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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 does the derivative of a square wave look like?
It is a series of impulses (Dirac Delta functions), each positioned at the point where the square wave changes amplitude. For a negative change in amplitude, the impulse is -inf; likewise, for a positive change in amplitude, the impulse is +inf.
The fourier expansion of the square wave is:
4/pi sum_{k=1}^\infty [ sin((2k-1)*w*t) / (2k-1) ] Likewise, its derivative is:
4/pi*w sum_{k=1}^\infty [ cos((2k-1)*w*t) ]
If you plot, the first 50 terms, you will get a pretty good idea of what it looks like. impulse
What is the another name for an indirect proof?
Another name for an indirect proof is a "proof by contradiction." In this method, one assumes the opposite of what is to be proved, leading to a logical contradiction, thereby establishing the truth of the original statement. This technique is commonly used in mathematics and logic to demonstrate the validity of propositions.
How do you get a negative answer when subtracting two positive numbers?
Have the second number be greater than the first.
geometically , the definite integral gives the area under the curve of the integrad .
500
What properties of a function can be discovered from its Maclaurin series?
Yes. If the Maclaurin expansion of a function locally converges to the function, then you know the function is smooth. In addition, if the residual of the Maclaurin expansion converges to 0, the function is analytic.
How many hours does 1 ton of pellets last?
The answer will depend on what the pellets are composed of and how they are being "consumed".
Nonisotropic or anisotropic refers to a medium in which some characteristics depends on the direction in which the medium is studied.
A very common anisotropic material is wood. It is much easier to split it along its grain than across the grain.
1/6
Why?
.125 times 2 is 25, 25 times 3 is 75, so 3 X 2 = 6
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Really, to answer the question we must formulate an equation,
what percent of .75 IS .125 can be expressed:
.125 = .75 * P (Where P represents the percent)
So a simple re-arrangement and we get:
P = .125/.75 = .166666666666 or rounded to 16.67%
which is what the question was really asking
Could also have gone 1/8 divided by 3/4 = 1/6 = .1666666666=>
Is the empty set an element of every set?
No. An empty set is a subset of every set but it is not an element of every set.
The collision theory is when atoms, molecules or ions bash together or collide together.
Collision theory states that the rate of a reaction may be increased by : increasing pressure; raising the amount of heat energy; raising the concentration of the reactant and by introducing a catalyst.
Differences between full range Fourier series and a Half range Fourier series?
half range--- 0 to x
full range--- -x to x
