Math and Arithmetic

Units of Measure

Geometry

Differential Equations

One ' (an apostrophe) means feet and 2 " (quotation marks) means inches.

229230231

Building and Carpentry

Weight and Mass

Differential Equations

The red clay bricks I bought today - measuring about 4" x 8" x 2 1/4" thick (10 cm x 20 cm x 5 1/2 cm) - weigh just under 6 lbs (about 2.7 Kilograms) apiece.

119120121

Math and Arithmetic

Differential Equations

f(x) = x2 - 3

By the power rule:

f'(x) = 2x2-1 - 0

= 2x

f''(x) = 2(1)x1-1

= 2

The second derivative of x2 - 3 is 2.

137138139

Math and Arithmetic

Differential Equations

ordinary differential equation is obtained only one independent variable and partial differential equation is obtained more than one variable.

131132133

Area

Differential Equations

Here we go....... 1 Bigha = 20 katha = 33 decimal 1 katha = 1.65 decimal

107108109

Science

Differential Equations

you times 45 x 1 = 45

123

Differential Equations

As per my knowledge,Maxwell's equations describes the relations between changing electric and magnetic fields. That means time varying electric field can be produced by time varying magnetic field and time varying magnetic field can be produced by time varying electric field.

113114115

Math and Arithmetic

Prefixes Suffixes and Root Words

Differential Equations

Billion has 9 zeros

Trillion has 12 zeros

Quadrillion has 15 zeros

Quintillion has 18 zeros

Sextillion has 21 zeros

Septillion has 24 zeros

Octillion has 27 zeros

Nonillion has 30 zeros

Decillion has 33 zeros

Undecillion has 36 zeros

Duodecillion has 39 zeros

Tredecillion has 42 zeros

Quattuordecillion has 45 zeros

Quindecillion has 48 zeros

Sexdecillion has 51 zeros

Septendecillion has 54 zeros

Octodecillion has 57 zeros

Novemdecillion has 60 zeros

Vigintillion has 63 zeros

Googol has 100 zeros.

Centillion has 303 zeros (except in Britain, where it has 600 zeros)

Googolplex has a googol of zeros

192021

Differential Equations

You can't convert a second order DE to first order except in special cases (like an ODE with y'' and y' but no y terms).

HOWEVER, you can convert a second order ODE into a systemof first order ODEs:

Assume it is of the form f(x, y, y', y'') = 0, where y(x) is the solution.

1) Let u1 = y and u2 = y'

2) Substitute y'' for u2', y' for u2, and y for u1 to get eq1

3) u2 = u1' is eq2.

eq1 and eq2 are a system of two first-order ODEs which represent the same problem.

878889

Engineering

Robotics

Differential Equations

It's a dynamical system that allows to reconstruct state vector of a nonlinear system using observation of the system output. See the Wikipedia article "State Observers".

818283

Chicago

Differential Equations

Root Beer

AnswerI Believe it was on Kedzie....somewhere between 61st and 67th. I think an A@W restaurant is there now. AnswerOr was this on W.Columbus?.

798081

Mathematical Finance

Statistics

Numerical Analysis and Simulation

Differential Equations

It is not possible to reproduce the equations on this website, however you can find a detailed derivation at the related link.

737475

College Applications and Entrance Requirements

Math and Arithmetic

Differential Equations

In mathematics and, in particular, functional analysis, convolution is a mathematical operator which takes two functions f and g and produces a third function that in a sense represents the amount of overlap between f and a reversed and translated version of g. A convolution is a kind of very general moving average, as one can see by taking one of the functions to be an indicator function of an interval. we mainly use impulse functions to convolute in dicreate cases

656667

Math and Arithmetic

Algebra

Differential Equations

If there is subtracting terms in either polynomial, change them to adding a negative. Each term in the first polynomial is multiplied by each term in the 2nd polynomial, then add all the resulting terms together (taking into account the signs of the resulting multiplications), simplify by combining like powers of the variable.

This is basically what you are doing when you multiply 2 numbers by hand, example: 997 x 42 = 41874

997

x 42

----- First you mutiply 2 x 7 = 14, put the 4 carry the 1, etc.

Imagine instead (4x + 2)(9x2 + 9x + 7) = 2*7 + 2*9*x + 2*9*x2 + (4*x)*7 + (4*x)*(9*x) + (4*x)*(9x2) = 14 + 46x + 54x2 + 36x3

For x = 10 --> 14 +460 + 5400 + 36000 = 41874.

717273

Cocktail and Mixed Drink Recipes

Differential Equations

5

567

Math and Arithmetic

Calculus

Geometry

Differential Equations

http://en.wikipedia.org/wiki/Navier-Stokes_equations
Please go to this page.

656667

Mathematical Finance

Differential Equations

In mathematics, a PDE is a Partial Differential Equation.

To partially differentiate an equation, read below:

Suppose you have a function f(x,y) and suppose you want to partially differentiate it w.r.t. x then you consider y as a constant and find d/dx(f(x,y)).

Eg. - Let f(x,y)=xy+x+y then on partially differentiating f(x,y) w.r.t. x -

d/dx(f(x,y))

= d/dx(xy) + d/dx(x) + d/dx(y)

= y(d/dx(x)) + 1 + 0 (as y is constant)

= y +1

Some application(s) of partial differential equations that I know -

1. Find the centre of a conic:

Suppose you have a curve as a function of x and y, say f(x,y).

Then to find its centre -

-> Partially differentiate f(x,y) w.r.t. x. Let the equation obtained be e1.

-> Partially differentiate f(x,y) w.r.t. y. Let the equation obtained be e2.

Solve e1 and e2 to get (x,y) which is the centre of the curve.

2. To find the (conservative) force acting on an object if its Potential energy is given as a function of distance:

-> Let the potential energy function be U(x,y).

-> To find the force acting on object in x-direction, find minus(partial derivative of U(x,y) w.r.t. x).

-> Same method to find force acting on the object in y-direction.

-> Only works for conservative force.

For more information, please see the related link.

646566

English Language

Math and Arithmetic

Differential Equations

12

636465

Math History

Differential Equations

66

012

Plumbing

Swimming Pools

Mathematical Analysis

Differential Equations

I'm no pool expert but I can do the basic maths. I'd presume the limiting factor on how much water will pass through a pipe is its cross sectional area, and that these are circular pipes. If so, the area of a 1.5 inch diameter pipe is pi x .75 x .75, and of a 2inch diameter pipe is pi x 1 x 1 . So two of the smaller pipes will have a combined area of 1.125pi sq. inches, more than the single bigger pipe at 1pi sq. inches. Two 1.5" pipes into a single 2" line is acceptable for your flow rates. The flow rate will depend more on your pump than the two 1.5" diameter lines. You could add a third, or even more lines and individually isolate them with ball valves so you can adjust the flow from each as per the requirements of the pool.

596061

Math and Arithmetic

Differential Equations

An equation means an expression with an equal sign in it (=), and that makes sense. For example 4 + 3 = 7 is an equation, while 4 + 3 = 6 or 4 + 5 are not equations. The first one is incorrect, while the second one is an expression.

The word equation describes a statement that two sets of something are equal to one another.

In mathematics, the two sets can consist of numbers, letters, or symbols.

In chemistry, an equation describes - in symbols - the changes that take place in a chemical reaction.

In everyday usage, an equation suggests one or more things are equal to one or more other things, or describe the varying aspects which need to be taken into consideration when analyzing a situation.

313233

Home Equity and Refinancing

Math and Arithmetic

Differential Equations

Yes, that's usually the minimum savings amount that I recommend to someone who is contemplating to refinance. If you save $100 a month that equals $1,200 a year, which totals to $18,000 in 15 years and $36,000 in 30 years. Weigh that wersus the costs (usually no more than $6000, worse case scenario) and that to me seems like a wise decision. If you need any help with this feel free to call my office (214)607-1445.

484950

American Cars

Weight and Mass

Mathematical Analysis

Differential Equations

How To

steel weighs 490 pounds per cubic foot. A piece of steel 12" x 12" x 1" weighs 40.83 pounds. 7.65 lbs per square foot So ... 48" x 96" = 4' x 8' = 32 square feet and 7.65 lbs per square foot x 32 square feet = 245 lbs per full 0.1875" thick sheet

515253

Quantum Mechanics

Waves Vibrations and Oscillations

Differential Equations

If V is only a function of x, then the equation's general solution can be nearly solved using the method of separation of variables.

Starting with the time dependent Schrödinger equation:

(iℏ)∂Ψ/∂t = -(ℏ2/2m)∂2Ψ/∂x2 + VΨ, where iis the imaginary number, ℏ is Plank's constant/2π, Ψ is the wave function, m is mass, x is position, t is time, and V is the potential and is only a function of x in this case.

Now we find solutions of Ψ that are products of functions of either variable, i.e.

Ψ(x,t) = ψ(x) f(t)

Taking the first partial of Ψ in the above equation with respect to t gives:

∂Ψ/∂t = ψ df/dt

Taking the second partial of Ψ in that same equation above with respect to x gives:

∂2Ψ/∂x2 = d2ψ/dx2 f

Substituting these ordinary derivatives into the time dependent Schrödinger equation gives:

(iℏψ)df/dt = -(ℏ2/2m)d2ψ/dx2f + Vψf

Dividing through by ψf gives:

(iℏ)(1/f)df/dt = -(ℏ2/2m)(1/ψ)d2ψ/dx2 + V

This makes the left side of the equation a function of tonly, and the right a function of x only; meaning both sides have to be a constant for the equation to hold (I'm not going to prove why this is so, because if you've understood what I've written up to this point, you're probably familiar with the separation of variables technique).

That allows us to make two separate ordinary differential equations:

1) (1/f)df/dt = -(iE/ℏ)

2) -(ℏ2/2m)d2ψ/dx2 + Vψ = Eψ, where E is the constant that both separated differential equations must equal to (I did a little bit of algebra to these equations also). This is known as the time independent Schrödinger equation.

To solve 1) just multiply both sides of the equation by dt and integrate:

ln(f) = -(iEt/ℏ) + C. Exponentiating and, since C will be absorbed later, removing C:

f(t) = e-(iEt/ℏ)

Now, we have gone as far as we can until the potential, V(x), is specified. That leaves us with the general solution to the time dependent Schrödinger equation being:

Ψ(x,t) = ψ(x) e-(iEt/ℏ)

There are many solvable examples of ψ(x) for specific V(x). I've linked some below. Also, if V is a function of both x and t, there are methods to find solutions, such as perturbation theory and adiabatic approximation.

414243

Math and Arithmetic

Electronics Engineering

Differential Equations

Quadrillion may mean either of the two numbers (depends on long and short scales):

- 1,000,000,000,000,000 (one thousand million million; 1015; SI prefix peta) - increasingly common meaning in English language usage.
- 1,000,000,000,000,000,000,000,000 (1024; SI prefix yotta) - increasingly rare meaning in English language usage.
It is 1,000,000,000,000,000.

- Simply put, in the English language, it is "one thousand trillion."

394041

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