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Calculus I

by The Saylor Foundation

This course material is only available in the iTunes U app on iPhone or iPad.

Course Description

This course is one of nearly 100 college-level, online courses created by Saylor Academy and available through your web browser on any device. Every Saylor Academy course offers a free certificate of completion and many courses connect to flexible and affordable college credit. Discover Saylor Academy’s full catalog here.

Purpose of Course
Calculus can be thought of as the mathematics of CHANGE.  Because everything in the world is changing, calculus helps us track those changes.  Algebra, by contrast, can be thought of as dealing with a large set of numbers that are inherently CONSTANT.  Solving an Algebra problem, like Y = 2X + 5, merely produces a pairing of two predetermined numbers, although an infinite set of pairs.  Algebra is even useful in rate problems, such as calculating how the money in your savings account increases because of the interest rate R, such as Y = X0+Rt where t is elapsed time and X0 is the initial deposit.  But with compounded interest, now things get complicated for algebra as the rate R is now itself a function of time with Y = X0 + R(t)t.  Now we have a rate of change which itself is changing.  Calculus “to the rescue,” as Isaac Newton introduced the world to mathematics specifically designed to handle “those things that change.” Calculus is among the most important and useful developments of human thought. Even though it is over 300 years old, it is still considered the beginning and cornerstone of modern mathematics.  It is a wonderful, beautiful, and useful set of ideas and techniques.  You will see the fundamental ideas of this course over and over again in future courses in mathematics as well as in all of the sciences, including physical, biological, social, economic, and engineering. However, calculus is an intellectual step up from your previous mathematics courses.  Many of the ideas you will learn in this course are more carefully defined and have both a functional and a graphical meaning.  Some of the algorithms are quite complicated, and in many cases, you will need to make a decision as to which appropriate algorithm to use.  Calculus offers a huge variety of applications and many of them will be saved for future courses you might take. This course is divided into four learning sections, or units, plus a reference section, or Appendix.  The course begins with a unit that provides a review of algebra specifically designed to help and prepare for the study of calculus.  The second unit discusses functions, graphs, limits, and continuity.  Understanding “limits” could not be more important as that topic really begins the study of calculus.  The third unit will introduce and explain derivatives.  With derivatives we are now ready to handle all those “things that change” mentioned above.  The fourth unit makes “visual sense” of derivatives by discussing derivatives and graphs.  Finally, the fifth unit provides a large collection of reference facts, geometry, and trigonometry that will assist in solving calculus problems long after the course is over.

This course has been developed through a partnership with the Washington State Board for Community and Technical Colleges. Unless otherwise noted, all materials are licensed under a Creative Commons Attribution 3.0 Unported License. The Saylor Foundation has modified some materials created by the Washington State Board for Community and Technical Colleges in order to best serve our users.

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