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Differential Equations
A differential equation, unlike other mathematical equations, has one or more of its unknowns undergoing a continual change. These equations mathematically describe the most significant phenomena in the universe, including Newtonian and quantum mechanics, waves and oscillators, biological growth and decay, heat, economics, and general relativity. Please direct all concerns about these intricate and all-encompassing equations here.
523 Questions
No, five is a prime number because there are only two whole numbers that when multiplied, equals five. (Those numbers are five and one.) In order for a number to be composite, it has to have factors other than itself and one.
When you have two parametric equations what's the name of the rule you can use to work out dy by dx?
The chain rule.
Application of gronwall's lemma in differential equations?
Used to prove uniqueness of solutions in ODE problems
Definition of partial differential equation with example?
A partial derivative is the derivative in respect to one dimension. You can use the rules and tricks of normal differentiation with partial derivatives if you hold the other variables as constants, but the actual definition is very similar to the definition of a normal derivative. In respect to x, it looks like:
fx(x,y)=[f(x+Δx,y)-f(x,y)]/Δx
and in respect to y:
fy(x,y)=[f(x,y+Δy)-f(x,y)]/Δy
Here's an example. take the function z=3x2+2y
we want to find the partial derivative in respect to x, so we can use basic differentiation techniques if we treat y as a constant, so zx'=6x+0 because the derivative of a constant (2y in this case) is always 0. this applies to any number of dimensions. if you were finding the partial in respect to a of f(a,b,c,d,e,f,g), you would just differentiate as normal and hold b through g as constants.
What is the global solution of an ordinary differential equation?
The global solution of an ordinary differential equation (ODE) is a solution of which there are no extensions; i.e. you can't add a solution to the global solution to make it more general, the global solution is as general as it gets.
Programmable electronic digital computer technologies.
What is one tenth out of one one hundredths of a meter?
(1/10) x (1/100) x (1 meter) = 1/1000 meter = 1 millimeter
What is the general form of linear differential equation?
Given the poor quality of this browser, it is difficult to illustrate the example sensibly but here is the best that I can do.
The general form is Ly = f(x) where L is a linear operator, y is the unknown function of x, and f is the given function.
L is of the form dny/dxn + g1(x)*dn-1y/dxn-1 + ... + gn-1(x)*dy/dx + gn(x)*y
Why you need the numerical solution of partial differential equations?
Very often because no analytical solution is available.
What is the differential form of Maxwell's equations?
Gauss' law: ∇ â— E = Ï/ε0,
Gauss' law for magnetism: ∇ ◠B = 0,
Maxwell-Faraday equation: ∇ X E =-∂B/∂t,
Ampère's circuital law with Maxwell's correction: ∇ X B = μ0J + μ0ε0∂E/∂t,
where E is the electric field, Ï is the charge density, ε0 is the electric constant, B is the magnetic field, t is time, μ0 is the magnetic constant, and J is the current density.
How can you save one hundred thousand dollars in five years?
384 per week. This works out to $19968 in one year
and $99840 in 5 years.
This calculation is without any interest. If you deposit the money in any bank, then the final amount you realize at the end of 5 years would be much much higher.
An Airy equation is an equation in mathematics, the simplest second-order linear differential equation with a turning point.
What do you mean by differential equation?
Differential equations are equations involve rates of change (differentials). These rates of change are usually shown in the equations as a variable prefixed by a d (e.g. dx for the rate of change of the variable x). The same notation is also used in integration, but the integrand symbol is also added in such equations.
What is an ordinary differential equation?
It is one in which there is only one independent variable, ie there are no partial derivatives.
For example, (dy/dx) + 2y = cosx + x
Where you use Partial Differential Equation in your daily life?
It's all around you, starting with equation of diffusion and ending with equation of propagation of sound and EM waves.
How are Laplace transforms useful?
Some differential equations can become a simple algebra problem. Take the Laplace transforms, then just rearrange to isolate the transformed function, then look up the reverse transform to find the solution.
What does infinitesimal calculus mean?
Infinitesimal calculus pretty much means non-rigorous calculus, i.e. calculus without the notion of limits to prove its validity. When Newton and Leibniz originally formulated calculus, they used derivatives and integrals in the same manner that they're still used today, but they provided no formalism as to how those techniques were mathematically valid, therefore causing quite a debate as to their worth. The infinitesimals themselves simply had to be accepted as valid, in and of themselves, for the theory to work.
Where can the lines contain the altitude of an obtuse triangle intersect?
They can only intersect at the circumcentre, which is a point outside the triangle, beyond the side opposite the obtuse angle.
What are the use of differential equation in dialy life?
A differential equation is a tool to certains carrers to find and solve all kinds of problems, in my case i'm a civil engineer and i use this tool to solve problems in the area of hidraulics, and in the area of structures. The differencial ecuations have all kinds of uses in the area of engieneering and in other fields too
What are some adjectives for the math term function?
Here are some:
odd, even; periodic, aperiodic;
algebraic, rational, trigonometric, exponential, logarithmic, inverse;
monotonic, monotonic increasing, monotonic decreasing,
real, complex;
discontinuous, discrete, continuous, differentiable;
circular, hyperbolic;
invertible.
Applications of differential equation in agriculture?
Heat and mass transfer in greenhouse, Heat Flux in a Grain Bin, Suspension systems in tractors, Fluid Flow in a Pipe, Concentration in a Chemical Reactor, Falling Water Table, etc.
Answered by Ramin Shamshiri, U. of Florida at Gainesville.
