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.
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