The Handy Math Answer Book
What is a good example of a topological structure? A good example of a topological structure is called the Möbius strip (also ca ...
called “rubber-sheet” geometry because objects examined in topology are under con- tinuous transformation (also called topologic ...
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ANALYSIS BASICS What is mathematical analysis? Mathmatical analysis is a branch of mathematics that uses the concepts and method ...
How did mathematical analysis develop after the 16th century? I deas about mathematical analysis took a long hiatus after the Gr ...
butions didadvance the field of calculus by showing that the area of a segment of a parabola is 4/3 the area of a triangle with ...
The Principiaor just Principia. In it he presents his theories of motion, gravity, and mechanics, thus explaining the bizarre or ...
Integral calculus—Integral calculus (logically) deals with integration and its appli- cation to solve differential equations; it ...
For example, in order to check that the sequence {2n}n≥ 1 is increasing: Let n≥1; that gives 2n^1 2 n2. Because 2 is greater ...
number we’ll call L; written in calculus, xnL. If the numbers do come closer, the sequence is said to be convergentand has a li ...
What does it mean if a series is convergent? Convergence of a series is related to the convergence of a sequence, but don’t conf ...
What is a geometric series? If we add the numbers in a geometric sequence, we end up with a geometric series. A geometric series ...
What are leftand right limits? When a function is not defined around the point c(see the notation in the equation above), but on ...
This example can be seen in the accompanying graph. What are vertical asymptotesin association with limits? Using the example ab ...
gives a solution of: and, thus, the implied limit is: This is because we know that: And as xgets larger (or closer to ±) the po ...
But for those who study calculus, it is an area of mathematics pioneered by Got- tfried Leibniz. His idea was based purely on th ...
DIFFERENTIAL CALCULUS What is differential calculus? Differential calculus is the part of “the” calculus that deals with derivat ...
What are the two waysof looking at the derivative? There are two major ways of looking at the derivative—the geometrical (or the ...
What is an exampleof computing the derivative? The following solves the derivative at xafor the function f(x) x^2 , using the ...
This equation is also seen written as Dn(y) dny/dxn. What is a partial derivative? Partial derivatives (seen written as the sym ...
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