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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
Why is it important to study set theory?
All things are sorted or categorized in this world. We need to know the proper equation to find the solution to which set theory is best for our purpose.
Can it be possible limit of logarithmic functions equal to logarithmic function of limit?
Yes it is possible.
If limit(f) > 0 then limit(loga(f)) = loga(limit(f)).
All logarithmic functions loga(x) are continuous as long as x > 0. Where-ever a function is continuous, you can make that kind of swap.
If vector A is perpendicular to vector B and C then Vector A is parallel to?
Vector A is parallel to the cross product of vectors B and C, and it is parallel to the axis that neither B or C lie along if the two other axes are defined as the axes that B and C lie along.
Anything divided by 0 is UNDEFINED thus its not possible
e.g. x/0 = undefined
x= any number
What are the different rules of finding the limit of function?
Given a function sequence f1(x), f2(x), f3(x)..., the limit can be defined in several ways:
- Point by point limit; that is, it converges to a new function at each point.
- Lp convergence; that is, it converges to a new function in Lp-norm.
- Almost everywhere convergent; that is, it converges to a new function except a set with measure zero.
For what purpose you use fourier transform in real life?
we use fourier transform to convert our signal form time domain to frequency domain.
This tells us how much a certain frequency is involve in our signal.
It also gives us many information that we cannot get from time domain.
And we can easily compare signals in frequency domain.
How does the graph of Fourier Series differ to the graph of Fourier Transform?
You can graph both with Energy on the y-axis and frequency on the x. Such a frequency domain graph of a fourier series will be discrete with a finite number of values corresponding to the coefficients a0, a1, a2, ...., b1, b2,...
Also, the fourier series will have a limited domain corresponding to the longest period of your original function.
A fourier transforms turns a sum into an integral and as such is a continuous function (with uncountably many values) over the entire domain (-inf,inf). Because the frequency domain is unrestricted, fourier transforms can be used to model nonperiodic functions as well while fourier series only work on periodic ones.
Series: discrete, limited domain
Transform: continuous, infinite domain.
Very good question, well written. It gave me all the details. I divided 20 into 1400. It told me you need 70 gallons. Then, I multiplied $4.00 by 70. I think the answer is $280.00
It was first discovered simultaneously by Isaac Newton and another mathematician named Gottfried Leibniz. (see related link). However, the notation that we use today is for the most part that of Leibniz. As far as development, it is still an actively researched field of mathematics with thousands of contributors.
Also, integral calculus is often attributed to Archimedes of Syracuse (c. 250 BC), having been largely ignored after him.
Do employers have to pay time and a half for overtime work of a contract laborer?
Generally, the wages paid for labor of a contact laborer are governed only by the contract. If the contract does not provide for overtime pay, none is due. Sometimes a contract employee will try to avoid this rule by denying that he is a contract employee. This may be disproved by a written contract, by the employer's records, or by the conditions of employment. The conditions of employment that establish an independent contractor vs employee relationship with the employer is a complicated area of the law. Either party may have tax problems if the relationship is misunderstood.
What is the answer when you estimate 4 and one third x 2 and four fifths?
Estimating 5 and 9/10ths times 2 and 2/3rds might be done by considering that 5 and 9/10ths is about 6, and 2 and 2/3rds is somewhat less than three. Six times three is eighteen, but it's less than that by a couple or three, so the answer is about fifteen or sixteen.
it's tricky
Well, that question is far too difficult to answer; you should take some Calc courses.
Calculus is the study of the rate at which something changes, in relation to something else... Think slope... except it gets complicated.
What is the science behind sterilized medical instruments?
The basic science is that living organisms, including bacteria, cannot survive in elevated temperatures. Medical instruments are wrapped in cloth and placed in an autoclave, which heats the instruments to about 134 degrees C (272 degrees F) for about 15 minutes. Sometimes the unit is pressurized.
Can you give an example of how Fast Fourier Transforms are used in financial models?
There is a beautiful paper by Ales Cerny entitled "Introduction to Fast Fourier Transform in finance", which gives many interesting examples.
Usage of maths in communication?
Asking what price something is, saying your age, pretty much everything you talk about: how many words you say, how many letters are in that word so forth
Compared to 101 kiloPascals (kPa) at sea level, she would experience 87.9 kPa.
Alleles can be either dominant or recessive. They can be identical or different for any given gene in a somatic cell, and can represent alternative forms of a gene.
