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# 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. While "test preparation" is not the main focus, this course is approved by the College Board as an AP Calculus BC class for students in grades 9-12 and goes beyond a standard Calculus BC curriculum.

25 weeks

SYLLABUS
25 weeks

## Schedule

### AoPS Holidays

There are no classes October 31, November 25 ‐ December 1, December 21 ‐ January 3, May 24 ‐ 26, July 4 ‐ 6, and August 29 ‐ September 1, 2025.

### 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

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

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!