Lecture: Correction To Heat Equation Discussion
Brad G. Osgood - Stanford
Description
Lecture Description
Correction To Heat Equation Discussion, Setup For Fourier Transform Derivation From Fourier Series, Results Of The Derivation: Fourier Transform And Inverse Fourier Transform, Definition Of The Fourier Transform (Analysis), Definition Of Fourier Inversion (Synthesis), Major Secret Of The Universe: Every Signal Has A Spectrum, Which Determines The Signal, Fourier Notation, Example: Rect Function, Example: Triangle Function
Course Description
Note: This course is being offered this summer by Stanford as an online course for credit.It can be taken individually, or as part of a master’s degree or graduate certificate earned online through the Stanford Center for Professional Development.
The goals for the course are to gain a facility with using the Fourier transform, both specific techniques and general principles, and learning to recognize when, why, and how it is used. Together with a great variety, the subject also has a great coherence, and the hope is students come to appreciate both.
Topics include: The Fourier transform as a tool for solving physical problems. Fourier series, the Fourier transform of continuous and discrete signals and its properties. The Dirac delta, distributions, and generalized transforms. Convolutions and correlations and applications; probability distributions, sampling theory, filters, and analysis of linear systems. The discrete Fourier transform and the FFT algorithm. Multidimensional Fourier transform and use in imaging. Further applications to optics, crystallography. Emphasis is on relating the theoretical principles to solving practical engineering and science problems.
from course: The Fourier Transform and its Applications
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