Calculus 1, Lecture 1: The Big Ideas (Rates & Areas, the Infinity Principle and Circular Area)

(0:00) Introduction. (0:20) Content will be written about at infinityisreallybig.com. (1:02) Seeing the big picture and glorifying God. (1:30) An ancient mystery (planetary motion). (5:28) Calculus and its applications, including those highlighted in "Infinite Powers", by Steven Strogatz. (9:12) The main applications studies in this course (motion, flows, growth & decay, finance, probability and statistics (foundations of data science). (12:53) One key equation (distance equals rate times time). (15:01) Car motion visuals and graphs (speed and distance traveled). (21:36) Fluid flow visuals and graphs (flow rates and total accumulated volume). (25:24) Population growth visuals and graphs (growth rates and total population). (28:24) What if the rate (derivative) is changing? Car motion at varying rates. (33:44) The Infinity Principle (by Steven Strogatz). (35:36) Zeno's paradox (Achilles and the Tortoise). (39:38) Why is the area of a circle pi*r^2? Animation of visual from "Infinite Powers". (44:28) Animation from 3Blue1Brown channel by Grant Sanderson.

Also the "The Beauty of Calculus" video:

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