Introduction to Differential Equations
Scientists and engineers understand the world through differential equations. You can too.
Course Information
About this Course
How do you design: A boat that doesn’t tip over as it bobs in the water? The suspension system of a car for a smooth ride? Circuits that tune to the correct frequencies in a cell phone?
How do you model: The growth of antibiotic resistant bacteria? Gene expression? Online purchasing trends?
The answer: Differential Equations.
Differential equations are the language of the models we use to describe the world around us. In this mathematics course, we will explore temperature, spring systems, circuits, population growth, and biological cell motion to illustrate how differential equations can be used to model nearly everything in the world around us.
We will develop the mathematical tools needed to solve linear differential equations. In the case of nonlinear differential equations, we will employ graphical methods and approximation to understand solutions.
This is part of a 5-part series in Differential Equations:
What you'll learn
- Use linear differential equations to model physical systems using the input/system response paradigm.
- Solve linear differential equations with constant coefficients.
- Gain intuition for the behavior of a damped harmonic oscillator.
- Understand solutions to nonlinear differential equations using qualitative methods.
Prerequisites
Single variable calculus
Meet your instructors
Haynes Miller
Professor of Mathematics, emeritus
Haynes Miller joined the MIT mathematics faculty as professor in 1986. A graduate of Harvard, he received the Ph.D. from Princeton under the direction of John Moore in 1974. Following assistant professorships at Harvard and Northwestern Universities, he joined the faculty of the University of Washington in 1977, and the faculty of Notre Dame as professor in 1984. Professor Miller is an algebraic topologist. In 1992-93, he served as Chair of the Pure Mathematics Committee. From 2004 to 2013 Professor Miller has chaired the Undergraduate Mathematics Committee, which he continued as Associate Department Head from July 2011-June 2013. He has worked on many educational initiatives, such as the Cambridge-MIT Exchange program, for which he received the Cambridge-MIT fellowship in 2003. Professor Miller was selected by MIT to be a MacVicar Faculty Fellow in 2005 for "exemplary and sustained contributions to the teaching and education of undergraduates at MIT." He also received the Graduate Student Council Teaching Award of the School of Science in 2006.
