Welcome to the Calculus course! Before we start, just a quick note about the intuition-first learning approach.
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.
Do you need to be a musician to enjoy a song? No way. There's a few levels of music understanding:
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.
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!