0
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
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.
When does the multiples of 12 and 20 meet?
- 12, 24, 36, 48, 60, 72, 84, 96, 108, 120, 132, 144, 156, 168, 180, 192, 204, 216, 228, 240, . . .
- 20, 40, 60, 80, 100, 120, 140, 160, 180, 200, 220, 240, 260, 280, 300, 320, 340, 360, 380, 400, . . .
How do you interpret a p value of 0.030?
p=0.030 means that there is a 3% chance that you are wrong to reject the null hypothesis (H0). In a lot of studies, p<0.05 is considered significant evidence and the H0 is rejected. However, this depends on the research done, sometimes the boundary is set at p<0.01 or even lower.
Example: a study tries to see if males are, on average, taller then woman
H0: Males do not have a higher average length than women
Ha: Males have a higher average length than women
P-value is set at 0.05
[Statistical analysis, including a check of all assumptions]
p=0.03<0.05
This dataset yielded a p<0.05. Therefore, the H0 is rejected. This study supports the conclusion that males have a higher average length than women
What are good books on differential equations for novices?
The book I used in college, and still use when needed, is A First Course in Differential Equations, by Dennis Zill. It's very clearly written with tons of problems and examples.
The book Mathematics From the Birth of Numbers, by Jan Gullberg, is a cool book in general and also has a short and sweet introduction to ordinary differential equations (ODEs) at the end. He derives the general theories of ODEs pretty much entirely through the use of applications.
Gradshteyn and Ryzhik's Table of Integrals, Series, and Products, which is a must-own book for mathematicians and scientists anyways, also has a rather short, but surprisingly detailed section on ODEs toward the end. I wouldn't recommend this for a novice, but it's a great reference to have once you've become familiar with differential equations.
Mathematical Methods in the Physical Sciences, by Mary Boas, is a classic text covering many topics, including ODEs and PDEs (partial differential equations). I'd get this book simply for the immense amount of very useful topics it introduces in all the fields of mathematics, including the calculus of variations, tensor analysis, and functional analysis.
Eventually, you'll need or want to learn about PDEs, and the most intuitive and comprehensible book I've seen regarding them is Partial Differential Equations for Scientists and Engineers, by Stanley Farlow. It's almost (if such a thing can be said about a rigorous math book) entertaining.
What is the limitations of schrodinger wave equation?
The biggest limitation by far is that an exact solution is possible for only a small number of initial conditions. For example, one can figure out the solution for permitted states of one electron around a nucleus. However, there is no exact solution for even two electrons around a nucleus.
Is a flagpole 8m or 8km in length?
8m, considering the distance a car travels can be calculated in km/h.
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
What are the Applications of differential compound?
Differential compounded generators are used in Ward Lenard motor generator loops. The shunt fields on these generators are separately excited and when the shunt field polarity is reversed by the controller the series field helps drive the generator voltage to zero thus aiding in the reversal of current.
What are the applications of partial differential equations in computer science?
All the optimization problems in Computer Science have a predecessor analogue in continuous domain and they are generally expressed in the form of either functional differential equation or partial differential equation. A classic example is the Hamiltonian Jacobi Bellman equation which is the precursor of Bellman Ford algorithm in CS.
What is a degree in a differential equation?
A degree of a differential equation is the highest power of highest order of a differential term of the equation.
For example,
5(d^4 x/dx^4) - (dx/dx)^2 =7
Here 5(d^4x/dx^2) has the highest order and so the degree will be it's power which is 1.
How op amp is used in an electronic analog computer to solve a differential equation?
In a computer there are many A/D converters that put analog into digital. This signal is what is usually then led into an op amp which in the right configuration can be designed into an integrator or differentiator which is then used to solve differential equations.
How first order derivative zero in differential equations?
Well, 0 is a constant, so the derivative of 0(, or any other constant) is 0. This information is coming from an 11 year old kid.
