Linear Differential Equations
Linear Differential Equation of nth Order Linear differential equation is in the form of Ly=f, where ‘L’ is a linear operator, ‘Y’ is a unknown function and ‘F’ is a known function of a same nature. In mathematical point of view first-order linear differential equation are those equation that can be kept in form. 1. A differential equation of the form where are constant and Q in any function of x or constant is called linear differential equating of nth order with constant co-effieient. Note: (1) (2) are...
read moreComplex Number Formula
Complex number Formula A complex number is one of the form of a + ib, where a and b are real number and . A is called real part of the complex number and b is called imaginary part of the complex number. 1.De movre’s Theorem De Movre’s Theorem is a relatively simple formula for calculating powers of complex numbers. De movre’s theorem states that for any positive integer 2.Square root of complex number and For . 3.Cube root of unity. Let For the requrd cube root of unity are or = omega) Note: i. ii. iii. for any integer...
read moreBernoulli’s Equation
Bernoulli’s Equation An equation of the form (i) where P, Q are function of x above is called Bernoulli’s equation. Note: To reduce it into linear So equation (i) reduces to , which is linear in...
read moreProperties of Definite Integral
Properties of Definite Integral Definite integral is part of integral or anti-derivative from which we get fixed answer rather than the range of answer or indefinite answers. Some of the important formulas are shown below:- Note: Even function: a function f(x) is called even function if f (-x) = f(x). A function f(x) is called odd function if f (-x) = -f(x). Some standard relations 6. If 7. If...
read moreIntegration Formula
Integration Integration is the operation of calculating the area between the curve of a function and the x-axis. Integral also includes antiderivative and primitive. Integration works by transforming a function into another function respectively. Some of the important integration formulas are listed below:- See also: integration...
read moreLinear Differential Equation Formula
Linear Differential Equation Formula Some of the important formulas for linear differential equation are listed below:- Integrating factor (I. F.) = To obtain solution of linear equation, we multiply both sides of given equation by I. F. If linear differential equation is of the form , where P and Q are function of y alone or constant, then...
read moreExact differential equation
Exact differential equation A differential equation is a equation used to define a relationship between a function and derivatives of that function. Differential equation is extremely used in the field of engineering, physics, economics and other disciplines. A differential equation of the form Mdx + N dy = 0, where M & N are function of x & y, is called exact if there exists a function f(x, y) such that Mdx + Ndy = d f (x, y). Note: a necessary and sufficient condition for the differential equation Mdx + Ndy = 0 to be...
read moreTriangle Formula
Triangle Formula A triangle is a basic geometrical shape, with consists of three corners or vertices and three sides which are called line segments. There are various types of triangles some of them are :- Equilateral triangle, isosceles triangle, Scalene triangle, Right triangle, Special right triangle etc. There are three angles in a triangle and the sum of angles within a triangle is equal to 180 degree. In simple word’s a triangle can be described as a 3 sided polygon and sometimes is is also called as trigon. Some of the...
read moreApplication of Antiderivative
Application of Antiderivative Antiderivates can be defined as the inverse function of derivatives. An antiderivative of a function f(x) is a function whose derivative is f(x). Some of the important formulas of Antiderivatives are as follows:- (i)Let f (x) be function of x, then definite integral g of f (x) with respect to x between the limit a & b is devoted by and defined by = which also known as limit of a sum. (ii)The area bounded by the curve y = f (x), x-axis and x = a and x = b is given by (iii)The area bounded by...
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Limit and continuity Formulas Concept of limit and continuity was developed in 17th century by mathematicians, primarily to foster the development of calculas. The concept of the limit is very important in terms of calculas. Some important formulas of limit and continuity are as follows:- 1. , for all rational value of n 2. or Note: indeterminate forms are...
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