Calculus Visualized - by Dennis F Davis

Описание: This 3-hour video covers most concepts in the first two semesters of calculus, primarily Differentiation and Integration.
The visual and animation style is intended to be informative and provide insights into the logical reasoning behind the rules and formulas in calculus.

Timestamps

0:00 Can you learn calculus in 3 hours?
2:23 Calculus is all about performing two operations on functions
3:32 Rate of change as slope of a straight line
5:37 The dilemma of the slope of a curvy line
7:04 The slope between very close points
11:30 The limit
15:36 The derivative (and differentials of x and y)
21:48 Differential notation
27:58 The constant rule of differentiation
29:15 The power rule of differentiation
35:36 Visual interpretation of the power rule
39:19 The addition (and subtraction) rule of differentiation
41:34 The product rule of differentiation
43:08 Combining rules of differentiation to find the derivative of a polynomial
44:53 Differentiation super-shortcuts for polynomials
48:03 Solving optimization problems with derivatives
52:46 The second derivative
59:59 Trig rules of differentiation (for sine and cosine)
1:05:54 Knowledge test: product rule example
1:06:32 The chain rule for differentiation (composite functions)
1:15:23 The quotient rule for differentiation
1:19:04 The derivative of the other trig functions (tan, cot, sec, cos)
1:20:55 Algebra overview: exponentials and logarithms
1:33:12 Differentiation rules for exponents
1:41:33 Differentiation rules for logarithms
1:45:32 The anti-derivative (aka integral)
1:46:21 The power rule for integration
1:48:32 The power rule for integration won't work for 1/x
1:52:37 The constant of integration +C
1:57:26 Anti-derivative notation
1:59:59 The integral as the area under a curve (using the limit)
2:12:05 Evaluating definite integrals
2:13:11 Definite and indefinite integrals (comparison)
2:15:30 The definite integral and signed area
2:18:10 The Fundamental Theorem of Calculus visualized
2:21:37 The integral as a running total of its derivative
2:24:25 The trig rule for integration (sine and cosine)
2:27:07 Definite integral example problem
2:32:53 u-Substitution
2:42:05 Integration by parts
2:56:03 The DI method for using integration by parts


PROMISED LINKS:
Binomial Expansion (with Pascal's Triangle):    • How to expand (a+b)^n (Binomial Theorem wi...  
Trigonometry Series (by me!):    • TR-00: Introduction to Trigonometry Series...  


KEY RESOURCES FOR PRACTICE:

Steve Chow: ‪@blackpenredpen‬
100 Derivatives:    • 100 derivatives (in one take)  
100 Integrals:    • 100 integrals (world record?)  
100 more Integrals:    • 100 integrals part 2 (EXTREME PASSION!)  
DI Method for Integration by Parts:    • integration by parts, DI method, VERY EASY  

Other Great Calculus Resources

Grant Sanderson: ‪@3blue1brown‬ Grant is the grand master of math visualization
Essence of Calculus Series:    • The essence of calculus  

Michel van Biezen: ‪@MichelvanBiezen‬ (iLectureOnline)
Huge calculus playlist:    • Calculus 1 CH 3  Derivatives (1 of 24) Simple  

Mathologer: ‪@Mathologer‬
Why is calculus so... EASY?:    • Why is calculus so ... EASY ?  

The Organic Chemistry Tutor: ‪@TheOrganicChemistryTutor‬
Learn Calculus Fast playlist:    • Calculus 1 Review -  Basic Introduction  

There are lots of good resources on YouTube in addition to these.

Key Words:
Maths, differentiation, derivative, integration, integral, limits, tutorial, overview, proof, proofs, animated, animation, explain, explained, A-level maths, O-level maths, IB math, power rule, product rule, quotient rule, u-substitution, integration by parts.