Calculus Visualized - by Dennis F Davis

Video Description

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.