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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

One two three?

Ingredients

  • 1 lb Ground beef
  • 1 Sm Cabbage
  • 1 cn Tomato soup undiluted
  • 1 Salt & pepper to taste

Alternately layer ground beef and cabbage in a large dutch oven ending with cabbage. Pour undiluted soup over the top. Add salt and pepper if desired. Cover and bake for 1 hour.

What is relation between laplace transform and fourier transform?

The Laplace transform is related to the Fourier transform, but whereas the Fourier transform expresses a function or signal as a series of modes ofvibration (frequencies), the Laplace transform resolves a function into its moments. Like the Fourier transform, the Laplace transform is used for solving differential and integral equations.

What is the difference between fourier series and discrete fourier transform?

Fourier series is the sum of sinusoids representing the given function which has to be analysed whereas discrete fourier transform is a function which we get when summation is done.

What is the most common 4 digit passcode?

Believe it or not loads of people use ones like 1234 or 0000

What is an open complex?

An open complexAn open complex is the complex of RNA polymerase and one DNA strand (The antisense strand) while a Closed complex is the complex of RNA Polymerase when it is bound to the double stranded DNA. The RNA Polymerase first creates the closed compex. The open complex is created when the double stranded DNA is separated to two strands.

Why does sin plus cos equal one?

There is no reason at all. For most angles sin plus cos do not equal one.

How do you define an upper bound of a subset?

Let B, ≤ be a partially ordered set and let C⊂ B with c Є C. Then the element bЄ B is an upper bound for C if c ≤ bfor each c Є C.

See related links for more information.

How do you calculate dollars and cents?

You add it. Or you can use decimals if i have $8.50 and i want to take out $5.00 i would use decimals and same if your adding subtracting etc.

If you don't know how to multiply decimals just ignore them then add them i the end, how you know where it goes? You count how many numbers are behind!

Same for division except you divide.

What example is there for when a power of 2 is equal to a power of 4 and greater than the number W?

4 = 2²

→ 4^x = 2^(2x)

We want 4^x > w

Taking logs gives:

x log 4 > log w

→ x > log w / log 4

This can be solved to find a value of x by using logs to any base (the same base for each log).

Note that as w become less positive the value of x decreases at a much faster rate.

As w tends towards 0+, x will become more and more negative.

If w is negative, log w does not exist and all values of x will solve the problem - this is obvious as 4 (and 2) to all powers are positive which are all greater than a negative number.

If you require an integer solution to the problem, then the set of solutions starts with the first integer that is greater than x and continues with each next integer higher.

Examples:

  • w = 40
The above gives x ≈ 2.661 → solution set of integers is {3, 4, 5, ...) with corresponding values {64, 256, 1024, ...}
  • w = 64
The above gives x = 3 → solution set of integers is {4, 5, 6, ...} with corresponding values {256, 1024, 4096, ...}

Is triple dot product defined?

If by "triple dot product" you mean u·v·w, then no, because that would imply the existence of a dot product between a vector and a scalar.

Who is this scientist created the Solar Disruption Theory?

Mark Hanson i guess.. but i'm not pretty sure with that but many people say it's Mark Hanson who created the SOLAR DISRUPTION.

Simplify 45 over 64?

45/64 is already in its simplest form

What is a weak solution?

the solution which has low dissolving power i guess

How can you simplify 1.1?

1.1, as a decimal number, cannot be simplified.

What is the error propagation in numerical methods?

Error propagation in numerical analysis is just calculating the uncertainty or error of an approximation against the actual value it is trying to approximate. This error is usually shown as either an absolute error, which shows how far away the approximation is as a number value, or as a relative error, which shows how far away the approximation is as a percentage value.