Art of Problem Solving Calculus Set
A comprehensive textbook covering single-variable calculus. Specific topics covered include limits, continuity, derivatives, integrals, power series, plane curves, and differential equations.
Calculus is part of the acclaimed Art of Problem Solving curriculum designed to challenge high-performing middle and high school students. Calculus covers all topics from a typical high school or first-year college calculus course, including: limits, continuity, differentiation, integration, power series, plane curves, and elementary differential equations. The text is written to challenge students at a much deeper level than a traditional high school or first-year college calculus course.
The book includes hundreds of problems, ranging from routine exercises to extremely challenging problems drawn from major mathematics competitions such as the Putnam Competition and the Harvard-MIT Math Tournament. Many of the problems have full, detailed solutions in the text, and the rest have full solutions in the accompanying Solutions Manual.
Paperback (2nd edition). Text: 336 pages. Solutions: 128 pages.
More intense than a normal high school or first-year college course, this is a full course in single-variable calculus.
The intermediate series picks up where the introductory series leaves off. Please read that description (immediately preceding this one) as it applies to this series as well. Note that all AOPS books are intended for high-performing (motivated) math students. These are rigorous texts that require a high level of commitment from students, but the benefits are worth the extra effort. For comparison, this curriculum is more advanced than Saxon and rather like Life of Fred on steroids. It is like LOF in that often, teaching takes place through problem solving, even in the solutions to the problems. These books are huge compared to the LOF volumes which are, even then, largely devoted to the story of Fred's life. Math in LOF is taught in that context; we understand that Fred needs to calculate the derivative of a stock market equation in order to invest his penny while the slope is increasing AND why discovering that vertical asymptote resulted in his becoming a millionaire. Here, the heart of the course is the problem-solving. Virtually all of the text is devoted to this. Students are preparing for problem-solving competitions here and learning techniques and strategies to win. The other MAJOR difference is the amazing, complete solution manual provided in the AOPS curriculum. After working in LOF Calculus with Stephen, I REALLY appreciate having more than just an answer (honestly, it would be nice to not have to work through the problems myself when a question arises-call me lazy).
Students beginning this series should have either completed the Introductory level or, if coming from another curriculum, have completed Algebra I and Geometry at a minimum. Even then, they should take the diagnostic test for AOPS Introduction to Algebra and only tackle Intermediate Algebra if indicated. After completing Intermediate Algebra, students can choose to take either Intermediate Counting & Probability or Precalculus next, or do both simultaneously. Both should be completed before beginning Calculus. A brief description of courses appears below; see our website Table of Contents pages for a more complete scope and sequence.