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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 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.

How do you figure out equivalent expressions using the same bases?

Logarithmic bases. exponential bases. addition, subtraction, multiplication, or division. more information needed to answer your question.

What is the measurement of 3 acres of land?

1 square mile is 640 acres so

3 acres = 3/640 sq mile

How many square yards are in a rectangle 12.00 feet wide and 900.00 feet long?

The area would be 10,800 square feet. Divide by 9 will give you 1,200 square yards.

How do you find the Nash equilibrium?

Step by step guide on how to find a Nash Equilibrium or Equilibria

Step 1. Look at the payoff matrix and figure out whose payoff's are whose:

Step 2. Figure out Player A's best response to all of player B's actions

Step 3. Figure out Player B's best response to all of player A's actions

Step 4. A Nash equilibrium exists where Player B's best response is the same as Player

Let f r to r be an elementary function let p and q be two distinct points on the graph of f what is slope of the line determined by these two points?

Let P and Q have coordinates (Px, Py) and (Qx, Qy), respectively (here x and y are intended as subscripts)

Note that Py = f(Px) and Qy = f(Qx)

Slope m = (vertical difference) / (horizontal difference)

m = (Qy-Py) / (Qx-Px)

What is the use of a differential?

Differentials can be used to approximate a nonlinear function as a linear function.

They can be used as a "factory" to quickly find partial derivatives.

They can be used to test if a function is smooth.

What is the angle called when light hits a mirror or glass block?

If I remember correctly, the angle that the light makes with the plane of the surface is called the incident angle.
Incident angle.

How many ounces go in 1 ton?

One ton is 2000 LB. One LB is 16 oz. 2000 x 16 = 32,000 oz per ton.

What is an effective mass of hole?

A hole, by definition, has nothing in it and so its mass is zero.

What are the four basic operation of venn diagram?

The four basic operations for sets A and B, in the universal set U are:

  • Union (A or B)
  • Intersection (A and B)
  • Symmetric Difference (A or B but not both)
  • Complement (not A - relative to U).

How do you enter data into TI83 to find explained variation total variation?

Some TI83's can be set up differently, so it is highly recommendable to read the user guide for the TI83 in question. The user would need to go into the VarStat option and enter all the appropriate fields to have the calculator bring in the appropriate variables and totals.

What are the odd integers greater than 40?

Any integer that is divisible by 2 with no remainder is even otherwise it is an odd integer

What is the advantage of using OLS method?

OLS leads to a closed-form solution. The problems in other metrics such as L1 do not. Furthermore, the statistical theory for OLS is much richer than for other metrics in spite of the fact that OLS leads to difficulties in dealing with 'outliers'.