Fourier series
A Fourier series is an expansion of a periodic function in terms of an infinite sum of sines and cosines. Fourier series make use of the orthogonality relationships of the sine and cosine functions. The computation and study of Fourier series…
Line Integral
Line integrals (also referred to as path or curvilinear integrals) extend the concept of simple integrals (used to find areas of flat, two-dimensional surfaces) to integrals that can be used to find areas of surfaces that "curve…
Cauchy- Riemann equations
Let (1) where (2) so (3) The total derivative of with respect to is then (4)(5) In terms of and , (5) becomes (6)(7) Along the real, or x-axis, , so (8) Along the imaginary, or y-axis, ,…
Analytic Functions
Analytic Functions are defined as per the converging series; that revolves around a particular variable x for which the series has been expanded. Almost all the functions that we obtained from…
Green’s theorem
The idea behind Green's theorem represents the circulation of FF around CC. If FF were the velocity field of water flow, for example, this integral would indicate how much the water tends to circulate around the…
Gradient of Vector Calculus
The gradient is a fancy word for derivative, or the rate of change of a function. It’s a vector (a direction to move) that Points in the direction of greatest increase of…
