Introduction to Differential Equations (edX)

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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.
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