Step Function and Delta Function

MIT RES.18-009 Learn Differential Equations: Up Close with Gilbert Strang and Cleve Moler, Fall 2015
Instructor: Gilbert Strang

A unit step function jumps from 0 to 1. Its slope is a delta function: zero everywhere except infinite at the jump.

License: Creative Commons BY-NC-SA

[alessandrobasso]

Watching lectures with this guy is like watching a Netflix series, you’re eager to see what’s going on in the next episode

[darkenviado]

This is what happens when a teacher actually knows what he is teaching. Amazing.

[AyushBhattfe]

Whenever I learn something new from the book, I always polish it with your lectures

[NothingMaster]

These lecture series are truly precious. MIT and all the professors involved in this monumental effort are to be commended for their superb contribution to the advancement and propagation of human knowledge. The same also goes for the anonymous financial contributors whose generous donations have made it possible for these lectures to be made available to the general public, free of charge. 👏🏻👏🏻👏🏻

[edmondscott]

Happy retirement Professor Strang. Your commentaries are very clear.

[CuongHut]

the moment he talks about the derivative of step function is zero except the one point everything happens and my mind was like 🤯🤯🤯 all the questions in my mind were explained. OMG, thank you so much professor

[feynmath]

His course on Linear algebra is fantastic and has helped me a lot.
I wish to thank him personally one day.
Thank You Prof. Strang

[XxToXicVaGxX]

Coolest chalkboard I've ever seen. MIT does things right. No doing an equation and going across the entire room until it's too long to even focus

[marianbucuci]

Thank you Professor Gilbert! May you have students as enthusiastic as your good explanations!

[not_ever]

7:26 this is how long it took for me to understand something my lecturer tried and failed to explain over the course of two hours. Wtf. I wish they could clone Gilbert Strang and have him teach in every institution.

[Smmmile]

Such a pleasure to watch the explanation of the derivative of the Step function and your explanation of the Sifting Property of the Delta Function. It's very valuable when doing Laplace and Fourier Transforms.

[klmklmism]

what an excellent way of teaching such complex terms. I just wanna give him a hug

[RonaldMulinde]

I can't thank you enough for sharing. i love the intuitive approach.

[souvikroy]

11:41 The intuition behind that equations is brilliant ❤️❤️❤️

[Gismho]

Superb explanation of the Heavyside and Delta functions. No textbook I've read mentions the Heavyside function's relation to the Delta function. The common "explanation" is to state that the integral of the Delta function is defined as one!!!

[anneoni]

I can't believe that in just 1 minute i understood step function! Best prof ever!! 🌹🌹🌹

[RadoslavFicko]

The Dirac distribution is the Fourier transform of unity and a special case of convolution, where A*f=g, g(x)=d(x-y). f(y)dy, if we imagine the gravitational interaction as a function of g(x) and the electromagnetic interaction as a function of f(y), then these forces (i.e. the lines of force) only interact when x is equal to y ( the Dirac impulse).

[synapticmemoryseepage]

A great conceptual simplification and learning device: a derivative shows when something changes.

[MicroageHD]

5:47 "If we take derivatives, we get crazyness". I feel ya 100% bruh :D

[radiac]

The Heaviside Step Function and the Dirac Delta Function are both extreme limits of their smoother, slightly more well-behaved counterparts, the Error Function and the Gaussian. The Gaussian is a smooth bell curve, exp(-(x squared)), and has finite area under it (it integrates to the square root of pi, famously). The Error Function is the name given to the function whose derivative is the Gaussian, though it has no real formulaic representation in x outside of its series expansion. The Error Function looks like a smooth version of the step function, one with a somewhat rounded off, curved step. In the limit as the full width at half maximum of the Gaussian goes infinitely narrow, it converges to the Dirac Delta Function, and in the limit of infinitely-square step shape, the Error Function converges to the Heaviside Step Function. Since the Gaussian is the derivative of the Error Function, (which can be shown by looking at the series expansions of both) it stands to reason that the Dirac Delta Function should be the derivative of the Heaviside Step Function.