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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

Is bronze hard to find?

Bronze is a widely available alloy made from copper and tin, so it is not particularly hard to find. It has been used for thousands of years and can be found in various artifacts, sculptures, and architectural elements around the world.

What strategy is used to multiply mentally?

Most people who multiply mentally are using some form of the distributive property. If you wanted to do something like 47 x 5 in your head, that's (40 x 5) + (7 x 5) = 200 + 35 = 235

What is the difference between fourier series and fourier transform with real life example please?

A Fourier series is a set of harmonics at frequencies f, 2f, 3f etc. that represents a repetitive function of time that has a period of 1/f.

A Fourier transform is a continuous linear function. The spectrum of a signal is the Fourier transform of its waveform. The waveform and spectrum are a Fourier transform pair.

How much square cm is equal to square feet?

As we know,

1 ft = 30.48 cm

1 square ft=(30.48)2 square cm

=30.48*30.48 square cm

=929.0304 square cm

How do you get the rate in percentage?

Multiply the rate by 100, then express it as a decimal number, followed by the % sign.

How many sides on a dodecagon?

There are 10 sides to a dodecagon and there are 12 sides on a dodecahedron.

* * * * *

There are, actually 12 sides to a dodecagon, not 10.

How do you find the diameter of a tank when you only have the circumference?

the question: a cylindrical tank has a circumference of 13.2, determine the diameter and the cross-sectional area of the tank?

How can you use math in the real world?

Maths is EVERYWHERE in the real world ! Take the simple act of buying a newspaper. How will you know (a) what money to give the vendor, and (b) if the vendor has given you the correct change. OR - how will you know if you've been paid the correct wages for your job ! And they're just simple examples !

Is it possible to have in a subset S from the set of Real numbers a finite number of upperbounds and yet have no least upperbound?

Let me rephrase it. You mean take a bounded subset of real numbers, S, and find a subset of all the upperbounds of S, say D, such that sup S is not in D?

If I get you right, then yes.

Take D := {a : a = sup s + n, n is natural and n < 4} so the first element is sup s + 1 > sup s, and the remaining two terms are even larger than the first one.

But I think I got you wrong, go through the Completeness Axiom.

That is for any two set A and B such that for all a in A, b in B, a <= b, and they share a maximum of one element, then there exist at least one number x such that a <= x <= b

In particular, A have a supremum, sup A <= x and B have an infimum inf B > = x

sup A <= inf B if they are equal then they must be x.

Kerja projek matematik tambahan tugasan 2 2011?

tentukan dimensi bagi kek berbentuk bulat berjisim 5 kg yang memerlukan jumlah krim segar yang minimum untuk dihias.gunakan sekurang-kurangnya dua kaedah penyelesaian yang berbeza termasuk penggunaan kaedah kalkulus.nyatakan sama Ada kek dengan dimensi tersebut sesuai untuk dibakar atau tidak.berikan penerangan bagi menyokong jawapan anda.

What would cause a 1996 Mercury Grand Marquis LS to feel like it is running over speed bumps when driving between 38-43 miles per hour?

I am going to answer my own question. I have found this site very helpful and hope I can contribute something to help others. I just purchased this car and did so on my son's advice. He is a police officer and drives a Ford Crown Victoria at work. He told me about the safety rating, gas mileage and comfort. He did not tell me all the little problems that went along with owning a Ford product! The used car I purchased is a one owner, well kept automobile from an older couple. I don't think they even knew that the transmission was "chattering" some at speeds of 31-43 mph. I didn't recognize it until sometime after I purchased the car. When I did realize I had a problem I kept thinking that this felt like either an electrical problem or I had this vague feeling of being familiar with the sound. I owned a GMC suburban and when it was only a few years old I had all the fluids changed for a long family vacation, even the rear end. During the trip, while pulling a large travel trailer, the right rear tire began to "chatter" around corners and finally almost seized up. I was really worried about the large bill for repairs but a kindly soul in a small town listened to my story and told me to go to a GM parts house and purchase a small bottle of additive for Limited slip rear ends (which he had discovered I had on my truck). The problem was solved instantly with a $6.00 bottle of additive. I kept telling people that would look at my Mercury that this felt the same way and that this car did have some sort of limited slip. Finally an older mechanic with his own transmission shop listened, drove the car and sent me for a bottle of GM limited slip additive. He said that the torque converter was made from the same materials and in very much the same way as a limited slip rear end. He said if the additive worked, then to drive it for a few hundred miles, have the transmission flushed and add another bottle of additive from GM. The problem was solved instantly from the first time I added the small bottle of additive. The mechanic is pleased and thought that the torque converter was the problem. If I have not had prior damage to the transmission, my problem should be solved for many miles to come.

Can a discontinuous function be developed in a Fourier series?

Yes, a Fourier series can be used to approximate a function with some discontinuities. This can be proved easily.

Drive law of reflection by using fermat's principle?

Out of all possible paths that light might take, to get from one point to another, it takes the path that requires the shortest time.

When would one use the Fourier Transform?

Physics would be one of a few examples of fourier transform. One would also use it when they are using engineering so, yeah that is basically it as far as the fourier transform is concerned.