2nd Video Solving the Beal Conjecture
Quaternionic Eulerian Calculus or QEC is a new revolutionary method of performing differential and integral calculus based upon the algebra of the quaternion. In this video I will rigorously establish the QEC limit and formally derive the QEC derivative and the QEC integral. To illustrate the power of QEC I will solve the Beal Conjecture.
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Arthur Latham Baker,
Quaternions as the result of algebraic operations.
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P.G. Tait,
An Elementary Treatise on Quaternions.
Cambridge at the University Press., 3rd edition, (1890)
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An Introduction to Quaternions.
Macmillan and Company, 2nd edition, (1882)
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A Primer of Quaternions.
Terre Haute, IND, (1896)
W.Johnson Jr.,
The Gyroscopic Force Theory Introducing Tovacian Chemistry.
Willie Johnson Jr. Publisher, (2011)
R. Arnold, L. Maunder,
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Academic Press Inc., New York, N.Y., (1961).
Chapters
0:00 Intro
2:05 What is Calculus
2:51 QEC Rules of Quaternions
7:49 Tovacian Conjugates
10:21 Establishing the Versine
11:01 Comparing and Contrasting the Newtonian and QECian Limits
16:18 The QECian Interpretation of the Newtonian Limit
23:48 Deriving the QEC Limit
28:39 The Slope of a Vertical Line is Zero
33:17 The QECian Concepts of Continuity and Discontinuity
36:48 Defining the Difference Quotient
41:08 The Difference Quotient: The QECian Method
48:03 The Difference Quotient: The Trigonometric Function Method
50:09 The Difference Quotient: The Secant Method
51:21 Deriving the Fermatian Derivative
57:09 The Derivative via the Centrode Method
101:29 Rodrigues Rotation Formula
104:55 The Quaternion Rotator
106:30 Solving the Beal Conjecture