Half-Life: Definition, Equations, and Extended Explanation - Physics …
Jul 23, 2014 · Definition/Summary The half-life, [itex]t_{1/2}[/itex], of an inverse exponential process (an exponential decay) is the time taken for the amount to reduce by one-half. It is …
What is the meaning of 'exp' in this math expression? - Physics …
Feb 6, 2004 · In summary, "exp" stands for "exponential" function and is used to represent the constant e raised to the input power. It is often used when it is difficult to display complex …
Scalar powers of a matrix exponential - Physics Forums
Aug 30, 2020 · To calculate a scalar power of a matrix exponential, the matrix is first exponentiated using the standard matrix exponential formula. Then, the resulting matrix is …
Logarithmic growth vs exponential growth - Physics Forums
May 26, 2017 · From Wikipedia: "Exponential growth is feasible when the growth rate of the value of a mathematical function is proportional to the function's current value, resulting in its growth …
Complex Exponential: Why is e Used? - Physics Forums
Jun 5, 2006 · In summary, the use of "e" as the base for the exponential in the formula e^{ix} = cos(x) + i sin(x) is not just a definition, but rather an important choice that allows for its …
Why do we have both sine and cosine? - Physics Forums
May 5, 2015 · The exponential definition of the trig functions came many centuries after the geometrical definition, and the familiar trig identities are probably easier to derive using the …
Why is e chosen as the natural base for logarithms? - Physics Forums
Apr 18, 2003 · e shows up everywhere is nature. Essentially it describe any phenomena that includes continuous build-up with certain rate. i.e. interests of your bank account, spiral pattern …
Can the inverse of a matrix exponential be proven using its …
Dec 25, 2013 · An exponential matrix is a special type of matrix that can be written in the form e A, where A is a square matrix. This is similar to how a number can be written in exponential …
What is the definition of exponentiation? - Physics Forums
Jul 11, 2009 · The confusion with exponents comes when the base is zero, negative, or when you have to "undo"an exponent with a logarithm. But the exponential function [tex]e^x[/tex] is …
What is the history and significance of Euler's formula? - Physics …
Jul 23, 2014 · Euler's formula is a mathematical equation that relates the exponential function, trigonometric functions, and imaginary numbers. It is written as e^(ix) = cos(x) + isin(x), where …