1. Then,  Fourier Series: Suppose that f(x) can be expressed as the following series sum because Fourier Series cf. Orthogonal Functions Note: At this point, this is true for f(x) that is periodic with period L. However, it can be extended to non- periodic functions later. Kronecker delta

2. Now, letThen

3. Fourier Transform Then,  Define Fourier Transform of f(x) as Since and integral is a “sum”, this means that function g(x) is expressible as a linear combination of cosines and sines, i.e., waves. (Inverse Fourier Transform)

4. Dirac Delta ‘Function’ – Impulse Distribution  A particular representation of Dirac Delta can be obtained via: Then, we write For any function g(x) that is continuous at x = 0,  We call the limit a Dirac delta function if: oror...

5.  Exponential Representation of the Delta Function Can also take this as the limit: Also,