Course Homepage Preface On Learning
1. 1-Minute Summary 2. X-Ray Vision 3. 3d Intuition
Learn The Lingo
4. Integrals, Derivatives 5. Computer Notation
Basic Understanding
6. Improved Algebra 7. Linear Changes 8. Squared Changes
Deeper Understanding
9. Infinity 10. Derivatives 11. Fundamental Theorem
Figure Out The Rules
12. Add, Multiply, Invert 13. Patterns In The Rules 14. Take Powers, Divide
Put It To Use
15. Archimedes' Formulas Summary

## Preface: Intuition-First Learning

Welcome to the Calculus course! Before we start, just a quick note about the intuition-first learning approach.

### Move From Blurry To Sharp

What's a better learning strategy: full detail from start-to-finish, or progressively sharpening a quick overview?

The linear, official, top-down approach doesn't work for me. Seeing a rough outline and improving it keeps our interest, and aware of how individual details are connected.

### Move from Appreciation To Performance

Do you need to be a musician to enjoy a song? No way. There's a few levels of music understanding:

• Appreciation: being able to enjoy music
• Natural Description: being able to hum a tune you heard or thought of
• Symbolic Description: being able to read and write the sheet music for a song
• Performance: being able to play music with the official instruments (i.e., not your mouth)
• Theory: being able to explain why harmonies work, or melodies sound somber, joyous, etc.

Math knowledge is the same. Start by appreciating, even enjoying, the idea. Describe it with your own words, in English. Then, learn the official symbols to make communication easier ("2 + 3 = 5" is better than "Two plus three equals five", right?).

When we're ready, we can "perform" math by doing the calculations ourselves, and diving into the detailed theory. But only if you want! Decide for yourself what level of understanding you'd like to reach.

### Move Through History

Many courses present the modern interpretation of math without looking at its origins.

Calculus was made by Newton to work out the laws of physics, right? Not exactly.

It was Archimedes, drawing shapes in the sand, who laid the foundations by imagining how circles and spheres were connected. He took shapes, morphed them, split them into tiny parts, and discovered connections through painstaking years of effort.

We're going to recreate his life's work in this course, in hours, using our calculus understanding. Geometry is a nice starting point because it's tangible and easy to visualize. (Physics? Not so much.)

Now, let's start the course!

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## Class Discussion

Guided class discussions are available in the complete edition.