From Words to Algebra (Elementary Mathematical Modeling for Calculus)

　

The objective of these learning/reviewing units are to help calculus students to master the art of dealing with the so called story problems encountered in calculus. To be more precise, we will review and practice the skills to identify variables, to set up formulas or equations, and to model a daily-life problem into its mathematical setting (so that we can use Calculus as a tool to solve such daily life problems).

Learning Units	Skills
1.	Converting words to algebra (identifying the operations) (More practices)
2.	Converting words to algebra (identifying the relations)
3.	Setting up equalities
4.	Setting up equalities (with facts from geometry)
5.	Working with Calculus (applied minimum and maximum problems) The emphasis of this learning/reviewing unit is on the mathematical modeling. When learning and practicing skills in this unit, a student must know the routine of using calculus to determine the minimum or maximum value of a function. Finding the maximum volume Finding the minimum area Finding the minimum distance 　 Related Reading: How to find extrema of a function over a closed interval How to find extrema of a function over an open interval
6.	Working with Calculus (related rate problems) The emphasis of this learning/reviewing unit is on the mathematical modeling. When learning and practicing skills in this unit, a student must know the routine of computing derivatives, and in particular, a student must know how to correctly use the Chain Rule and the routine to compute derivatives using implicit differentiation.  Rates involving area Rates involving volume Related Reading: Chain Rule Implicit differentiation How to find related rates?