Taylor Series - Difference Equations to Differential Equations
... a power series representation for a given function by manipulating some other known representation, then we know that this series is the Taylor series for that function. This is in fact the way many Taylor series representations are found in practice. ...
... a power series representation for a given function by manipulating some other known representation, then we know that this series is the Taylor series for that function. This is in fact the way many Taylor series representations are found in practice. ...
INITIAL VALUE PROBLEMS IN DISCRETE FRACTIONAL
... The purpose and contribution of this paper is to introduce a well-defined ν-th (0 < ν ≤ 1) order fractional difference equation, produce a method of solution for the general nonlinear problem, and exhibit two more methods of solution for the linear problem of half-order with constant coefficients. Fract ...
... The purpose and contribution of this paper is to introduce a well-defined ν-th (0 < ν ≤ 1) order fractional difference equation, produce a method of solution for the general nonlinear problem, and exhibit two more methods of solution for the linear problem of half-order with constant coefficients. Fract ...
Fundamental theorem of calculus
The fundamental theorem of calculus is a theorem that links the concept of the derivative of a function with the concept of the function's integral.The first part of the theorem, sometimes called the first fundamental theorem of calculus, is that the definite integration of a function is related to its antiderivative, and can be reversed by differentiation. This part of the theorem is also important because it guarantees the existence of antiderivatives for continuous functions.The second part of the theorem, sometimes called the second fundamental theorem of calculus, is that the definite integral of a function can be computed by using any one of its infinitely-many antiderivatives. This part of the theorem has key practical applications because it markedly simplifies the computation of definite integrals.