BERG > NEXUS Project > Development page > Assessing Competencies
Rates of Change
Understanding to describe the way things change mathematically is a critical tool in understanding a wide variety of phenomena relevant to biology ranging from fluid flow to epidemiology. Some of the specific knowledge and skills that students need to know in order to both be able to use this idea formally and to make sense of it include the following.
- Students should be able to clearly distinguish and not confuse a quantity, a change in that quantity, and the rate of change of that quantity (either with respect to space, time, or some other parameter).
- Students should be able to calculate the derivative of basic functions, including powers, exponents, and trig functions, with respect to a variable that appears in conjunction with a constant (f(ax)).
- Students should be able to determine the dimensionality of a derivative and explain why it has the dimensions it does.
- Students should be able to infer the rate of change of a function from a graph of the function.
- Students should be able to infer the shape of the graph of a function from a graph of its derivative.
- Students should be able to interpret rates of change as ways of inferring values of a function at points where it had not been previously known.
- Students should be able to use the above idea to solve a simple differential equation numerically by stepping using a spreadsheet or another programming environment.
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