Summer Course: Calculus

The Calculus Course addresses a variety of topics centered around the theme of "calculus with infinite processes", largely the content of BC-level AP Calculus that isn't in the AB-level syllabus. It is needed throughout probability and statistics at all levels, as well as to understand approximation procedures that arise in all quantitative fields (including economics and computer graphics).

After an initial review of limit rules, the course goes on to discuss sequences of numbers and functions, as well as limits "at infinity" for each (needed for any sensible discussion of the long-term behavior of a numerical process, such as iterative procedures and complexity in computer science, dynamic models throughout economics, and repeated trials with data in any field). Integration is discussed for rational functions (a loose end from Math 20) and especially (improper) integrals for unbounded functions and "to infinity": this shows up in contexts as diverse as escape velocity for a rocket, the present value of a perpetual yield asset, and important calculations in probability (including the famous "bell curve" and to understand why many statistical tests work as they do).

The course then turns to infinite series (how to "sum" an infinite collection of numbers), some useful convergence and divergence rest for these, and the associated killer app: power series and their properties, as well as Taylor approximations, all of which provide the framework that underlies virtually all mathematical models used in any quantitative field.

Details

MATH 21

• Class Number: 23547
• Course Cost: $5788.00
• Population: High School, Undergraduate, Graduate
• Units: 4
• Interest Area: Math and Data Science
• Course Format & Length: In-Person, 8 weeks
• Instructors: TBD

Events and Engagement

Workshops

Hosted through the Summer Academic Resource Center (SARC), we offer a variety of educational workshops to complement your academic pursuits. Presenters varying from Stanford affiliates, community partners, and graduate tutors will cover a wide range of topics from academic skills to career exploration. Past workshops included college preparedness, software exploration, and building your professional network.

Stanford Spaces

Explore the intellectual ecosystem of the Stanford campus. Tour museums like the Cantor Arts Center, visit unique campus spaces like the d.school, Frost Amphitheater, and O’Donohue Family Farm, and get to know the unique community of companies and innovators that gather at Stanford Research Park.

Stanford Voices

These small gatherings give you an opportunity to connect with Stanford faculty, fellows, and alumni to hear about their work or research, as well as the road that brought them there. Ask questions and continue your intellectual exploration—whether you're taking a course on the topic this summer or just curious.