Generalized functions

Unit doublet

In mathematics, the unit doublet is the derivative of the Dirac delta function. It can be used to differentiate signals in electrical engineering: If u1 is the unit doublet, then where is the convolution operator. The function is zero for all values except zero, where its behaviour is interesting. Its integral over any interval enclosing zero is zero. However, the integral of its absolute value over any region enclosing zero goes to infinity. The function can be thought of as the limiting case of two rectangles, one in the second quadrant, and the other in the fourth. The length of each rectangle is k, whereas their breadth is 1/k2, where k tends to zero. (Wikipedia).

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Polar coordinate integral

This is a follow-up of the integral of exp(-x^2) video on blackpenredpen's channel, in case you're wondering how to get that extra factor of r in the integral. It's mathemagical! :D Here's the like to the original video: Gaussian Integral https://youtu.be/r9W8YWELXvg

From playlist Double and Triple Integrals

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What does a triple integral represent?

► My Multiple Integrals course: https://www.kristakingmath.com/multiple-integrals-course Skip to section: 0:15 // Recap of what the double integral represents 1:22 // The triple integral has two uses (volume and mass) 1:45 // How to use the triple integral to find volume 8:59 // Why the

From playlist Calculus III

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What does a double integral represent?

► My Multiple Integrals course: https://www.kristakingmath.com/multiple-integrals-course It can be difficult to visualize what a double integral represents, which is why in this video we’ll be answering the question, “What am I finding when I evaluate a double integral?” In order to answ

From playlist Calculus III

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What is a Double Integral?

Have you ever wondered what a double integral is and what it has to do with cake? If so, watch this video and find out. Here I show step-by-step how to calculate a double integral, which is the multivariable calculus analog of an integral, enjoy! Double and Triple Integrals: https://www.y

From playlist Double and Triple Integrals

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Engineering MAE 130A. Lecture 24. Intro to Fluid Mechanics

UCI Engineering MAE 130A: Intro to Fluid Mechanics (Fall 2013) Lec 24. Intro to Fluid Mechanics View the complete course: http://ocw.uci.edu/courses/engineering_mae_130a_intro_to_fluid_mechanics.html Instructor: Roger Rangel, Ph.D. License: Creative Commons CC-BY-SA Terms of Use: http://o

From playlist Engineering MAE 130A. Intro to Fluid Mechanics

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Engineering MAE 130A. Lecture 21. Intro to Fluid Mechanics.

UCI Engineering MAE 130A: Intro to Fluid Mechanics (Fall 2013) Lec 21. Intro to Fluid Mechanics View the complete course: http://ocw.uci.edu/courses/engineering_mae_130a_intro_to_fluid_mechanics.html Instructor: Roger Rangel, Ph.D. License: Creative Commons CC-BY-SA Terms of Use: http://o

From playlist Engineering MAE 130A. Intro to Fluid Mechanics

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Engineering MAE 130A. Lecture 20. Intro to Fluid Mechanics

UCI Engineering MAE 130A: Intro to Fluid Mechanics (Fall 2013) Lec 20. Intro to Fluid Mechanics View the complete course: http://ocw.uci.edu/courses/engineering_mae_130a_intro_to_fluid_mechanics.html Instructor: Roger Rangel, Ph.D. License: Creative Commons CC-BY-SA Terms of Use: http://o

From playlist Engineering MAE 130A. Intro to Fluid Mechanics

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Chem 125. Advanced Organic Chemistry. 27. Determining Stereochemistry and Regiochemistry by NMR.

UCI Chem 125 Advanced Organic Chemistry (Spring 2016) Chem 125. Advanced Organic Chemistry. 27. Determining Stereochemistry and Regiochemistry by NMR. View the complete course: http://ocw.uci.edu/courses/chem_125_advanced_organic_chemistry.html Instructor: James S. Nowick, Ph.D. L

From playlist Chem125: Advanced Organic Chemistry

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Chem 203. Organic Spectroscopy. Lecture 14. Spin-Spin Coupling

UCI Chem 203 Organic Spectroscopy (Fall 2011) Lec 14. Organic Spectroscopy --Spin-Spin Coupling in Stereochemistry and Structure Determination. View the complete course: http://ocw.uci.edu/courses/chem_203_organic_spectroscopy.html Instructor: James Nowick, Ph.D. License: Creative Commons

From playlist Chem 203: Organic Spectroscopy

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Chem 203. Lecture 15: Coupling Involving Other Nuclei

Full Chem 203 Playlist: https://www.youtube.com/playlist?list=PLqOZ6FD_RQ7nUiPCa47zSrMWArKAdwfcD UCI Chem 203 Organic Spectroscopy (Fall 2020) Lecture 15: Coupling Involving Other Nuclei Instructor: James S. Nowick, Ph.D. License: Creative Commons BY-NC-SA Terms of Use: http://open.uci.ed

From playlist Chemistry 203, Organic Spectroscopy (2020)

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Chem 203. Organic Spectroscopy. Lecture 15. Coupling Involving Other Nuclei

UCI Chem 203 Organic Spectroscopy (Fall 2011) Lec 15. Organic Spectroscopy -- Coupling Involving Other Nuclei View the complete course: http://ocw.uci.edu/courses/chem_203_organic_spectroscopy.html Instructor: James Nowick, Ph.D. License: Creative Commons BY-NC-SA Terms of Use: http://ocw

From playlist Chem 203: Organic Spectroscopy

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Chem 203. Lecture 16: Coupling Involving Other Nuclei cont & Dynamic Processes in NMR Spectroscopy

Full Chem 203 Playlist: https://www.youtube.com/playlist?list=PLqOZ6FD_RQ7nUiPCa47zSrMWArKAdwfcD UCI Chem 203 Organic Spectroscopy (Fall 2020) Lecture 16: Coupling Involving Other Nuclei continued & Dynamic Processes in NMR Spectroscopy Instructor: James S. Nowick, Ph.D. License: Creativ

From playlist Chemistry 203, Organic Spectroscopy (2020)

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Chem 203. Lecture 14: Spin-Spin Coupling in Structure and Stereochemistry Determination

Full Chem 203 Playlist: https://www.youtube.com/playlist?list=PLqOZ6FD_RQ7nUiPCa47zSrMWArKAdwfcD UCI Chem 203 Organic Spectroscopy (Fall 2020) Lecture14: Spin Spin Coupling in Structure and Stereochemistry Determination Instructor: James S. Nowick, Ph.D. License: Creative Commons BY-NC-SA

From playlist Chemistry 203, Organic Spectroscopy (2020)

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Chem 203. Organic Spectroscopy. Lecture 13. Coupling Analysis in Systems (continued)

UCI Chem 203 Organic Spectroscopy (Fall 2011) Lec 13. Organic Spectroscopy -- Coupling Analysis in First-Order and Near-First-Order Systems -- Part 2 View the complete course: http://ocw.uci.edu/courses/chem_203_organic_spectroscopy.html Instructor: James Nowick, Ph.D. License: Creative C

From playlist Chem 203: Organic Spectroscopy

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14_1 The Double Integral

An introduction to the double integral. Whereas the single integral determines the area under a curve, the double integral of a two variable function determines the volume under a surface as marked out by a region on the XY plane.

From playlist Advanced Calculus / Multivariable Calculus

Related pages

Limiting case (mathematics) | Cartesian coordinate system | Convolution | Dirac delta function