Introductory Differential Equations
- 6th Edition - December 21, 2023
- Authors: Martha L. Abell, James P. Braselton
- Language: English
- Paperback ISBN:9 7 8 - 0 - 4 4 3 - 1 6 0 5 8 - 5
- eBook ISBN:9 7 8 - 0 - 4 4 3 - 1 6 0 5 9 - 2
**2025 Textbook and Academic Authors Association (TAA) McGuffey Longevity Award Winner**Introductory Differential Equations, Sixth Edition provides the foundations to assist stud… Read more
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Request a sales quote**2025 Textbook and Academic Authors Association (TAA) McGuffey Longevity Award Winner**
Introductory Differential Equations, Sixth Edition provides the foundations to assist students in learning not only how to read and understand differential equations, but also how to read technical material in more advanced texts as they progress through their studies. The book's accessible explanations and many robust sample problems are appropriate for a first semester course in introductory ordinary differential equations (including Laplace transforms), for a second course in Fourier series and boundary value problems, and for students with no background on the subject.
Introductory Differential Equations, Sixth Edition provides the foundations to assist students in learning not only how to read and understand differential equations, but also how to read technical material in more advanced texts as they progress through their studies. The book's accessible explanations and many robust sample problems are appropriate for a first semester course in introductory ordinary differential equations (including Laplace transforms), for a second course in Fourier series and boundary value problems, and for students with no background on the subject.
- Gives students a complete foundation on the subject, providing a strong basis for learning how to read technical material in more advanced texts
- Includes new, comprehensive exercise sets throughout, ranging from straightforward to challenging
- Offers applications and extended projects relevant to the real-world through the use of examples in a broad range of contexts
- Provides online support, including a full solutions manual for qualified instructors and a partial solutions manual for students
Undergraduate students from a variety of majors, taking courses in Mathematics departments typically titled: (Introductory) Differential Equations, (Introductory) Ordinary Differential Equations, Applied Mathematics, Professionals / researchers / academics who require an introduction or refresher to the subject
- Cover image
- Title page
- Table of Contents
- Copyright
- Preface
- Technology
- Applications
- Style
- Features
- Pedagogical features
- Content
- Chapter 1: Introduction to differential equations
- 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
- Bibliography
- Chapter 2: First order ordinary differential equations
- 2.1. Introduction to first order equations
- Exercises 2.1
- 2.2. Separable equations
- Exercises 2.2
- 2.3. First order linear equations: undetermined coefficients
- Exercises 2.3
- 2.4. First order linear equations: integrating factor
- Exercises 2.4
- 2.5. Exact differential equations
- Exercises 2.5
- 2.6. Substitution methods and special equations
- Exercises 2.6
- 2.7. Numerical methods for first order equations
- Exercises 2.7
- Chapter 2 summary: essential concepts and formulas
- Chapter 2 review exercises
- Differential equations at work
- Bibliography
- Chapter 3: Applications of first order differential equations
- 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
- Bibliography
- Chapter 4: Higher order linear equations
- 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
- Bibliography
- Chapter 5: Applications of higher order differential equations
- 5.1. Simple harmonic motion
- Exercises 5.1
- 5.2. Damped motion
- Exercises 5.2
- 5.3. Forced motion
- Exercises 5.3
- 5.4. Other applications
- Exercises 5.4
- 5.5. The pendulum problem
- Exercises 5.5
- Chapter 5 summary: essential concepts and formulas
- Chapter 5 review exercises
- Differential equations at work
- Bibliography
- Chapter 6: Systems of differential equations
- 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
- 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
- Bibliography
- Chapter 8: Introduction to the Laplace transform
- 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
- Exercises 8.7
- Chapter 8 summary: essential concepts and formulas
- Chapter 8 review exercises
- Differential equations at work
- Bibliography
- Bibliography
- Index
- No. of pages: 528
- Language: English
- Edition: 6
- Published: December 21, 2023
- Imprint: Academic Press
- Paperback ISBN: 9780443160585
- eBook ISBN: 9780443160592
MA
Martha L. Abell
Martha L. Abell and James P. Braselton are graduates of the Georgia Institute of Technology and the Ohio State University, respectively, and teach at Georgia Southern University, Statesboro where they have extensive experience instructing students at both the undergraduate and graduate levels. Other books by the authors include Differential Equations with Mathematica and Mathematica by Example.
Affiliations and expertise
Professor EmeritaJB
James P. Braselton
Martha L. Abell and James P. Braselton are graduates of the Georgia Institute of Technology and the Ohio State University, respectively, and teach at Georgia Southern University, Statesboro where they have extensive experience instructing students at both the undergraduate and graduate levels. Other books by the authors include Differential Equations with Mathematica and Mathematica by Example.
Affiliations and expertise
Associate Professor EmeritusRead Introductory Differential Equations on ScienceDirect