Exercises 8.6
- Exercises 8.7
- Chapter 8 Review ExercisesIndex
Product details
- No. of pages: 530
- Language: English
- Copyright: © Academic Press 2014
- Published: July 22, 2014
- Imprint: Academic Press
- eBook ISBN: 9780124172821
About the Authors
Martha Abell
Affiliations and Expertise
James Braselton
Affiliations and Expertise
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