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From students
"I just wanted to tell you that I am really enjoying the class so far! There are very few other classes I have taken in any discipline that have left me feeling so happy and fulfilled after struggling through a problem. Thank you and I look forward to the rest of the class."
A course in single-variable calculus. This course covers limits, continuity, derivatives and their applications, definite and indefinite integrals, infinite sequences and series, plane curves, polar coordinates, and basic differential equations. At the conclusion of the course, students should have sufficient preparation to take the AP Calculus BC exam; however, "AP exam preparation" is not the main focus of the course. (Note: this exam is not offered by Art of Problem Solving—you will have to privately arrange to take the exam at a local school if you are interested.)
There are two main things we hope to accomplish (that many high-school calculus courses do not):
For better or worse, the standard high-school calculus curriculum usually only stresses #1 a little bit and #2 not at all, in favor of repeated examples of solving essentially the same problem over and over again.
However, our course is not "rigorous" in the sense that a college-level Real Analysis course would be. Although we will try to gain a deeper understanding of many calculus concepts, we will not commit to rigorously proving every result. (On the other hand, the class will be supplemented with lecture notes that will go into the rigor of calculus in more detail, for the interested student.)
Week 1: Precalculus review
Week 2: Trig functions, logarithms, and exponentials
Week 3: Limits and continuity
Weeks 4-5: Derivative basics
Weeks 6-9: Applications of the derivative
Weeks 10-12: Antidifferentiation (indefinite intgerals)
Weeks 13-15: Definite integrals
Week 16: Infinity
Weeks 17-19: Sequences and series
Week 20: Plane curves
Week 21: Polar coordinates
Weeks 22-23: Differential equations
Week 24: Some harder problems
Week 25: Course review
There will be problem sets every 4 weeks (for a total of 6 problem sets during the course). Problem sets will contain both routine "review" problems to reinforce the basics, and harder, less trivial problems to develop calculus problem-solving skills. Students must complete the problem sets if they expect to learn calculus. Students will receive detailed feedback on their solutions. There will also be weekly problems (for which students will not receive feedback) after each class to reinforce that day's material.
Students who wish to enroll in calculus should be able to easily do most or all of the problems on the following diagnostic test without using a calculator:
We cannot stress this enough: students who do not have a solid algebra background will not be successful in a good calculus course. It is vital that students have mastered the basic high-school math curriculum—algebra, geometry, trigonometry—before attempting a calculus course. Also, this class is considerably more difficult than a typical high-school calculus course, as there will be a greater emphasis on solving hard problems, and less emphasis on "routine" calculations.
Taking calculus as the "next" course after an algebra or trigonometry course is not the right decision for many students. See our articles The Calculus Trap and Why Discrete Math Is Important for more discussion of this.
The Art of Problem Solving Calculus text will be available in fall, 2009. The cost of the textbook is included in the price of the class, and students enrolled in the class will receive the book when it is available.
We recommend that students have a graphing calculator to use as a tool in their study of calculus, and to have it with them at each class session. However, this is not required, and we will not be emphasizing calculator techniques. The AP Calculus exam (which Art of Problem Solving does not offer nor endorse) requires a graphing calculator; a list of AP-approved calculators is on the College Board website.
Future dates for this course have not been scheduled yet.
