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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
What is cauchy riemen equation?
partial of u with respect to x = partial of v with respect to y
partial of u with respect to y = -1*partial of v with respect to x
A Bessel function is any of a class of functions which are solutions to a particular form of differential equation and are typically used to describe waves in a cylindrically symmetric system.
How do you derive Poisson's equation from Maxwell's equations?
Start with the differential form of Gauss's law:
∇ â— E = Ï/ε0, the divergence of the electric field is equal to the total charge density divided by the permittivity of free space.
Make the following substitution, assuming electrostatic charges:
E = -∇φ, the electric field at a point is equal to the negative gradient of the scalar electric potential.
This gives:
∇ ◠∇φ = -Ï/ε0
From an identity of vector calculus we get the following:
∇2φ = -Ï/ε0, which is Poisson's equation with f = -Ï/ε0.
What is the general equation of heat loss?
If you're looking for an equation that describes the loss of heat of an object in terms of time and the ambient temperature I would recommend Newton's law of cooling.
Look for it here http://www.ugrad.math.ubc.ca/coursedoc/math100/notes/diffeqs/cool.html
9.6 = 48/5 as an improper fraction in its lowest terms
An osculator is a surface that touches (or kisses) another so that they share a tangent at the point of contact.
What is the answer for y-13 equals -5?
y-13= -5 ----> add 13 to both sides
y-13 +13= -5 +13 ----> simplify
y=8
What are the disadvantages of differential compound motor?
Differential compound motors can be complex and costly to manufacture due to their intricate design, which may require precise engineering and additional components. They also typically have a more complicated control system, which can complicate maintenance and operation. Additionally, their performance can be affected by changes in load, potentially leading to instability or inefficient operation if not properly managed. Lastly, these motors may have lower efficiency compared to simpler motor designs under certain conditions.
Algebra is a branch of mathematics concerning the study of structures, relation and quantity. Together with geometry, analysis, combinatorics and number theory, Algebra is one of the main branches of mathematics.
What are the applications of maxwell's equations?
Maxwell's equations form the foundation of classical electromagnetism and have numerous applications across various fields. They are essential in designing electrical circuits, antennas, and wireless communication systems, enabling technologies like radio, television, and mobile phones. Additionally, they are critical in understanding electromagnetic wave propagation, optics, and technologies such as MRI in medical imaging. Furthermore, Maxwell's equations are fundamental in advancing theoretical physics, influencing areas like quantum mechanics and relativity.
What is the vibration equation?
There is no generic "vibration" equation, as many different things can vibrate with many different boundary conditions. There is, however, a generic wave equation which, as I just hinted at, can be used to formulate equations for specific vibrations.
Given a function u(x,y,z,t) where x, y, and z are spatial coordinates in Euclidean space and t is time, the wave equation is given as:
∂2u/∂t2 = vp2∇2u,
where vp is the phase velocity of the wave and ∇2 is the Laplacian.
For the specific example of a vibrating string with a small amplitude, the wave equation becomes:
∂2y/∂t2 = v2∂2y/∂x2,
where y(x,t) and v is the velocity of the wave.
The remarkable thing about the wave equation is how often Mother Nature uses it. The "u(x,y,z,t)" can describe the vibration of a drum head, the electromagnetic fields of light, the ripples on water, the sound of your voice and much more.
