ORDINARY DIFFERENTIAL EQUATION
A differential equation is called linear if (i) every dependent variable and every derivative involved occurs in the first degree only, and (ii) no products of dependent variables and/or derivatives occur. A differential equation which is not linear is called a non-linear differential equation.
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, in computer science to verify the correctness of programs.
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 which refer to other conic sections, the ellipse in particular.
“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.