Scientists and engineers understand the world through differential equations. You can too. 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.
Class Deals by MOOC List - Click here and see EdX's Active Discounts, Deals, and Promo Codes.
EdX keeps courses open for enrollment after they end to allow learners to explore content and continue learning. All features and materials may not be available, and course content will not be updated. Check back often to see when new course start dates are announced.
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.
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 course is part of the Differential Equations XSeries Program.
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.
Course 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
