## STATISTICS NOTE BY DIPS ACADEMY

Statistics is a branch of mathematics dealing with the collection, analysis, interpretation, presentation, and organization of data. In applying statistics to, e.g., a scientific, industrial, or social problem, it is conventional to begin with a statistical population or a statistical model process to be studied. Populations can be diverse topics such as “all people living …

## REAL ANALYSIS NOTE BY DIPS ACADEMY

Real analysis (traditionally, the theory of functions of a real variable) is a branch of mathematical analysis dealing with the real numbers and real-valued functions of a real variable. In particular, it deals with the analytic properties of real functions and sequences, including convergence and limits of sequences of real numbers, the calculus of the …

## DIFFERENTIAL EQUATION HAND WRITTEN NOTE

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, …

## LINEAR TRANSFORMATION HAND WRITTEN NOTE BY DIPS ACADEMY

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 …

## BASIC CONCEPTS OF LINEAR ALGEBRA NOTES

Linear algebra is the branch of mathematics concerning vector spaces and linear mappings between such spaces. It includes the study of lines, planes, and subspaces, but is also concerned with properties common to all vector spaces. PAGE:- 225 The set of points with coordinates that satisfy a linear equation forms a hyperplane in an n-dimensional …

## INTERGRAL CALCULUS HAND WRITTEN NOTE BY DIPS ACADEMY

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 …

## INTERGRAL EQUATION NOTE BY DIPS ACADEMY

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 …

## COMPLEX ANALYSIS NOTE BY DIPS ACADEMY

Complex analysis, traditionally known as the theory of functions of a complex variable, is the branch of mathematical analysis that investigates functions of complex numbers.  It is useful in many branches of mathematics, including algebraic geometry, number theory, analytic combinatorics, applied mathematics; as well as in physics, including the branches of hydrodynamics, thermodynamics, and particularly …

## MODERN ALGEBRA:- RING THEORY NOTE BY DIPS ACADEMY

In mathematics, a ring is one of the fundamental algebraic structures used in abstract algebra. It consists of a set equipped with two binary operations that generalize the arithmetic operations of addition and multiplication. Through this generalization, theorems from arithmetic are extended to non-numerical objects such as polynomials, series, matrices and functions.  A ring is …

## LINEAR TRANSFORMATION AND REAL ANALYSIS HAND WRITTEN NOTE BY DIPS ACADEMY

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 …