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 = 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.'

Type of Material:

Online Course

Recommended Uses:

Homework, individual, self-paced

Students hoping for online course credit or looking for supplemental material in preparing for or taking a traditional Calculus course.

Technical Requirements:

To receive credit the student must have a WebCam enabled computer for the final exam.

Identify Major Learning Goals:

This is a standard Calculus Course, with reading material, self tests, problem sets and a final exam.

Target Student Population:

College General Ed, College Lower Division

While this course is aimed at students, teachers may want to view it to get ideas and examine the teaching materials provided.

Prerequisite Knowledge or Skills:

Students must have a math background that prepares the students for Calculus. The material states that the student must have a sound background in algebra, but many students of calculus find that a course in Geometry and Solid Geometry helps. Students must be self motivated enough to read the material and work the practice problems.

Content Quality

Rating:

Strengths:

Sections contain illustrated information, practice problems, problem sets (need login) and review materials. Each unit concludes with a graded problem set that is only available to those who log in with a full user account.

Concerns:

Students using school computers may be prohibited by school rules from logging into this course, but the materials do contain practice problems with answers that do not require a log in.

Potential Effectiveness as a Teaching Tool

Rating:

Strengths:

Each section has clear Learning Outcomes.The material in all units is complete and comprehensive.There are practice problems for each unit.

Concerns:

None.

Ease of Use for Both Students and Faculty

Rating:

Strengths:

Sections are labeled, there are images to aid the learner. There is even a help area the user can click on.

Concerns:

None.

Other Issues and Comments:

Excellent resource for teachers and students. Students in this course may use the material to review and practice. They may also take the course for credit. Teachers may examine the material to expand the ways that they can better help students.

Creative Commons:

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