A differential equation is a mathematical equation that relates some function with its derivatives. In applications, the functions usually represent physical quantities, the derivatives represent their rates of change, and the equation defines a relationship between the two. Because such relations are extremely common, differential equations play a prominent role in many disciplines including engineering, … Read more
In mathematics, a linear map (also called a linear mapping, linear transformation or, in some contexts, linear function) is a mapping V → W between two modules (including vector spaces) that preserves (in the sense defined below) the operations of addition and scalar multiplication. An important special case is when V = W, in which … Read more
A matrix is a collection of numbers ordered by rows and columns. It is customary to enclose the elements of a matrix in parentheses, brackets, or braces. For example, the following is a matrix: This matrix has two rows and three columns, so it is referred to as a “2 by 3” matrix. The elements … Read more
The fundamental concepts and theory of integral and differential calculus, primarily the relationship between differentiation and integration, as well as their application to the solution of applied problems, were developed in the works of P. de Fermat, I. Newton and G. Leibniz at the end of the 17th century. Their investigations were the beginning of … Read more
Here we are with BEST PHYSICS, CHEMISTRY & BIOLOGY CHAPTER WISE HAND WRITTEN NOTE for you, To improve your exam preparation. We suggest you Download all Books and notes. we will post important PDF every day. These PDF will help you a lot in your competitive exams. Jigs Solanki provides you with the best chosen … Read more
A linear transformation is a function from one vector space to another that respects the underlying (linear) structure of each vector space. A linear transformation is also known as a linear operator or map. The range of the transformation may be the same as the domain, and when that happens, the transformation is known as … Read more
In algebra, ring theory is the study of ring algebraic structures in which addition and multiplication are defined and have similar properties to those operations defined for the integers. Ring theory studies the structure of rings, their representations, or, in different language, modules, special classes of rings (group rings, division rings, universal enveloping algebras), as … Read more
Linear algebra is central to almost all areas of mathematics. For instance, linear algebra is fundamental in modern presentations of geometry, including for defining basic objects such as lines, planes and rotations. Also, functional analysis may be basically viewed as the application of linear algebra to spaces of functions. Linear algebra is also used in … Read more
Numerical analysis continues this long tradition of practical mathematical calculations. Much like the Babylonian approximation of the square root of 2, modern numerical analysis does not seek exact answers, because exact answers are often impossible to obtain in practice. Instead, much of numerical analysis is concerned with obtaining approximate solutions while maintaining reasonable bounds on … Read more
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