Calculus

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.

25 weeks

Diagnostics

ARE YOU READY?
25 weeks ARE YOU READY?  

Schedule

Fall 2015This course will be offered in Fall 2015. Click here to join our mailing list to be notified when the course schedule is available.

AoPS Holidays

There are no classes on May 25, July 3, September 7, or November 23-27.

Who Should Take?

Students who wish to enroll in Calculus should be able to easily solve most or all of the problems on the diagnostic test above without using a calculator.

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.

Lessons

Lesson 1 Sets and Functions
Lesson 2 Trig Functions, Logarithms, and Exponentials
Lesson 3 Limits and Continuity
Lesson 4 Definition of the Derivative
Lesson 5 Chain Rule and Implicit Differentiation
Lesson 6 Interpretation of the Derivative
Lesson 7 Optimization
Lesson 8 More Derivative Applications
Lesson 9 Related Rates
Lesson 10 The Fundamental Theorem of Calculus
Lesson 11 Integration I
Lesson 12 Integration II
Lesson 13 Integration III
Lesson 14 Applications of the Integral
Lesson 15 Infinity
Lesson 16 Improper Integrals
Lesson 17 Sequences
Lesson 18 Taylor Series
Lesson 19 Parametric Curves
Lesson 20 Polar Coordinates
Lesson 21 Extra Problems Day
Lesson 22 Differential Equations I
Lesson 23 Differential Equations II
Lesson 24 Some Harder Problems
Lesson 25 Course Review

Required Textbook

Calculus
By David Patrick

A comprehensive textbook covering single-variable calculus. Specific topics covered include limits, continuity, derivatives, integrals, power series, plane curves, and differential equations.

I thoroughly enjoyed this course while learning a ton! While challenging, the homework was rewarding to complete. It taught me not only the core material, but also how to extend and combine everything I learned thus far. My favorite part, however, was how the instructor would always delve into applications of Calculus after teaching the material. Seeing that Calculus is constantly applied in many fields of physics helped bring it alive for me. I rarely walk out of an AP test feeling good, but I feel great about taking the AP Calculus BC exam--this course was excellent preparation for it. Thanks again--I've learned so much!

ACS WASC
ACCREDITED
SCHOOL

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