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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 an infinite sequence and an infinite series?

A series is a special case of a sequence where the n'th term is the sum of n numbers a1, a2, ..., an. In other words, it is a sequence in the form S1 = a1 S2 = a1 + a2 S3 = a1 + a2 + a3 ... Sn = a1 + a2 + ... + an

What is the difference between unilateral and bilateral laplace transform?

unilateral means limit is 0 to infinite and bilateral means -infinite to +infinite in laplace transform

Why is infinity minus infinity undefined?

Infinity is a concept, not an actual number.

Someone may say the number of stars is infinite, or that the number of fractions between 0 and 1 is infinite, or that the number of even numbers is infinite. But these are not things that can be subtracted.

What is 6 cubed in expontentional form?

It is 216 and as a product of its prime factors in exponents: 2^3*3^3 = 216

All kinds of reasoning in geometry?

*analogy- comparison if two things alike in some aspects or they will be semble

one another in other aspect.

*intuition - mental ability same as guessing.

*inductive - forming of general statement from particular specific case.

*deductive - making conclusion from general to particular stances.

Is -3.5 is a solution for inequality x-6?

No, because x-6 is an expression: it is not an inequality.

Does the relationship between the circumference and the diameter change when you use a different unit?

No. The units don't matter, the circumference always equals pi times the diameter. (This is only true of the circumference and diameter are in the same units. If for example, the circumference was in feet and the diameter in inches, the feet must be change to inches or the inches to feet in order for this relationship to be true.)

How do you make .56 into a fraction?

5.6=5.60

So it is like 5 60/100.

Simplify it to 5 6/10 because 10 times 6=60 and 10 times 10=100.

Simplify it again to 5 3/5.

So it is 5 and 3/5.

;) :D

What is 30 percent off of 66 dollars?

30% off = 70% left.

So answer = 66*70/100 = 46.20 dollars.

What is larger 1 second or 1 centisecond?

1 second = 100 centiseconds.

To help you remember, 1 meter = 100 centimeters and centi- anything is the same.

How do you know a line is linear?

Y = mx + b

No exponent on the x variable is one very telling sign that this is a line.

Difference between laplace transform and z transform?

the difference is the "S" and "Z" parameters.

S used for analog computation while Z for digital processing.

basically Z is the digital approximation of the analog frequency domain signal.

Z=exp(sT)

where T is the sampling time.