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Mathematical Analysis

Mathematical analysis is, simply put, the study of limits and how they can be manipulated. Starting with an exhaustive study of sets, mathematical analysis then continues on to the rigorous development of calculus, differential equations, model theory, and topology. Topics including real and complex analysis, differential equations and vector calculus can be discussed in this category.

2,575 Questions

Who are the permanent members of the United Nations?

The list changes every few years. Please see the accompanying link for the current list.

What is Working Capital Ratio or Current Ratio?

The Working Capital Ratio or Current Ratio is a financial ratio that measures whether or not a company has enough cash to pay off all the debt payments that are due over the next 1 year (12 months) It compares the organizations current assets and its current liabilities.

Formula:

WCR = Current Assets / Current Liabilities

Ex: Let us say ABC Corp has total assets of 5 crores and owes State Bank of India a loan of 3 crores to be repaid before the end of next year, the WCR for them would be

WCR = 5,00,00,000/3,00,00,000 = 1.66

This effectively means that, as of today ABC corp has 1.66 rupees for every rupee of debt it owes SBI.

Though this is good, an acceptable WCR in market terms is 2 or greater which shows that the company is sufficiently liquid and financially stable.

What are the seven base units in the SI unit system?

They are

  • Length: Metre
  • Mass: Kilogram
  • Time: Second
  • Electric Current: Ampere
  • Temperature: Kelvin
  • Luminosity: Candela
  • Amount of a Substance: Mole

What is the Fourier transform of the signum function?

The Fourier transfer of the signum function, sgn(t) is 2/(iω), where ω is the angular frequency (2πf), and i is the imaginary number.

How does vector calculus apply in fluid mechanics?

The velocity at each point in the fluid is a vector. If the fluid is compressible, the divergence of the velocity vector is nonzero in general. In a vortex the curl is nonzero.

Why is probability an exact science?

The origin of logic comes from scientific deduction of thought. The only science that is exact, is the science and facts that cannot be known for sure.or at least seen with a physical eye. In the beginning God created the heavens and the earth. So the probability of an exact science is... inconceivable.

Fourier analysis shows that the saw tooth wave consists of which type of wave?

Fourier analysis shows that the saw wave is constructed through manipulation of a sine wave, I can't remember the maths behind it but it's definitely a sine wave.

What is the quotients of the first 15 terms of Lucas sequence?

I don't know the exact numbers without using a calculator but they aproach phi, 1.6180339..., if that helps you at all. All sequences that use the formula Xn-1+Xn-2= Xn approach phi.

The temperature at sea level is 20 degrees cecilius the air pressure is 101.3 kpa what is the temperature at the top of a mountain 3000m above sea level?

The temperature at sea level is 20 degrees celsius. What is the temperature at the top of a mountain 3000 m above sea level?

Decrease of temperature with height: 6.5 Kelvin per km to about 11 km altitude.

That is for a height of 3 km = 3000 m about 6.5 times 3 = 19.5 degrees colder than the ground. So if at ground it is 20°C, at the top of the mountain (3000 m) it will be about 0°C.

What date is Thanksgiving?

Thanksgiving, or Thanksgiving Day, is celebrated on the fourth Thursday in November in the United States. The exact date changes every year.

A legendary Thanksgiving celebration was held in 1621

On a graph which axis is horizontal and which axis is vertical?

The convention for an x-y graph is as follows:

y |

|

|_____

x

where the x-axis is horizontal and the y-axis is vertical.

What does sx mean in mathematical term?

sx is not a standard term in mathematics so more context is needed.

Mesh analysis examples with complex numbers?

instead of using mesh loop analysis, because most calculators don't operate in variable and complex mode at the same time, you have to use substitution.

What is after calculus?

Calc 2, then Calc 3, then usually Differential Equations

What is sin in math terms?

when you have a right triangle and one of the two non-right angles is theta, sin(theta) is the side of the triangle opposite theta (the side not touching theta) divided by the side that does not touch the right angle