Differential Equations: Fourier Series and Partial Differential Equations
After this course, you will be able to use Fourier series to solve Differential Equations with periodic input or boundary conditions.
Differential Equations: Fourier Series and Partial Differential Equations
After this course, you will be able to use Fourier series to solve Differential Equations with periodic input or boundary conditions.
Differential equations are the mathematical language we use to describe the world around us. Many phenomena are not modeled by differential equations, but by partial differential equations depending on more than one independent variable. In this course, we will use the Fourier series methods to solve ODEs and separable partial differential equations. You will learn how to describe any periodic function using Fourier series, and will be able to use resonance and to determine the behavior of systems with periodic input signals that can be described in terms of Fourier series. This course will use MATLAB to assist computations.
What you'll learn
- How to describe periodic functions using Fourier series.
- How to solve ODEs with Fourier series input.
- How to solve separable PDEs using Fourier series inputs and boundary conditions.
Prerequisites
Introduction to Differential Equations (basic), some linear algebra preferred
Meet your instructors
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Professor of Mathematics -
Professor of Mathematics, emeritus -
Lecturer in Mathematics
David Jerison
David Jerison
Professor of Mathematics
David Jerison received his Ph.D. from Princeton University in 1980, and joined the mathematics faculty at MIT in 1981. In 1985, he received an A.P. Sloan Foundation Fellowship and a Presidential Young Investigator Award. In 1999 he was elected to the American Academy of Arts and Sciences. In 2004, he was selected for a Margaret MacVicar Faculty Fellowship in recognition of his teaching. In 2012, the American Mathematical Society awarded him and his collaborator Jack Lee the Bergman Prize in Complex Analysis.
Professor Jerison's research focuses on PDEs and Fourier Analysis. He has taught single variable calculus, multivariable calculus, and differential equations at MIT several times each.
Arthur Mattuck
Arthur Mattuck
Professor of Mathematics, emeritus
Arthur Mattuck received his Ph.D. from Princeton University in 1954. He joined the MIT mathematics faculty in 1958. His research interests focus on problems in algebraic geometry. In 1992, he was among the first group of faculty to be designated Margaret MacVicar Fellows.
Professor Mattuck has been widely recognized as one of the Institute's most effective and innovative lecturers of core subjects, developing much of the calculus sequence used at MIT. His 1981 publication, The Torch and the Firehose: A Guide To Section Teaching, has served as a model guide both within MIT and outside.
Jennifer French
Jennifer French
Lecturer in Mathematics
Jen French worked on developing online educational math content for 10 years with the MIT Department of mathematics. In that time she developed 10 MOOCs, several interactive visualizations, and a sketchResponse tool to enable instructors to auto grade student math sketches. She is currently teaching math in a first-year cohort at MIT called Concourse.