Unit Synopsis: Unit 3 features uses and applications of the derivative for purposes of function analysis, estimation and optimization. This is the last major unit on differentiation. As with unit 2, this unit is divided into two parts.
The following programs written for the TI-83 are useful for the numerical and graphical study of definite integrals and differential equations. RSUMS is a program that allows you to calculate the left, right, and average (Trapezoid Rule) Riemann sums for a function of x that you enter into the calculator's equation editor. SLOPEFLD is a program that will draw a slope field for a differential equation in x and y that you enter into the calculator's equation editor. You must disable the graphing aspect of the editor (toggle the "=" sign) after entering the differential equation and before executing the program. EULERT is a program that numerically performs Euler approximations on a differential equation in x and y that you enter into the calculator's equation editor. EULERG is a program that graphically performs Euler approximations on a differential equation in x and y that you enter into the calculator's equation editor. Again, you must disable the graphing aspect of the editor (toggle the "=" sign) after entering the differential equation and before executing the program. The above programs were obtained courtesy of Mr. John Jensen of Rio Salado College in Tempe, Arizona.
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