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This Blog is only based on making discussion on different types of mathematical theorems and related solutions.It may useful for those people who want to learn more theorems of different scientists. Here is the collection of all the theorems from primary level, whichay helpful for readers'

         Hello my motive is to clarify and discuss the theorems described by different mathematicians all over the world.

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Accuracy Of Numbers

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              Accuracy Of Numbers 1.  Approximate Numbers :            There are two types of numbers exact and approximate . Exact numbers are 2,4,9,13,7,2,6.45....etc . But there are numbers such as 4/3 =1.3333....  ,          √(2)= 1.41413 and finite number of digits . These may be approximated by numbers 1.3333, 1.4141 , 3.1416 respectively . Such numbers which represent the given numbers to certain degree of accuracy are called approximate numbers .  2. Significant Figures :                     The digits used to express a number is called significant digits (figures) . Thus each of the numbers 7845, 3.589, 0.4758 contains four significant figures while the numbers 0.00389 , 0.000587 and 0.0000296 contain only three significant figures since zeros only help to fix the position of the decimal point . Similarly the numbers 45000 and 7300.00 have two significant figures only . 3. Rounding Off :                   There are numbers with
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PFAFFIAN Differential Equations And It's Solutions

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PFAFFIAN Differential Equations And It's Solutions :-      The relation              n             Σ  Fᵢ(x₁,x₂,......xₙ) dxᵢ = 0            i=1   where Fᵢ's (i=1,2,....n) are functions of all or some of the n independent variables x₁,x₂,.....xₙ is called a Pfaffian differential equation . Here we shall study Pfaffian differential equation in three independent variables which is of the form              P dx + Q dy + R dz = 0    ...........(1)    where P, Q , R are functions of x , y and z . Setting -->                        -->               X = (P,Q,R)  and dr = (dx,dy,dz), equation (1) can be written in the vector notation as                   -->  -->                  X . dr    = 0                  ..............(2)  If there exists a function μ(x,y,z) such that μ(P dx + Q dy + R dz) is an exact differential dΦ , the equation is said to be integrable and to possess an integrating factor μ(x,y,z) . In such case(1) becomes
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Derivation Of Composite Trapezoidal Rule

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Derivation Of Composite Trapezoidal Rule :                                                   b       Let us find the value of ∫ f(x) dx                                                  a numerically by composite trapezoidal rule. Solution :              Let [a,b] be divided into n equal sub intervals of length h each . Let                            a= x₀,x₁,x₂,.......xₙ=b  be the points of sub division .  i.e x₁ = x₀+ih  for i= 0,1,2,......n By Newton's Forward Difference Interpolation  f(x) = f(x₀)+uΔf(x₀) +u(u-1)/2!  Δ²f(x₀)+........        where x = x₀+uh b                 ∫ f(x) dx = a       xₙ          ∫ [f(x₀)+uΔf(x₀)+u(u-1)/2!  Δ²f(x₀)+...]dx           x₀              n        = h∫ [f(x₀)+uΔf(x₀)+u(u-1)/2  Δ²f(x₀)+...]dx             0     =h[uf(x₀) +u²/2 Δf(x₀) +                                                                                                       n                                  (u³/6 -u²/4)Δ²f
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