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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.
The five modules in this seriesare being offered as an XSeries on edX. Please visit the Differential EquationsXSeries Program Pageto learn more and to enroll in the modules.
Photo by user: bizoo_n. Copyright © 2016 Adobe Systems Incorporated. Used with permission.
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- 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.
Prerequisite
Single variable calculus
Syllabus
Unit 1
- Introduction to differential equations and modeling
- Complex numbers
- Solving first order linear differential equations
Unit 2
- The complex exponential
- Sinusoids
- Higher order linear differential equations
- Characteristic polynomial
Unit 3
- Harmonic oscillators
- Operators
- Complex replacement
- Resonance
Unit 4
- Graphical methods and nonlinear differential equations
- Autonomous equations
- Numerical methods
Instructors
David Jerison
Professor of Mathematics
Massachusetts Institute of Technology
Arthur Mattuck
Emeritus Professor of Mathematics
Massachusetts Institute of Technology
Haynes Miller
Professor of Mathematics
Massachusetts Institute of Technology
Jennifer French
Digital Learning Scientist and Lecturer
Massachusetts Institute of Technology
Duncan Levear
Postdoctoral Associate/DLL
Massachusetts Institute of Technology
Content Designer
MIT is a world-class educational institution where teaching and research — with relevance to the practical world as a guiding principle — continue to be its primary purpose.
MIT is independent, coeducational, and privately endowed. Its five schools and one college encompass numerous academic departments, divisions and degree-granting programs, as well as interdisciplinary centers, laboratories and programs whose work cuts across traditional departmental boundaries.
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Excelente!
Excelente!
