Introduction to Applied Calculus

This course primarily involves an area of math known as differential calculus. In the study of differential calculus, we'll look at the definition, properties, and applications of the derivative.  The derivative is a useful tool for studying the graph of a function and the rate at which something changes.  We'll address applications of calculus in economics, business, biology, and other areas.  Because the course is designed to address applications, we tend to look at lots of word problems.

The history of calculus dates back to the Seventeenth Century, when Gottfried Wilhelm Leibniz and Sir Isaac Newton contributed to its development.   They actually quarreled over who deserves more of the credit for inventing calculus.  Newton apparently made his discoveries a little sooner, but Leibniz published before Newton.  Lebniz's notation is commonly used even today.

There are lots of reasons for studying calculus (besides its being required for your major). With calculus, we're able to study dynamically changing quantities.  Calculus is important in the study of biology, business, chemistry, economics, engineering, finance, and physics. Calculus sometimes is involved in financial planning, putting satellites into orbit, building stable bridges, and prescribing drug doses that are safe and effective.

Even if you don't wish to do any of these things, studying calculus will help you to cultivate an analytical way of approaching problems and situations.  This mindset helps one to become a better decision maker.  It also will make you better prepared to take other application courses, such as statistics.

To succeed in calculus, you'll need a good background in algebra, patience, and disciplined study habits.  There may be times when you have to work pretty hard to grasp new concepts.  This is a course in which few can afford to get behind; if you put in the work initially, though, the course will be fun.  

Make sure that you thoroughly read each covered section in the text.  Be prepared to read a section more than once (or even twice) before understanding it.  Always ask yourself "why?" -- why is the author discussing this right now?  why is the next step justified?  why was that step necessary? ....  Work hard to answer these questions, and talk to me when you can't come up with a good answer.

References:

  1. Calculus, 5th Edition, by Stanley Grossman and Richard Lane.  Published by Saunders College, 1993.
  2. A History of Mathematics: An Introduction, Second Edition, by Victor J. Katz.  Published by Addison Wesley Longman, Inc., 1998.
     
     
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