All of Calculus in Under 13 Minutes

Описание: All of calculus, built step by step from one dot riding one curve: slope as rise over run, speed, the question of the slope at one point, secant lines, zooming in, the tangent line and the derivative, limits, dy/dx, the slope of x squared (2x) and the power rule, negative slopes, maxima and minima (the fence problem, a thrown ball), the second derivative, area under a speed graph, Riemann strips, the integral, the area function and the fundamental theorem of calculus, antiderivatives and + C, the area of a circle, the natural logarithm and e, e^x as its own derivative, growth and decay, differential equations and Euler's method, the slopes of sine and cosine, the chain rule, infinite sums, Taylor series, and Newton's method.

History along the way: Archimedes and the parabola (3rd century BC), Newton (1660s) and Leibniz (published 1684), the integral sign (Leibniz, 1675), and Newton's Principia (1687).

0:00 One dot, one curve
0:34 Slope
1:04 Curves and the big question
1:46 Secant lines
2:11 Zooming in: the tangent line
2:23 The derivative
2:35 Limits
3:02 The slope of x²
3:46 The power rule
4:15 Maxima and minima
4:27 The fence problem
5:03 The second derivative
5:21 Area under a curve
5:58 Riemann sums
6:28 The integral
6:43 Archimedes
6:58 The fundamental theorem
7:56 The area of a circle
8:13 Newton and Leibniz
8:59 + C
9:14 ln x and e
9:33 e^x
10:04 Differential equations
10:33 Sine, cosine and the chain rule
11:01 Infinite sums
11:16 Taylor series
11:47 Newton's method
12:26 Recap

#calculus #math #derivatives