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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 equivalent fraction for 2 5?
Multiply both the numerator (top) and the denominator (bottom) of the fraction by any non-zero integer. You will have an equivalent fraction.
Why do you use laplace transform?
The most generalized reason would be:
"To solve initial-valued differential equations of the 2nd (or higher) order." Laplace is a little powerful for 1st order, but it will solve them as well.
There is a limitation here: Laplace will only generate an exact answer if initial conditions are provided. Laplace cannot be used for boundary-valued problems.
In terms of electronics engineering, the Laplace transform is used to get your model into the s-domain, so that s-domain analysis may be performed (finding zeroes and poles of your characteristic equation).
This is particularly useful if one needs to determine the kind of response an RC, RLC, or LC circuit will provide (i.e. underdamped, overdamped, critically damped).
Once in the s-domain, we may begin discussing the components in terms of impedance. Sometimes it is easier to calculate the voltage or current across a capacitor or an inductor in terms of the components' impedances, rather than find it in a t-domain model.
The node-voltage and mesh-current methods used to analyze a circuit in the t-domain work in the s-domain as well.
What is larger than a terabyte?
1024 terabytes equals 1 petabyte, 1024 petabytes equals 1 exabyte, 1024 exabytes equals 1 zetabyte, and 1024 zetabytes equals 1 yottabyte. Stay tuned...
There are infinitely many possible rules. One simple rule, for input n isU(n) = (n^2 + 3n + 2)/2 = (n + 1)*(n + 2)/2
or, equivalently, the sum of all the integers from 1 to n+1.
When can you say that it is a prism?
A prism is a polyhedron (a many sided 3D shape) with two identical and parallel faces called the bases. The vertices of the two bases are joined by straight lines forming a number of rectangular faces. For example, a pentagonal prism consists of 2 pentagonal faces and 5 rectangular faces, and has 15 edges and 10 vertices.
5 = 1 x (1 + .06/4)4Y
5 = (1.015)4Y
log(5) = 4Y log(1.015)
4Y = log(5)/log(1.015)
Y = 0.25 log(5)/log(1.015) = 0.25 (0.69897) / (0.00646604) = 27.025 years
That means you won't quite be there at the end of the 27th year,
but the interest payment at the end of the first quarter of the 28th
year will put you over the top.
How you can use fourier analysis in the communication?
Fourier analysis is used in communication systems to analyze and process signals by decomposing them into their frequency components. This allows for the effective modulation and demodulation of signals, enabling clearer transmission over various media. Additionally, it aids in filtering out noise and optimizing bandwidth usage, improving the quality and efficiency of data transmission in applications such as radio, television, and digital communication.
Why is it important to be able to identify sets and set theory as related to business operations?
Why is it important to be able to identify sets and set theory as related to business operations?
How do you multipy a fraction with a mixed number?
Convert it into an improper fraction then multiply.
Example:
1 1/2 * 3 3/4
is
3/2 * 15/4 = 45/8 or 5 5/8
Write thus:
3/1 x 3/10
Then multiply across:
3 x 3 = 9
1 x 10 = 10
Which gives the answer of 9 over 10 (9/10)
To me, I believe that a power set is not empty. Here is my thought:
∅ ∊ P(A) where P(A) is the power set and A is the set.
This implies:
∅ ⊆ A
This means that A = ∅, but ∅ ∉ A. ∅ ∊ A if A = {∅} [It makes sense that ∅ ∊ {∅}]. Then, {∅} ⊆ A, so {∅} ∊ P(A) = {∅, {∅}}. That P(A) is not empty since it contains {∅} and ∅.
What is countable set in measure theory?
A countable set is an infinite set that can be put into a one-to one correspondence with the counting numbers. In other words, it is possible to arrange all of the elements of the set in a sequence with a first element, a second element, and so on.
Georg Cantor proved that the rational numbers are countable, but the real numbers are not.
One proof (not Cantor's) that the rationals are countable: Choose any rational number, write it out in its simplest form. Whatever number you wrote is represented by a finitely long string of either the numerals or the division slash (possibly preceded the negative sign). If you consider a base-eleven number system with the division slash as the eleventh numeral, then whatever rational number you just wrote out corresponds directly and unambiguously to one specific integer. Since there exists a mapping scheme that assigns any arbitrary rational number to a specific integer, the rational numbers are countable.
How does the slope affect the steepness of a line?
The larger the absolute value of the slope if, the more vertical, or steeper, the line is. A horizontal line has slope 0, a line that is just a very little bit steep, might have slope, 1/10, a line that is very steep might have slope 10/1 or 10, or even 1000000 and as that number gets bigger and bigger, the line becomes almost vertical. For practical purposes, the slope, or steepness, of the line can be determined by rise over run, or, with a 0/0 intercept, then y over x, or, y1-y2 over x1-x2.
What does the word integers mean in math?
The integers are the infinite collection of all the natural numbers (including zero): 0, 1, 2, 3, 4,... etc., together with the negatives of the non-zero natural numbers: -1, -2, -3, -4, ...
As a set, the integers are usually denoted by the symbol Z (often in a blackboard font), and written {...-3, -2, -1, 0, 1, 2, 3, ...}.
What is another way to say twelve over twelve?
One would suffice in mathematics, because twelve twelfths of something is a whole.
resolved
