Differential equations are mathematical models that describe how certain quantities such as the position or velocity of a physical object change in response to changes in its surroundings. They allow one to make predictions about what will happen if you alter a variable, for example if you change the size of the soft drink can, or how your pie might bake when it starts out on a plate at different sizes. Differential Equations is a department that studies this field and aims to teach students how to use differential equations to solve many types of problems. Differential equations also study how these quantities change as a function of time, and often they are expressed in terms of functions or trigonometric functions.
Professor William Briggs is the chair of the department, and he believes that it’s important to teach students not just the techniques of solving differential equations but also the theory behind them. “We want students to learn why they’re solving those equations and what they’re really doing,” he said. He teaches a class called “Applied Differential Equations,” which focuses on how to think about differential equations and solve problems that arise in real life, such as climate change. “It’s like physics meets ecology. It’s a unique class in terms of its combination of applied mathematics and real-world applications,” he said.
The classic fifth edition of A First Course in Differential Equations is the definitive introduction to nonlinear differential equations. It is a perfect companion for anyone studying math, science, engineering, or economics. Its approachable and interactive style makes it ideal for students at all levels.
The book is extensively illustrated with worked examples illustrating the use of differential equations, and can be used with any standard calculus text. The text provides an introduction to linear algebra and the solution of ordinary differential equations and provides many worked out examples.
The book is well regarded and has received considerable praise from both students and their instructors. In 1970 a reviewer for the Mathematics Teacher (p. 319) stated that “It would be hard to exaggerate the usefulness of this book for instructors who are new to differential equations. It is attractively priced, provides a mass of excellent information, and is written in a clear, concise manner.” A criticism of the first edition was that it did not contain enough exercises. This has been addressed in the second and third editions.
The fifth edition of the book is also used in some graduate courses at the University of Oklahoma where Pugh is a professor.