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This is a free online course offered by the Saylor Foundation.'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...
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This is a free online course offered by the Saylor Foundation.
'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 = X_{0}+Rt where t is elapsed time and X_{0} 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 = X_{0}+ 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.'
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MERLOT (www.merlot.org) and Quality Matters(www.qualitymatters.org) are collaborating on a project where Quality Matters will apply its expert capabilities in peer reviewing online courses to the open and free online courses in MERLOT. QM Peer Reviewers benefit from the practice of applying their review skills, and MERLOT users benefit from the reviews that can help them make better choices of materials.
The QM Peer Review Process: This was an unofficial QM review in which reviewers applied the QM Higher Education Rubric (4th Edition). The project began in July 2014, with the reviews completed by September 2014. A QM Master Reviewer led each QM Peer Review team.
Guidance for Faculty Adoption: The final report contains detailed reviewer feedback, organized by QM Standard, about the strengths of the course and areas for improvement. Faculty are encouraged to consider all of the feedback as they customize this material for use in their own courses and to share with the community their amendments to improve the quality of the course.
The QM Course Review Final Report - Higher Education is provided below. Please note that the QM Rubric is owned with full copyright by Maryland Online, Inc. (“MOL”).and administered by QM under exclusive license.
This course received 80 out of 95 possible points in the review, and did not meet the following QM standards.