## Calculus — Tutoring, AP Calculus Preparation, and Full Courses

**As will be explained below, it is strongly recommended that calculus students start off their calculus course, whether high school or college, under the guidance of a competent and experienced tutor who is highly proficient in calculus.**

### What is Calculus?

Except for statistics, mathematics courses taught in high school beyond basic Algebra and Geometry are primarily intended to prepare students for calculus. What is calculus, and why do many academic college degrees require it?

Calculus is essentially the mathematics of change. Our universe is fundamentally characterized by change, and to better understand the world around us, including human affairs, we find calculus provides valuable insights that benefit all students, even those who are pursuing liberal arts degrees. Of course, calculus is the language of science and engineering, and those pursuing technical degrees *must* become proficient in calculus.

A rigorous course in calculus is not easy. Some students who found precalculus relatively easy discover calculus to be difficult. Why? Calculus is a major a departure from all prior math classes — new concepts such as the limit, continuity, the differential/derivative, the integral, and infinite series, among other topics, require a student to study math in a more intuitive, and less mechanical, manner. In high school math, many students do well without having to deeply understand the underlying concepts. Not so in calculus, which requires fundamental understanding of the concepts and to apply those concepts in intuitive ways to solve calculus problems.

### High School vs. College Calculus

Most college and university math departments insist that calculus is best taught at the college level. Why they hold this view will not be discussed here since the arguments are lengthy (and compelling.) Suffice to say, most universities, especially the higher-tier ones, will not accept high school calculus courses alone for calculus credit. This is why they require a high school student who has taken a high school calculus course to pass the challenging AP Calculus exam (either the *AB* or the more difficult and broader *BC*) with a very high score, usually a minimum of a ‘4’ (with a maximum score of ‘5’) in order to be given some college credit in calculus.

Passing the AP Calculus exam with a high score assures the university that the student has mastered both the mechanics and the underlying principles of calculus, is ready to take higher level math classes (such as calculus 2 or 3), and is prepared for basic science classes which require a working knowledge of calculus, such as physics.

### How Do I Prepare, or Know I am Prepared, for Calculus?

**Before a student enrolls in a calculus 1 course, it is very important that he or she recently mastered a comprehensive precalculus course**, including a complete study of unit circle trigonometry and related topics.

Sometimes I tutor a student who, for some unusual circumstance, was allowed to enter calculus 1 without sufficient precalculus preparation, or who took precalculus some time ago but has forgotten much of it. I have tutored a number of adults who returned to college after a number of years and jumped right into calculus without refreshing their knowledge of precalculus. In many cases they end up having to withdraw from calculus, or worse failing, oftentimes causing difficulty with their employer who is helping pay for their education — don’t let this happen to you!

It is important to note that calculus assumes the student has *fully* mastered all math up through precalculus (including unit circle trigonometry) — it is rare for any calculus course to review the math the student is expected to know and be proficient. Calculus is a lot like being thrown in the deep end of the pool — the student is expected to already know how to “swim”.

If you are unsure whether you are adequately prepared for high school or college calculus, there are a number of precalculus end-of-course tests (and similar tests) freely available on the Internet (for example, look for practice CLEP precalculus tests.) If you take such a test and do well, then you may be ready for calculus. Alternatively, you may peruse a reputable precalculus textbook (such as an edition authored by Larson and Hostetler.) If a significant number of the topics in the test or textbook are unfamiliar to you, then you will need to take precalculus, or even a course to prepare for a formal precalculus course.

### Why Most Calculus Students Need a Tutor

**It is strongly recommended that calculus students start off their calculus course, whether high school or college, under the guidance of a competent and experienced tutor who is highly proficient in calculus.**

The most critical time in learning calculus is in the first few weeks of the course, and not at the end! If the fundamental concepts introduced early in the course such as the limit, continuity, and the definition (and meaning) of a differential/derivative are not mastered and understood at an intuitive, fundamental level, then the rest of the course will literally "eat the student alive." Student withdrawal rates in calculus (particularly calculus 1) are quite high — hiring a tutor late in the course to help a student dig himself or herself out of a deep hole is usually too late. One cannot become proficient in calculus until the fundamentals are fully grasped — there is no shortcut to learning calculus!

### Why have Dr. Jon Noring **(“Dr. Calculus”)** as Your Calculus Tutor?

As a former Ph.D. research engineer/scientist for three prestigious DOE National Labs, I have a high level of proficiency, both theoretical and practical, in higher mathematics. My proficiency includes all levels of calculus, ordinary and partial differential equations, and numerical analysis. I have taught calculus at the high school level, and have successfully tutored all levels of calculus to a number of high school and college students, including preparation for the AP Calculus exam. Calculus is my specialty!

In addition, I know how to relate to students no matter their learning styles and personalities. I will help each student to individually break through the “brick wall” which has kept him or her from advancing in calculus.

For more information on my tutoring service, refer to my tutoring page.

### High School Level Calculus Courses

For more information on setting up a calculus class for homeschooled high school students, and to prepare them for the AP Calculus exam, refer to my page High School Math Courses for Homeschooled Students.