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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 difference between the fourier laplace transform?
They are similar. In many problems, both methods can be used. You can view Fourier transform is the Laplace transform on the circle, that is |z|=1. When you do Fourier transform, you don't need to worry about the convergence region. However, you need to find the convergence region for each Laplace transform.
The discrete version of Fourier transform is discrete Fourier transform, and the discrete version of Laplace transform is Z-transform.
Where do you put the carry in Lattice Multiplication?
Put it on the next number, and add them carry to the number.
How old would you be is born October 16 1993?
- A person born on October 16, 1993 would be 19 years old and on October 16, 2012 (This year) they would be 20 years old.
What set of 12 numbers has the following landmarks minimum 28 maximum 34 mode 29 median 30?
You are given the minimum 28 and maximum 34, which means that all the numbers are in the set (28, 29, 30, 31, 32, 33, 34). Since there are fewer than 12 numbers in the set to choose from, there will have to be repeats. You are given the mode 29, which means that 29 appears more often than any other number in the set. The median is 30, which means that half the numbers are above 30 and half are below. There are many different ways to construct a set meeting those conditions. One such set would be (28, 29, 29, 29, 29, 30, 30, 31, 32, 33, 34, 34).
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 .
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.
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