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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
What is the purpose of calculus?
To solve problems that involve infinitesimal quantities. Such problems are solving for the slope of or area under a curve.
What is a product in a multiplication sentence?
The product of a multiplication sentence is the answer.
Difference between fourier transform and first fourier transform?
The question almost certainly intends "fast" instead of "first". The difference between a Fourier Transform and a Fast Fourier Transform is only the amount of effort required to generate the result. Both have the same the result. The original Fourier Transform requires an amount of effort which is proportional to the square of the amount of data being used. So if the amount of data doubles, the amount of effort to calculate the result quadruples. In contrast, the subsequently discovered Fast Fourier Transform requires an amount of effort proportional to the product of the amount of data and the base-two logarithm of the amount of data. Thus, if the amount of data doubles, the amount of effort increases but by less than a quadruple. With each doubling of the data size, the amount of effort increases by a diminishing factor which slowly drops toward but never reaches two.
What is a reasonable interval?
Ah, a reasonable interval is like a gentle pause between two moments, allowing you to breathe and reflect. It's a space where you can gather your thoughts and feelings before moving forward. Just like in painting, it's important to give yourself these intervals to appreciate the beauty of the process and make thoughtful decisions.
Advantages of laplace transform in solving differential equations?
please follow this link,
u can see its brief advantage compared to the usual method
http://books.google.com/books?id=zMcAXrJpyPkC&pg=PA902&lpg=PA902&dq=advantages+of+laplace+transform+for+solving+differential+equations&source=bl&ots=txzL6fkRMR&sig=rFigMIeYaT3T65q-ydLM8kjioyE&hl=en&ei=KQ3kSrr5CILA-Qann4nJCQ&sa=X&oi=book_result&ct=result&resnum=8&ved=0CCMQ6AEwBw#v=onepage&q=&f=false
Is the limit exists for a monotone sequence An?
If a monotone sequence An is convergent, then a limit exists for it. On the other hand, if the sequence is divergent, then a limit does not exist.
What is the difference between an open circle and a close circle on a number line?
an open circle on a number line means the answer is just less than or greater than (< or >), but a closed circle means the answer is less than or equal to, or greater than or equal to (< or > with a line under it)
What are the properties of a dot product?
In mathematics, the dot product is an algebraic operation that takes two equal-length sequences of numbers (usually vectors) and returns a single number obtained by multiplying corresponding entries and adding up those products. The name is derived from the interpunct "â—" that is often used to designate this operation; the alternative name scalar product emphasizes the scalar result, rather than a vector result.
The principal use of this product is the inner product in a Euclidean vector space: when two vectors are expressed in an Orthonormal basis, the dot product of their coordinate vectors gives their inner product. For this geometric interpretation, scalars must be taken to be Real. The dot product can be defined in a more general field, for instance the complex number field, but many properties would be different. In three dimensional space, the dot product contrasts with the cross product, which produces a vector as result.
Why isn't zero divided by zero either zero or one?
Consider the equation 0 times x = 0.
This is true for every number x.
Divide both sides by 0; we get x = 0/0.
So zero divided by zero could be any number at all; it could be -42, or 273.15, or anything else.
If we try to pick one value for 0/0, we will eventually get into trouble.
Examples:
Say 0/0 = 1 = 1/1.
Multiply the numerator of both sides by 3. Then
(3 times 0)/0 = (3 times 1)/1.
Therefore 0/0 = 3.
Since 0/0 = 1, we get 1 = 3, which we really don't want, as all of our mathematics will become useless.
Say 0/0 = 0.
Then 0/0 = 0/1.
Turn both fractions upside down. We get
0/0 = 1/0, but since 0/0 = 0, we get
0 = 1/0.
Multiplying both sides by 0 gives
0 times 0 = 1,
so 0 = 1, which we don't want either.
The best thing to do is not to give 0/0 any value; we say 0/0 is undefined. Also we take x/0 to be undefined for every number x.
How do you find the perimeter of an oval?
This is not easy. If an approximation is sufficient, you could (for example):
* measure it with a piece of string, or
* approximate your oval using circular arcs and add up the lengths of those arcs.
If your oval is an ellipse you could use elliptic integrals, in which case you might want to provide specific details about the oval.
You can also use this formula:"a' and "b" are the semi major and minor axises of the oval. if the way i explained it isn't clear then go to:
http://mathcentral.uregina.ca/QQ/database/QQ.09.04/john3.html
that's where i got my info. And the picture isn't mine, its from that website.
State and prove convolution theorem for fourier transform?
Convolution Theorems
The convolution theorem states that convolution in time domain corresponds to multiplication in frequency domain and vice versa:
What is a quantity whose values changes?
computer iscalled deligent and versatile machine because it never filltiared like human beings
usually figures in math is dealing with a diagram in a text book or numbers dealing with money
