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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
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.
Why active differentiator circuits are not used in analog computer to solve differential equations?
The op amp differentiator is generally not used in any analog computer application. The basic reason for this is that high-frequency noise signals will not be suppressed by this circuit; rather they will be amplified far beyond the amplification of the desired signal.
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."
Derivation of navier-stokes equation for a cylindrical coordinates for a compressible laminar flow?
it is easy you can see any textbook........
What is the use of a differential?
Differentials can be used to approximate a nonlinear function as a linear function.
They can be used as a "factory" to quickly find partial derivatives.
They can be used to test if a function is smooth.
What are the odd integers greater than 40?
Any integer that is divisible by 2 with no remainder is even otherwise it is an odd integer
What is differential equation in mathematics?
It is an equation containing differentials or derivatives, there are situations when variables increase or decrease at certain rates. A direct relationshin between the variables can be found if the differential equation can be solved. Solving differential equations involves an integration process:first order dy _____ which introduces one constant arbitrary dx And secnd order which introduces two arbitrary constant arbitraries 2 d y ______ 2 d x dx
What are the degrees of differential equation?
The degree of a differential equation is the POWER of the derivative of the highest order. Using f' to denote df/fx, f'' to denote d2f/dx2 (I hate this browser!!!), and so on, an equation of the form (f'')^2 + (f')^3 - x^4 = 17 is of second degree.
Uses of differential equation in computer engineering?
A computer engineer won't usually need this directly to develop computer programs, for example; he would need this if he specifically helps solving problems in related areas, such as engineering, physics, etc.
A computer engineer won't usually need this directly to develop computer programs, for example; he would need this if he specifically helps solving problems in related areas, such as engineering, physics, etc.
A computer engineer won't usually need this directly to develop computer programs, for example; he would need this if he specifically helps solving problems in related areas, such as engineering, physics, etc.
A computer engineer won't usually need this directly to develop computer programs, for example; he would need this if he specifically helps solving problems in related areas, such as engineering, physics, etc.
Daily life examples about differential equations?
Here are two variables
Demand and Price, whereas Price is Independent variable &
Demand is dependent variable, i.e. if price of something changes the demand will also be affected. Now simple Differential Equation is
d (Demand)= constant
d (Price)
But keep in mind that Price is a function not a simple variable.
