Differential Equations: Calculus: TI Math Nspired

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Differential Equations

Differential equations are in some sense the “reason for being” of the calculus, with the Fundamental Theorem of Calculus being one solution of the most basic differential equation: given dy/dx = f (x), what is y = F(x)? This unit examines some specific examples of the differential equations (leading to the exponential and logarithmic functions) as well as the important numerical technique of Euler’s Method for approximating solutions to differential equations. Other lessons consider some specific differential equations arising in the context of science.

Calculus: Differential Equations Activities

Title
Simple Harmonic Motion With an example of the motion of a child on a swing, the activity begins with the trigonometric function between time and displacement and differentiates up to acceleration. Standards \| Textbook	3144	14
Infestation to Extermination Students investigate exponential growth and decay through the situation of infestation and extermination. Standards \| Textbook	2906	11
Exponential Functions and the Natural Logarithm Discover a surprising property involving the relative growth rate of an exponential function. Standards \| Textbook	4706	11
Euler's Method Introduction Visualize the graph of an approximate solution to a differential equation and estimate a specific value of a solution. Standards \| Textbook	4755	13
Euler's Method Dynamic graphical representation of Euler's method that can be plotted one step at a time. Standards \| Textbook	4870	11
Torricelli's Law Students examine the velocity of water flowing through the tap of a tank, finding an equation to model the height of the water in the tank as the tank is drained. Standards \| Textbook	3407	12