Course description
Introduction to Differential Equations
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.
Upcoming start dates
Who should attend?
Prerequisites
Single variable calculus
Training content
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
Course delivery details
This course is offered through Massachusetts Institute of Technology, a partner institute of EdX.
3-6 hours per week
Costs
- Verified Track -$100
- Audit Track - Free
Certification / Credits
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.
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edX
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