微積分学: 概念入門 | パート B: 積分

This 10-week course teaches the conceptual groundwork that upholds calculus and explores fun examples of its application. With a focus on the ideas and the beauty of calculus, students will develop a rich understanding of this art.

This class is NOT a replacement for a standard calculus course. While we will be solving problems and performing calculations in class, it does not drill calculus problem-solving or cover all of the topics that are in a first-year calculus course. Instead, we focus on developing a conceptual understanding an appreciation, filled with fun real-world anecdotes and applications. Then who is this course for? Students who intend to take calculus and would like a preview that will help them succeed in their coming course, students who are currently enrolled in a course, students who have already studied calculus and would like to fortify their understanding, as well as students who don't intend to pursue a mathematically technical education but would still like to experience the beauty of calculus.

This course is offered in two parts. Part A: Derivatives and Part B: Integrals represent the two main concepts that make up calculus, roughly corresponding to the first and second halves of an introductory course. However, the standard ordering of these courses is somewhat arbitrary: derviatives and integrals are two sides of the same coin, and neither one is naturally *first*. Thus, I have designed these courses so that they may be taken in any order, or even concurrently!

The textbook for this course is Change Is the Only Constant: The Wisdom of Calculus in a Madcap World by Ben Orlin. Students are encouraged but not required to purchase the text. The text provides a more complete (and more humorous!) exploration of the concepts we will discuss in class.

Our class topics will be as follows (corresponding textbook chapters noted as well):
Lesson 1: Infinite Sums (ch. XVI & XVII)
Lesson 2: Approximation Techniques (ch. XVIII)
Lesson 3: Fundamental Theorem of Calculus (ch. XIX)
Lesson 4: Integration Rules (ch. XXI)
Lesson 5: Summing Happiness (ch. XXIII)
Lesson 6: Mean Value Theorem (ch. XXVI)
Lesson 7: Volumes of Solids (ch. XIV, XXV)
Lesson 8: Integrals to Infinity (ch. XXVII)
Lesson 9: Calculus in Statistics (ch. XXVIII)
Lesson 10: Wrapping Up