JUST A SNIPPET
THROUGH THE EYES OF A TOPOLOGIST
An ordinary differential equation is a differential equation containing one or more functions of one independent variable and the derivatives of those functions.
In mathematics, an integral transform maps a function from its original function space into another function space via integration, where some of the properties of the original function might be more easily characterized and manipulated than in the original function space.
Logic is the discipline that deals with the methods of reasoning. On an elementary level, logic provides rules and techniques for determining whether a given argument is valid. Logical reasoning is used in mathematics to prove theorems, and in computer science to verify the correctness of programs.
Fourier series is an expansion of a periodic function f(x) in terms of an infinite sum of sines and cosines. Fourier series make use of the orthogonality relationships of the sine and cosine functions.
JACOBI ELLIPTIC FUNCTIONS
Jacobi elliptic functions are found in the description of the motion of a pendulum, as well as in the design of electronic elliptic filters. While trigonometric functions are defined with reference to a circle, the Jacobi elliptic functions are a generalization that refers to other conic sections, the ellipse in particular.
As long as algebra and geometry have been separated, their progress have been slow and their uses limited; but when these two sciences have been united, they have lent each mutual forces, and have marched together towards perfection.
THE HEAT EQUATION
The heat equation is among the most widely studied topics in pure mathematics, and its analysis is regarded as fundamental to the broader field of partial differential equations. Solutions to the heat equation are sometimes known as caloric functions.
“Group Theory is the branch of Mathematics that answers the question ‘ What is symmetry?’ “- Nathan C. Carter
Definition 1.1– A group ‘G’ is a set with two operations or functions, one called multiplication (or addition in some cases) m : G X G → G and the other called the inverse i: G → G.
Just as the Fourier transform for an infinite interval is related to the Fourier series over a finite interval, so the Hankel transform over an infinite interval is related to the Fourier–Bessel series over a finite interval.
In mathematics, a surface is a geometrical shape that resembles a deformed plane. The most familiar examples arise as boundaries of solid objects in ordinary three-dimensional Euclidean space R3, such as spheres.