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Relativity Science Calculator Mathematical References


Some Quick and Dirty Mathematical References

"Do not worry about your difficulties in mathematics, I assure you that mine are greater" - Albert Einstein ( 1879 - 1955 )

Square Roots of Negatives

Relativity Science Calculator Mathematical References

Some Quick and Dirty Relativity Approximations

I

relativity mathematical approximations

Relativity Science Calculator Mathematical References

II

Relativity Science Calculator Mathematical References

III

Relativity Science Calculator Mathematical ReferencesRelativity Science Calculator Mathematical ReferencesRelativity Science Calculator Mathematical References


Integration By Parts

calculus integration by parts


Natural Logarithm, ln x

definition natural logarithm

definition natural logarithm ln(x)

fundamental theorem of calculus

§ Some implications for natural logs:

calculus chain rule

§ Properties of ln:

natural ln log rules


The Inverse of ln x and the number e


natural logarithm e

§ Definition of number e:

definition logarithm number e

§ Number e defined numerically:

defining logarithm number e numerically

§ Properties of ln x and e:

logarithm inverses

§ Laws of exponents for ex:

laws of exponents of natural log e


The calculus for ln x and ex

calculus differentiation natural log e


The Hyperbolic Function

Every function that is defined on an interval centered at the origin is comprised of even and odd components as follows:

hyperbolic functions

The importance of this class of functions lies in the fact that they best describe the hanging catenary shapes of electrical powerline cables, wave motion in certain elastic solids, and are involved in the differential equations for heat transfer in metals, as well as demonstrating time and distance dilations in special relativity mathematics.

§ Derived hyperbolic identities:

hyperbolic identities

§ The derivatives for these hyperbolic functions:

Relativity Science Calculator Mathematical References


Maclaurin Series for Some Trig Functions

Relativity Science Calculator Mathematical References

§ Small trignometric approximations:

Relativity Science Calculator Mathematical Referencesradian measureradian measureradian measureradian measure

§ Maclaurin Series and hence Binomial Expansion vital in deriving Relativity Science Calculator Mathematical References:

Relativity Science Calculator Mathematical References


Rotation of Axis

Relativity Science Calculator Mathematical References


Definitions from Geometry and Rotational Kinematics

Relativity Science Calculator Mathematical Referencesangular momentumangular velocity derivation


Spherical Coordinates

Relativity Science Calculator Mathematical References


Unit Circle: Radian Measure

Relativity Science Calculator Mathematical References


Relativity Science Calculator Mathematical References

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Relativity Science Calculator Mathematical References

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