Examples of differential equations with solutions

“Ordinary Differential Equations:-            In mathematics, the term “Ordinary Differential Equations” also known as ODE is a relation that contains only one independent variable and one or more of its derivatives with respect to the variable. In other words, the ODE’S is represented as the relation having one real variable x, the real dependent variable y, with some of its derivatives. Y’,y”, ….yn ,…with...

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Fourier Transform Question || Engineering mathematics

FOURIER TRANSFORM:- The Fourier transform (FT)         decomposes a function of time (a signal) into its constituent frequencies. This is similar to the way a musical chord can be expressed in terms of the volumes and frequencies of its constituent notes. The term Fourier transform refers to both the frequency domain representation and the mathematical operation that associates...

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Fourier Transform

The Fourier Transform  1.1 Fourier transforms as integrals        There are several ways to define the Fourier transform of a function f : R → C. In this section, we define it using an integral representation and state some basic uniqueness and inversion properties, without proof. Thereafter, we will consider the transform as being defined as a suitable limit of Fourier series, and will prove the results stated here.  The...

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