“Calculus” is a word that strikes fear in the hearts of many, but the underlying concepts of Calculus can easily be explained in a few minutes on a single sheet of paper using only basic algebra. Calculus is also used as a gateway course in many universities to “weed out” students from technical courses of study. Students who may have performed quite well in all of their other mathematics courses can falter and stumble at the first weeks of a Calculus course, or find themselves unable to explain in plain English the meaning and use of a derivative or integral.

However, Calculus can not only be a fun and mind enriching class, but a student who does well in Calculus will be much more prepared to perform smoothly in classes like differential equations, mathematical modeling, or higher level statistics courses.

Depending on the level of your Calculus course, you may begin by looking at proving limits using delta-epsilon proofs (sometimes non-Greek letters are substituted). The process of delta-epsilon proofs can be quite baffling as presented in most textbooks, but can be understood and mastered quickly with a bit of personal instruction.

What follows is a slow development of the concept of the derivative using methods for approximating the slope of a curved function at given points. The remainder of the first half of your textbook should focus on methods for finding derivatives of different types of functions. These methods can be thought of as a discrete set of tools.

The trick to learning these methods is learning to recognize when and where they can be applied, and then applying them constructively. Once the derivative has been introduced, this is what most of your beginning study of Calculus.

The second half of your textbook should begin with an introduction to the anti-derivative (or indefinite integral), its meaning and its uses. For this, you may have to spend some time learning to work with Riemann Sums.

Then, like in the first half of your textbook, you will spend the second half of your textbook learning methods for and recognizing patterns needed for taking integrals.

Calculus can be a difficult course, but with the help of a tutor who can simplify concepts and explain their roles in the “big picture” of Calculus, you can master your class and impress your professor.

I provide supplementary instruction (tutoring) for Calculus for $45 an hour. I provide more comprehensive homeschool instruction, including assigning homework and administering tests and quizzes for $50 an hour.