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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
Set and the different of sets?
there are 5 diffeerent sets Natural Numbers whole numbers integers rational numbers irrational numbers.
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 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.
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
How many electrons would fit in the universe?
somewhere around 4*10^184 planck cubes could fit in the obervable universe and those are a lot smaller than electrons. So that number would be somewhere between a googol and this number.
What is the difference between a 'dot product' and a 'cross product'?
Given two vectors, a and b, their dot product, represented as a ● b, is equal to their magnitudes multiplied by the cosine of the angle between them, θ, and is a scalar value.
a ● b = ║a║║b║cos(θ)
Cross Product:Given two vectors, a and b, their cross product, which is a vector, is represented as a X b and is equal to their magnitudes multiplied by the sine of the angle between them, θ, and then multiplied by a unit vector, n, which points perpendicularly away, via the right-hand rule, from the plane that a and bdefine.
a X b= ║a║║b║sin(θ)n
What are the intervals in a coordinate graph?
They depend on what is being graphed and in the level of detail of the information.
The S transform in circuit analysis and design is method for transforming the differential equations describing a circuit in terms of dt into differential equations describing a circuit in terms of ds. With t representing the time domain and s representing the frequency domain.
Usually the writing of the time domain equations for the circuit is skipped and the circuit is redrawn in the frequency domain first and the equations are taken directly from this transformed circuit. This is actually much simpler and faster than transforming the time domain equations of the circuit would be.
The S transform and Laplace transform are related operations but different; the S transform operates on circuits and describes how they modify signals, the Laplace transform operates on signals.
