Learn Differential Equations II

Description

In this course, you will :

• Discover how to draw nonlinear pairs with a direction field.
• Apply multivariable calculus concepts to a key pair of nonlinear equations.
• Learn why linearization works so well by borrowing topological ideas.
• Learn how to break down a difficult linear pde into a series of simpler problems.
• Learn about the similarities and differences between signal analysis and linear pdes.
• Practice using the Fourier transform on the heat equation to learn how to use it effectively.
• Discover how infinite sums make it easier to solve difficult differential equations.
• Investigate some of the peculiarities and unique characteristics of infinite series.
• What's a good way to tell power series apart?

Syllabus :

1. Nonlinear Equations

• Lotka-Volterra 
• Linearization
• The Hartman-Grobman Theorem

 

2. Partial Differential Equations

• 1D Waves & d'Alembert's Formula
• Sources & Boundary Conditions
• Challenge: 2D & 3D Waves
• Separation of Variables & Waves

 

3. Transform Methods

• The Fourier Transform
• Practice: Fourier & The Heat Equation
• Practice: Fourier & Laplace's Equation
• Challenge: Fourier & 3D Waves

 

4. Power Series

• Series Solutions
• The Airy Equation
• Interlude: Return of the Wronskian

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