Posts Tagged ‘m’
Friday, November 20th, 2009
How to Pick Variables
Description
A detailed tutorial on how to pick variables. Step by step tutorial including several examples of how to pick variables for reference.
Overview
Variables are letters picked to represent unknown values in expressions and equations. Usually they are lowercase, but they can be made uppercase. When trying to pick a variable, you must choose wisely. x is the most common variable, followed by n. x is picked because people associate it with the unknown, and n is picked because it stands for “number.” The variable should be easily recognizable – you should not use a variable that looks like another number or some symbol of a mathematical operation. You should check to see what is included in your equation – for instance, m stands for slope, so if you are doing an equation with slope you need to pick a different variable to avoid confusion. And you should always pick a variable that makes sense – the first letter of your subject matter usually works quite well.
Tags: a, algebra, b, c, choose, equation, expression, lowercase, m, mathematical, n!, number, operation, slope, symbol, unknown, uppercase, value, variable, variables, x, y, z
Posted in Algebra | No Comments »
Thursday, November 5th, 2009
Saddle-Point Approximation Explained
Description
A detailed tutorial on saddle-point approximation. Step by step tutorial including several examples of saddle-point approximation for reference.
Overview
Saddle-point approximation is also referred to as the method of steepest descent and Laplace’s method. It is a way of approximating integrals in the form 
. f(x) is some twice-differentiable function, M is a large number, and the integral endpoints a and b have a possibilty of being infinite.
Tags: a, approximation, b, Calculus, descent, differentiable, function, infinite, infinity, integral, Laplace, large, m, method, number, point, saddle, saddle-point, steepest, twice, twice-differentiable
Posted in Calculus | No Comments »
Thursday, November 5th, 2009
Overview of Mass-Energy Equivalence
Description
A detailed tutorial on mass-energy equivalence. Step by step tutorial including several examples of mass-energy equivalence for reference.
Overview
Mass-energy equivalence is the concept that the mass of a body is the measure of its energy content. This is often expressed by a formula written by Einstein, who is also the one that proposed the idea of mass-energy equivalence. This formula is 
, where E is energy, m is the mass, and c is the speed of light in a vacuum.
Tags: Albert, body, c, content, differential equations, E, Einstein, energy, equivalence, equivalent, formula, idea, light, m, mass, measure, speed, vacuum
Posted in Differential Equations | No Comments »
Friday, October 16th, 2009
Overview of the Mach Number
Description
A detailed tutorial on how to solve for Mach numbers. Step by step tutorial including several examples of how to solve for Mach numbers for reference.
Overview
A Mach number is the speed of an object moving through the air, or any fluid substance, divided by the speed of sound as it is in that substance. It is often used to represent an object such as an aircraft or a missile’s speed, when it is travelling at the speed of sound or multiples of the speed of sound. This can be portrayed mathematically in the equation M = vs / u, where M is the Mach number, vs is the speed of the source (the object relative to the medium), and u is the speed of sound in the medium.
Tags: air, aircraft, algebra, fluid, m, Mach, Math, medium, missile, number, object, s, sound, source, speed, substance, u, v
Posted in Algebra | No Comments »
Thursday, October 1st, 2009
Boundedness Theorem Explained
Description
A detailed tutorial of the boundedness theorem. Step by step tutorial including an explanation of the boundedness theorem for reference. Knowledge of the boundedness theorem is required in calculus.
Overview
The boundedness theorem is a theorem that is very closely linked to the extreme value theorem. The boundedness theorem states that a continuous function f in the closed interval [a, b] is bounded on that interval. In mathematical terms, this means that there exist real numbers m and M such that ![m \le f(x) \le M\quad\text{for all }x \in [a,b].\,](http://s.wordpress.com/latex.php?latex=m%20%5Cle%20f%28x%29%20%5Cle%20M%5Cquad%5Ctext%7Bfor%20all%20%7Dx%20%5Cin%20%5Ba%2Cb%5D.%5C%2C&bg=ffffff&fg=000000&s=0 "m \le f(x) \le M\quad\text{for all }x \in [a,b].\,")
This translates to mean “m is less than or equal to f(x) which is less than or equal to M for all x belonging to [a, b]“.
Tags: a, b, bounded, boundedness theorem, c, Calculus, closed, continuous, d, EVT, extreme value theorem, f(c), f(d), f(x), function, graph, local, m, Math, maxima, maximum, minima, minumum, value, x
Posted in Calculus | No Comments »
Thursday, September 24th, 2009
Intermediate Value Theorem Explained
Description
A detailed tutorial of the intermediate value theorem. Step by step tutorial including an explanation of the intermediate value theorem for reference. Knowledge of the intermediate value theorem is required in calculus.
Overview
The intermediate value theorem states that for each value between the upper bound and the greatest lower bound of the graph of a continuous function that there is a corresponding value in its domain. In mathematical terms, the intermediate value theorem states that if f is a continuous function on the closed interval [a, b] and M is a number between f(a) and f(b), then there exists at least one number c that f(c) = M. When writing proofs in calculus, you can say that something has been proven by the IVT if you used the intermediate value theorem to reach your conclusion.
Tags: a, b, c, Calculus, continuous, corresponding, domain, f(a), f(b), f(c), function, graph, greatest lower bound, intermediate value theorem, IVT, m, Math, upper bound, value
Posted in Calculus | No Comments »
Tuesday, September 15th, 2009
Finding the Slope of a Line
Description
A detailed tutorial on how to find the slope of a line. Step by step tutorial including several examples of how to find the slope of a line for reference.
Overview
Finding slope isn’t all that difficult. The slope of a line is the numerical expression of the slant of a line on a graph. The slope is represented by the letter m and is written in the format of rise over run – in other words, from point to point, how many spaces up the line goes and how many spaces over. Negative numbers are used if the slope runs either down or to the left instead of up and to the right. If the graph is already provided, the slope can be found by counting. But the correct way to find slope is to use a formula.
m = (change in y) / (change in x)
In order to use this formula, you need to have two points on the line. The change in x is the first x-coordinate minus the second x-coordinate, and the change in y is the first y-coordinate minus the second y-coordinate. The equations in the numerator and denominator are solved seperately and will form one fraction, which will be the slope.
Tags: algebra, change in x, change in y, formula, fraction, graph, graphing, line, m, Math, rise over run, slope, x-coordinate, y-coordinate
Posted in Algebra | 1 Comment »
