What You Will Learn!
- Advanced Mathematics required in technical courses/ graduate/ post graduate level
Description
This course covers all the details of Fourier Transform (FT) like complex exponential form of Fourier series, Fourier integral theorem, Equivalent forms of Fourier integral, Sine and Cosine integrals, Fourier sine and cosine transform and their inverse, several numericals solved on each type. I have given home assignments at the end of every lecture. Solve it and tally your answers with the given answer key. Definition, Dirichlet's conditions, Full Range Fourier Series, Half Range Fourier Series, Harmonic Analysis and Applications to Problems in Engineering.
Periodic functions occur frequently in engineering problems. Such periodic functions are often complicated. Therefore, it is desirable to represent these in terms of the simple periodic functions of sine and cosine. A development of a given periodic function into a series of sines and cosines was studied by the French physicist and mathematician Joseph Fourier (1768-1830). The series of sines and cosines was named after him.
Fourier Series Expansion of a Function over (−π, π), Fourier Series Expansion of f(x) = x over (−π, π), Fourier Series Expansion of a Function Over (−p, p), Fourier Series Expansion of the Function |x|, Exponential Form of a Fourier Series Expansion,
Fourier Integral Transform Pairs, Fourier Cosine Integrals, Fourier Sine Integrals, Even Function, Odd Function, A Function Which is Neither Even nor Odd,
Who Should Attend!
- 12+ graders, graduate/ post graduate students, diploma (polytechnic), engineering students
