MATH201 - First Order Differential Equations

This is the second course in a series of courses on ordinary differential equations or ODEs. This course in particular is on the subject of first order ODEs. The courses in this series so far are

• MATH200 - Introduction to Differential Equations
• MATH201 - First Order Differential Equations
• MATH202 - Applications of First Order ODEs
• MATH203 - Second Order Differential Equations

At this time only the first three courses are available, and this description will be updated as other courses in this series are available. We mentioned the next in the series because it is the furthest along and should be available soon.

The course outline is as follows:

• Introduction
• Review
• Simple Examples of First Order ODEs
  • Equations of the form y'=0
  • Equations of the form y'=ƒ(x)
  • Equations of the form y'-y=0
• First order linear differential equations
  • Standard Linear Form
  • Methods of Solution
    • Separation of Variables
    • Use of an Integrating Factor
  • General Solution
  • Existence and Uniqueness
• First order non-linear ODEs
  • Solvable Forms
    • Homogeneous equations
    • Exact Equations
    • Bernoulli Equations
  • Existence and Uniqueness
• Numerical Methods
  • Euler's Method
  • Second Order Runge-Kutta Method
  • Three Term Taylor Series
  • Fourth Order Runga-Kutta
  • Numerical Integration
  • Pitfalls of Numerical Methods
• Summary

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