Calculus and Pre-Calculus Get Started!

I recently became super charged about writing about Calculus and Pre-Calculus when I learned about Laplace and Fourier Transformations.

The Laplace Transform (transformation) is used to simplify the solving of calculus differential equations and calculus integral equations. The Laplace transform does this by transforming the calculus problem to an algebraic problem. The algebraic problem is much easier to solve than the calculus problem.

The Fourier Transform (transformation) is used to simplify the solving of complex wave functions. This author has found a link that explains the Fourier Transform real good. Please read the link directly below. The Fourier Transform has many uses; one use is to solve certain differential equations, it can be used to solve image wave equations, it can be used to solve sound wave equations, and it has others uses. 

The easy way to explain the Fourier Transform in lay language is with the following analogy: when a composer such as Beethoven or Mozart compose an opera they compose a piece for the voice, they compose a piece for the wind instruments, they compose a piece for the string instruments, they compose a piece for the piano, and a piece for the percussion instruments.  Then then composer blends them together.  The Fourier Transform will allow you to "decompose" this blend of music to the voice, wind, string, piano, and percussion compositions. Then you can take the appropriate decomposed composition and work on it to get the answer you seek without having the complications of the blended composition to deal with.