Advance Maths: Part II: Fourier Transform

Name: Advance Maths: Part II: Fourier Transform
Rating: 4.6 (7 reviews)

Fourier Transform

Created bySeema Ranaware

Last updated 5/2020

English

What you'll learn

Advanced Mathematics required in technical courses/ graduate/ post graduate level

Course content

2 sections • 13 lectures • 2h 29m total length

Introduction1:05
Explore advanced maths topics such as differential equations, partial differential equations, complex differentiation, complex integration, and the Laplace transform, with a roadmap to future topics.

FT116:10
Explore the fundamentals of the Fourier transform, highlighting the roles of even and odd functions, integral representations, and the treatment of infinity in defining transform pairs.
FT218:25
Explore the Fourier transform in advanced maths part II, using function representations, substitution, and piecewise analysis to evaluate integrals across x-ranges from zero to infinity.
FT314:18
Explore the Fourier transform through definite integrals, working with zero-to-infinity limits, and apply integration techniques to derive and interpret transform expressions.
FT415:36
Apply Fourier transform techniques to piecewise functions, evaluating limits from zero to infinity, and derive the transform coefficients using sine and cosine forms.
FT512:48
Explore Fourier transform techniques to solve given functions and reveal their integral representations. Analyze inverse transforms, limits, and cosine and sine components to understand the transform back process.
FT65:44
Explore the Fourier transform of a given function, evaluating the integral via its integral representation and limits from zero to infinity. Practice includes matching steps and addressing convergence with examples.
FT79:02
Investigate a piecewise, x-dependent function within the Fourier transform framework, using integral representations and parameter lambda x to capture values ranging over 0 to infinity.
FT810:20
Learn the Fourier transform of even functions, applying definite integrals from zero to infinity and variable substitutions to derive transform relationships and limit behavior.
FT95:04
Explore the Fourier transform properties, including infinity and zero limits, complex representations, and X configurations like X equals minus X to illustrate integration-based results.
FT1016:03
Advance maths part ii covers the Fourier transform by formulating integrals over the entire real line, analyzing piecewise cases, and manipulating complex expressions with modulus and limits.
FT1116:40
Students explore the Fourier transform by applying the formula, evaluating limits from minus infinity to plus infinity, and deriving the transform components A and B for a given function.
FT128:18
Explore the Fourier transform by applying limits and substitution to evaluate from minus infinity to infinity, using guided steps and the IRS formula.

Requirements

should have knowledge of basic algebra, trigonometry, derivatives and integration

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 this course is for:

12+ graders, graduate/ post graduate students, diploma (polytechnic), engineering students

Advance Maths: Part II: Fourier Transform

What you'll learn

Explore related topics

Course content

Introduction1 lecture • 1min

Fourier Transform (FT)12 lectures • 2hr 28min

Requirements

Description

Who this course is for: