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): https://www.youtube.com/watch?v=cvhyJT9c0ac
Trigonometry Series (by me!): https://www.youtube.com/watch?v=U23JMdBIJ0M&list=PLhSQQGbiWoTChZSbP-XcXH40IT7vfyyFk&pp=gAQB
KEY RESOURCES FOR PRACTICE:
Steve Chow: @blackpenredpen
100 Derivatives: https://www.youtube.com/watch?v=AegzQ_dip8k
100 Integrals: https://www.youtube.com/watch?v=dgm4-3-Iv3s
100 more Integrals: https://www.youtube.com/watch?v=jQz1gQ24OHc
DI Method for Integration by Parts: https://www.youtube.com/watch?v=2I-_SV8cwsw
Other Great Calculus Resources
Grant Sanderson: @3blue1brown Grant is the grand master of math visualization
Essence of Calculus Series: https://www.youtube.com/watch?v=WUvTyaaNkzM&list=PLZHQObOWTQDMsr9K-rj53DwVRMYO3t5Yr
Michel van Biezen: @MichelvanBiezen (iLectureOnline)
Huge calculus playlist: https://www.youtube.com/watch?v=6vRKEXf7uE8&list=PLX2gX-ftPVXWMrapS-ROUEKCxv5lpA5zh
Mathologer: @Mathologer
Why is calculus so... EASY?: https://www.youtube.com/watch?v=kuOxDh3egN0
The Organic Chemistry Tutor: @TheOrganicChemistryTutor
Learn Calculus Fast playlist: https://www.youtube.com/watch?v=GiCojsAWRj0&list=PL0o_zxa4K1BWYThyV4T2Allw6zY0jEumv
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.