Continuation; Applications to Temperature, Mixing, RC-circuit, Decay, and Growth Models
In this lecture, the professor applies ODEs to real-world situations such as temperature, mixing, RC-circuits, decay, and growth models. He starts off by reviewing some basic knowledge on solving equations with sinusoidal inputs and complex numbers. Then he explains the polar and Cartesian methods of solving the equations and connects them with a famous trigonometric identity formula. The lecture provides a comprehensive explanation of how to convert complex solutions into real numbers and the importance of understanding the phase lag and amplitude in solving ODEs.
Continuation; Applications to Temperature, Mixing, RC-circuit, Decay, and Growth Models -- Lecture 8. More applications of ODEs in real-world situations.
Arthur Mattuck, 18.03 Differential Equations, Spring 2006. (Massachusetts Institute of Technology: MIT OpenCourseWare), http://ocw.mit.edu (Accessed November 26, 2008). License: Creative Commons BY-NC-SA.
More info at: http://ocw.mit.edu/terms
- Lecture Notes - Lecture Notes
- Problem Set 2 - Problem Set 2
- Problem Set 2 Solutions - Problem Set 2 Solutions
- Recitation Problems - Recitation Problems and classwork exercises
- Recitation Solutions - Recitation problem solutions
- Muddy Card Responses - Muddy Card Responses are explanations of topics that were confusing to students
- What are some real-world applications to ODEs?
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Staff Review
This lesson takes off from the previous lesson and does more application with complex numbers, exponentials, and trig functions. This is a very involved lesson including many applications to temperature, decay and growth models, mixing, and circuits. Also, vectors are mixed in.
