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Calculus for Business, Economics, and the Social and Life Sciences, Brief Version
by Laurence D. Hoffman, Gerald L. Bradley, Dave Sobecki, Michael Price , 11th Edition
Additional Details
Language: English
Publisher: McGraw-Hill Higher Education
Softcover:International Edition
ISBN 10: 007131797X
ISBN 13: 9780071317979
Refer to US ISBN: 9780073532387
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Basically, this is differential calculus.
MATH130 taught me how calculus works, so we can safely say, "It works, bitches."
Refer to xkcd.com/54/ for the original joke.
How to learn Calculus in an elegant, brain-bending manner. My closest analogy is Darwin’s Theory of Evolution: once understood, you start seeing Nature in terms of survival. You understand why drugs lead to resistant germs (survival of the fittest). You know why sugar and fat taste sweet (encourage consumption of high-calorie foods in times of scarcity). It all fits together.
At the top left, I've written the equation that Google Sheets gave me for the Angry Bird's motion. This is a best fit parabola that takes into account the errors in all data points, so it's the best description of what the bird was doing.
We took the derivative to get a velocity function. Note that this came out linear
We took the derivative again to get an acceleration function. Note that this came out constant, with the value -9.074. In other words, the bird had a constant acceleration of -9.074.
Tracking back, we see that -9.074 in the velocity equation. So that term must be acceleration. Since the constant term in this equation must be a velocity, it's the original velocity. So apparently the equation for velocity at any time is v=v0+at.
Tracking back further, we see that the -9.074 isn't in the position equation, but half of it is. Also, the original velocity is there too. This gives us the position equation y=(1/2)at^2 + v0t + y0.
These two equations can be used to describe the velocity and position not just of this bird, but of ANY objects with constant acceleration like that which gravity gives.
For the record, the accepted value of the acceleration of gravity is -9.8 m/s/s. There was some experimental error in my measurement.
Okay, she's not perfect, but she's cute. This little Hello Kitty is my cross sections calculus project.
PS: I've returned to Flickr :)
Differential calculus and Being Zero(0_)
Basically,
because very small zero( 0 ) is not Not-being(_0) but Being Zero(0_),
In the real world, very small zero( 0 ) is 0.0000000000000000000000000000000001,
though very small zero( 0 ) is not Not-being(_0) but Being Zero(0_),
we think and calculate that very small zero( 0 ) is Not-being(_0).
(Very small average velocity) is Velocity.
( Average of Very small average velocity) removes Being Zero(0_) from Calculus.
Logically, ( Average of Very small average velocity) is Velocity.
Liuhui Brahmagupta (2011.03.25)
Differential and Integral calculus
(1/3). Position, ( Velocity = Displacement / Time ), ( Speed = Distance / Time )
(2/3). Average Velocity, Change -> 0 : Instantaneous Velocity
(3/3). Average Instantaneous Velocity, Change -> 0 : Instantaneous Acceleration
(1/3). Position : Y = X^2
(2/3). Instantaneous Velocity : Y' = 2X^2-1 = 2X^1 = 2X
(3/3). Instantaneous Acceleration : Y'' = 2(1 * X^1-1) = 2(X^1-1) = 2(X^0) = 2(1) = 2
Instantaneous Acceleration ( Y'' = 2 ) -> (Integral calculus) -> Instantaneous Velocity (Y' = 2X )
Instantaneous Velocity (Y' = 2X ) -> (Integral calculus) -> Position ( Y = X^2 )
The Math & Science Institute (MSI) is an academically rigorous program designed for students with a keen interest in pursuing degrees in science, technology, engineering and math (STEM). The Institute consists of seven college-credit courses:
-- BioTechnology
-- Environment and Energy Technology
-- Physics
-- Anatomy & Physiology
-- Statistics
-- Calculus