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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 mathematical analysis?
Analysis can be thought of as a continuation of calculus. It deals with topics such as measure, limits, and integration/differentiation, and spaces (such as metric spaces).
When cross and dot product equal what is angle between A and B?
A · B = |A| |B| cos(Θ)
A x B = |A| |B| sin(Θ)
If [ A · B = A x B ] then cos(Θ) = sin(Θ).
Θ = 45°
What is the radical symbol really mean?
it is a progressive deformation of the letter r
first algebrists wrote r2 which became √2
Why empty set is open on the basis of def?
The empty set is open because the statement: "if x in A, some neighborhood of x is a subset of A" is true!
If A is empty, the hypothesis: "if x in A" is false and so the statement is vacuously true.
How hard would you have to push a 50 kg skater to increase her speed by 2 m sec sec?
Any force in the direction she's moving will cause her speed to increase.
The more force you use, the faster her speed will increase.
If you want to increase her speed by 2 m per sec in one second, then you want her
acceleration to be (change in speed)/(time for the change) = 2/1 = 2 m/sec2 .
F = M A = (50) (2) = 100 newtons
If you want to increase her speed by 2 m per sec in 0.1 second, then you want her
acceleration to be (change in speed)/(time for the change) = 2/0.1 = 20 m/sec2 .
F = M A = (50) (20) = 1,000 newtons.
If you want to increase her speed by 2 m per sec in 1 minute, then you want her
acceleration to be (change in speed)/(time for the change) = 2/60 .
F = M A = (50) (2/60) = 1.667 newtons.
There is no answer to this question. Feet is a unit of length, while 40 m x 2 m defines an area.
If you want square feet in that area, you multiply length times width to find that it's 80 square meters.
An inch is defined as 2.54 cm, so a foot would be 30.48 cm or 0.3048 meters. A square foot would be 0.3048 * 0.3048 square meters = 0.09290304 square meters.
Divide that 80 square meters to find out how many 0.09290304 chunks there are, and you find there are 861.112833 square feet in a rectangle 40m long and 2m wide.
What is the best estimate for the answer to 294.32 and ndash 198.37?
By definition, the "best" is always the exact value which, in this case, is 95.95
294.32 = 300 - 6 approx
198.37 = 200 - 2 approx.
So a good estimate for 294.32 - 198.37
is (300 - 6) - (200 - 2) = 300 - 6 - 200 + 2 = 300 - 200 - 6 + 2 = 100 - 4 = 96.
A less good estimate is 300 - 200 = 100.
What are limitations of z transform?
1.z transform can not aaply in continious signal.
2.z transform can not analyse analog filter
by - prakash kr
What is the difference in the sum of the interior angles of a decagon compared to a triangle?
The sum of the interior angles of a decagon is 1440 degrees
The sum of the interior angles of a triangle is 180 degreesThe difference in the sum of the interior angles of a decagon compared to a triangle
= 1440 degrees minus 180 degrees
= 1260 degrees
Set and the different of sets?
there are 5 diffeerent sets Natural Numbers whole numbers integers rational numbers irrational numbers.
How do you determine if a function is linear?
A function is linear if it is of the form f(x) = mx + c where m and c are constants and a is not zero.
The function implies that an increase of one unit in the input variable, x, always results in an increase of m units in the output.
What is the differentence between calculus and vector calculus?
Hence the reason for why it is called Vector Calculus, Vector Calc. is simply an expansion in the calculus subject are in math. It deals with Taylor's Formula (in calc 2 you learn the taylor polynomial and the taylor series), theorems from Green, Gauss, and Stokes, and much more.
How do you write 60 remainder 1 in decimal form?
that depends on the divisor.
601 divided by 10 = 60 R1; so 1/10 =0.1 => 60.1
121 divided by 2 = 60 R1; so 1/2 =0.5 => 60.5
So, in words, 1 is divided by the original divisor and that decimal form is added to 60.
How do you calculate 0.19 percent as a decimal?
0.19% means 0.19/100
= 0.0019
================just move the two decimal places here
