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About This Course

Why Calculus Matters Now More Than Ever

Calculus is one of the most widely studied subjects in mathematics education worldwide. Here are some statistics that demonstrate its reach:

In the United States (2026 projections):

  • Approximately 800,000 high school students take calculus each year1
  • About 700,000 college students enroll in calculus courses annually2
  • Over 446,000 students take AP Calculus AB and BC exams each year3
  • Only 48% of U.S. high schools offer calculus, creating significant access disparities1

Worldwide:

  • An estimated 5 million students study calculus globally each year
  • Calculus serves as a gateway course for STEM fields including engineering, physics, computer science, and economics

These numbers represent millions of students working to master the same concepts you'll learn in this course. You're joining a global community of learners building the mathematical foundation for understanding change, motion, and optimization.

Delta Can Help

Did you know that traditional calculus textbooks at many US colleges and universities cost between $200 and $300?4 That's a steep slope to climb before you even start learning! And here's the real kicker—those expensive books don't even have interactive MicroSims to help you see what's happening.

I believe every student deserves access to high-quality calculus education, regardless of their budget. That's why this entire textbook is free and open source, with over 150 interactive simulations that let you explore calculus concepts hands-on. No paywalls, no access codes, no "edition 47 with slightly rearranged homework problems."

Let me help you master calculus without breaking the bank. Together, we've got this!

Learning Through Interactive Visualization

This course takes a fundamentally different approach to teaching calculus. Instead of drowning in abstract notation, you will build deep intuition through over 150 interactive MicroSimulations. These browser-based visualizations let you experiment with vectors, matrices, transformations, and decompositions in real-time.

Watch eigenvectors remain unchanged as transformations stretch space around them. See how SVD decomposes images into fundamental components. Explore how gradient descent navigates loss landscapes. Manipulate quaternions and witness how they elegantly solve the gimbal lock problem. These are not passive animations—they are hands-on laboratories where you control the parameters and discover the concepts yourself.

You Will Have Fun

Yes, you read that right. This course is designed to be genuinely enjoyable. The MicroSims turn abstract concepts into interactive playgrounds. The connections to real-world AI applications give every topic immediate relevance. And the satisfaction of truly understanding how modern technology works is deeply rewarding.

Whether you aspire to build the next breakthrough in AI, create stunning computer graphics, develop autonomous systems, or simply want to understand the mathematical foundations of our increasingly algorithmic world—this course will give you the tools, the intuition, and the confidence to succeed.

Let's explore the beauty of calculus together!

Background

The concepts covered by this book was generated by the following prompt:

Prompt

What standard organizations describe the concepts that should be covered in a high-school Calculus course that would maximize the probability that the student would get college credits for taking the course?

Our tools have also matured since January 2025 when we first started using AI to generate textbooks. This version of our intelligent textbook was generated using Claude Code Skills on February 3rd, 2026. We also put a much stronger focus on creating high-quality MicroSims that bring abstract concepts to life.

— Dan McCreary, February 3rd 2025

References

  1. Mathematical Association of America. The decline in high school calculus. MAA Math Values. ↩↩

  2. Duke University Mathematics Department. Who Studies Calculus and Why. ↩

  3. College Board. 2025 AP Score Distributions. AP Students. ↩

  4. Active Calculus. The cost of calculus texts. Notes that Calculus: Early Transcendentals (8th ed.) has a list price of $299.95, with discounted new copies around $250. ↩