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Book DetailsAMS/MAA TextbooksVolume: 25; 2014; 315 pp
Now available in Second Edition: TEXT/43
This book presents a modern treatment of material traditionally covered in the sophomore-level course in ordinary differential equations. While this course is usually required for engineering students the material is attractive to students in any field of applied science, including those in the biological sciences.
The standard analytic methods for solving first and second-order differential equations are covered in the first three chapters. Numerical and graphical methods are considered, side-by-side with the analytic methods, and are then used throughout the text. An early emphasis on the graphical treatment of autonomous first-order equations leads easily into a discussion of bifurcation of solutions with respect to parameters. The fourth chapter begins the study of linear systems of first-order equations and includes a section containing all of the material on matrix algebra needed in the remainder of the text. Building on the linear analysis, the fifth chapter brings the student to a level where two-dimensional nonlinear systems can be analyzed graphically via the phase plane. The study of bifurcations is extended to systems of equations, using several compelling examples, many of which are drawn from population biology. In this chapter the student is gently introduced to some of the more important results in the theory of dynamical systems. A student project, involving a problem recently appearing in the mathematical literature on dynamical systems, is included at the end of Chapter 5. A full treatment of the Laplace transform is given in Chapter 6, with several of the examples taken from the biological sciences. An appendix contains completely worked-out solutions to all of the odd-numbered exercises.
The book is aimed at students with a good calculus background that want to learn more about how calculus is used to solve real problems in today's world. It can be used as a text for the introductory differential equations course, and is readable enough to be used even if the class is being "flipped." The book is also accessible as a self-study text for anyone who has completed two terms of calculus, including highly motivated high school students. Graduate students preparing to take courses in dynamical systems theory will also find this text useful.
Ancillaries:
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Table of Contents
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Chapters
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Chapter 1. Introduction to Differential Equations
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Chapter 2. First-order Differential Equations
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Chapter 3. Second-order Differential Equations
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Chapter 4. Linear Systems of First-order Differential Equations
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Chapter 5. Geometry of Autonomous Systems
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Chapter 6. Laplace Transforms
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Appendix A. Answers to Odd-numbered Exercises
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Appendix B. Derivative and Integral Formulas
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Appendix C. Cofactor Method for Determinants
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Appendix D. Cramer’s Rule for Solving Systems of Linear Equations
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Appendix E. The Wronskian
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Appendix F. Table Of Laplace Transforms
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Additional Material
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Reviews
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This is a textbook that could be used for a standard undergraduate course in ordinary differential equations. It is substantially cheaper than most of the alternatives from commercial publishers, it is well-written, and it appears to have been carefully proofread. The target audience seems to be students whose background in mathematics is not particularly strong. ... The approach is modern in the sense that computer algebra systems are presented as important tools for the student, and also in the sense that geometric treatment of nonlinear equations gets substantial attention.
Christopher P. Grant, Mathematical Review Clippings -
Although Noonburg's book is slim, it covers (and covers well) all of the familiar topics one expects to find in a first semester sophomore-level ODE course, and then some. It also has some interesting features that distinguish it from most of the existing textbook literature ... The author's writing style is very clear and should be quite accessible to most students reading the book. There are lots of worked examples and interesting applications, including some fairly unusual ones. ... This book offers a clean, concise, modern, reader-friendly approach to the subject, at a price that won t make an instructor feel guilty about assigning it. It is certainly worth a very serious look.
Mark Hunacek MAA Reviews -
... The writing is clear, the problems are good, and the material is well motivated and largely self-contained. Some previous acquaintance with linear algebra would, however, be helpful. In summary, this new book is highly recommended for students anxious to discover new techniques.
SIAM Review
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- Book Details
- Table of Contents
- Additional Material
- Reviews
Now available in Second Edition: TEXT/43
This book presents a modern treatment of material traditionally covered in the sophomore-level course in ordinary differential equations. While this course is usually required for engineering students the material is attractive to students in any field of applied science, including those in the biological sciences.
The standard analytic methods for solving first and second-order differential equations are covered in the first three chapters. Numerical and graphical methods are considered, side-by-side with the analytic methods, and are then used throughout the text. An early emphasis on the graphical treatment of autonomous first-order equations leads easily into a discussion of bifurcation of solutions with respect to parameters. The fourth chapter begins the study of linear systems of first-order equations and includes a section containing all of the material on matrix algebra needed in the remainder of the text. Building on the linear analysis, the fifth chapter brings the student to a level where two-dimensional nonlinear systems can be analyzed graphically via the phase plane. The study of bifurcations is extended to systems of equations, using several compelling examples, many of which are drawn from population biology. In this chapter the student is gently introduced to some of the more important results in the theory of dynamical systems. A student project, involving a problem recently appearing in the mathematical literature on dynamical systems, is included at the end of Chapter 5. A full treatment of the Laplace transform is given in Chapter 6, with several of the examples taken from the biological sciences. An appendix contains completely worked-out solutions to all of the odd-numbered exercises.
The book is aimed at students with a good calculus background that want to learn more about how calculus is used to solve real problems in today's world. It can be used as a text for the introductory differential equations course, and is readable enough to be used even if the class is being "flipped." The book is also accessible as a self-study text for anyone who has completed two terms of calculus, including highly motivated high school students. Graduate students preparing to take courses in dynamical systems theory will also find this text useful.
Ancillaries:
-
Chapters
-
Chapter 1. Introduction to Differential Equations
-
Chapter 2. First-order Differential Equations
-
Chapter 3. Second-order Differential Equations
-
Chapter 4. Linear Systems of First-order Differential Equations
-
Chapter 5. Geometry of Autonomous Systems
-
Chapter 6. Laplace Transforms
-
Appendix A. Answers to Odd-numbered Exercises
-
Appendix B. Derivative and Integral Formulas
-
Appendix C. Cofactor Method for Determinants
-
Appendix D. Cramer’s Rule for Solving Systems of Linear Equations
-
Appendix E. The Wronskian
-
Appendix F. Table Of Laplace Transforms
-
This is a textbook that could be used for a standard undergraduate course in ordinary differential equations. It is substantially cheaper than most of the alternatives from commercial publishers, it is well-written, and it appears to have been carefully proofread. The target audience seems to be students whose background in mathematics is not particularly strong. ... The approach is modern in the sense that computer algebra systems are presented as important tools for the student, and also in the sense that geometric treatment of nonlinear equations gets substantial attention.
Christopher P. Grant, Mathematical Review Clippings -
Although Noonburg's book is slim, it covers (and covers well) all of the familiar topics one expects to find in a first semester sophomore-level ODE course, and then some. It also has some interesting features that distinguish it from most of the existing textbook literature ... The author's writing style is very clear and should be quite accessible to most students reading the book. There are lots of worked examples and interesting applications, including some fairly unusual ones. ... This book offers a clean, concise, modern, reader-friendly approach to the subject, at a price that won t make an instructor feel guilty about assigning it. It is certainly worth a very serious look.
Mark Hunacek MAA Reviews -
... The writing is clear, the problems are good, and the material is well motivated and largely self-contained. Some previous acquaintance with linear algebra would, however, be helpful. In summary, this new book is highly recommended for students anxious to discover new techniques.
SIAM Review
