# Download Calculus in Context, The Five College Calculus Project by James Callahan, Kenneth Hoffman, David Cox, Donal O’Shea PDF

By James Callahan, Kenneth Hoffman, David Cox, Donal O’Shea ,Harriet Pollatsek, Lester Senechal

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Extra info for Calculus in Context, The Five College Calculus Project

Example text

1. THE SPREAD OF DISEASE 21 day the river might even vanish! Here is a passage that shows us some of the pitfalls in using rates to predict the future and the past. In the space of one hundred and seventy six years the Lower Mississippi has shortened itself two hundred and forty-two miles. That is an average of a trifle over a mile and a third per year. Therefore, any calm person, who is not blind or idiotic, can see that in the Old O¨olitic Silurian Period, just a million years ago next November, the Lower Mississippi was upwards of one million three hundred thousand miles long, and stuck out over the Gulf of Mexico like a fishing-pole.

You will find that we will use the other forms more often. Copyright 1994, 2008 Five Colleges, Inc. 2. THE MATHEMATICAL IDEAS 35 Functions of Several Variables Language and notation. Many functions depend on more than one variable. For example, sunrise depends on the day of the year but it also depends on the latitude (position north or south of the equator) of the observer. Likewise, the crop yield from an acre of land depends on the amount of fertilizer used, but it also depends on the amount of rainfall, on the composition of the soil, on the amount of weeding done—to mention just a few of the other variables that a farmer has to contend with.

Of course, if we had to give a million instructions to make the computer carry out a million steps, there would be no savings in labor. The trick is to write a program with just a few instructions that can be repeated over and over again to do all the calculations we want. The usual way to do this is to arrange the instructions in a loop. To give you an idea what a loop Copyright 1994, 2008 Five Colleges, Inc. DVI file created at 11:39, 1 February 2008 16 CHAPTER 1. A CONTEXT FOR CALCULUS is, we’ll look at the S-I-R calculations.