Intro to the Levi-Civita symbol and an example with a cross product.

Views: 28651
PhysicsHelps

solve vector cross product using calculator.In this video you will able to solve cross product of vector directly using calculator.using 991es plus calculator the solution of vector is very easy and by using calculator save your precious time.and no chance of error in solving using calculator.the cross product value will be accurate.

Views: 40719
Arohan kumar

In this video I have discussed about operations on DFA like Union,Concatenation, cross product, Complementaion,Reversal

Views: 151742
Gate Lectures by Ravindrababu Ravula

In this video I have discussed about how to construct a minimal DFA that accepts set of all strings over {a,b} in which number of a's and number of b's both are even.
I have also discussed about Cross Product of DFA.

Views: 269252
Gate Lectures by Ravindrababu Ravula

031 - Magnetic Force
In this video Paul Andersen explains how a charge particle will experience a magnetic force when it is moving through a magnetic field. The right-hand rule is described as a method for determining the direction of the force. The magnitude of the force is a product of the charge, velocity and magnitude of the magnetic field.
Do you speak another language? Help me translate my videos:
http://www.bozemanscience.com/translations/
Music Attribution
Title: String Theory
Artist: Herman Jolly
http://sunsetvalley.bandcamp.com/track/string-theory
All of the images are licensed under creative commons and public domain licensing:
"File:Aurora Borealis and Australis Poster.jpg." Wikipedia, the Free Encyclopedia, April 18, 2014. http://en.wikipedia.org/w/index.php?title=File:Aurora_Borealis_and_Australis_Poster.jpg&oldid=604103133.
image, Mifeet, based on Douglas Morrison's. Czech Version of an Illustration of Fleming's Left Hand Rule, December 26, 2007. en.wiki. http://commons.wikimedia.org/wiki/File:LeftHandOutline_czech.png.
P.wormer. English: Right-Hand Rule for Vector Product. Move Open Palm of Right Hand from X to Y, Then Thumb Is Direction of Z ≡ X×y., December 21, 2010. Own work. http://commons.wikimedia.org/wiki/File:Right-hand-rule.jpg.
SVDer, Right_hand_rule_cross_product svg: User:Acdxderivative work: English: Illustration of the Right-Hand and Left-Hand Coordinate Systems., 14:06 (UTC). Right_hand_rule_cross_product.svg. http://commons.wikimedia.org/wiki/File:Coordinate_systems.png.
TKKN2, Flickr User. 3 Neodymium Magnets on a Crt Screen, June 13, 2007. Flickr. http://commons.wikimedia.org/wiki/File:Magnets_on_crt_screen.jpg.
User:Acdx. English: Illustration of the Right-Hand Rule for the Cross Product., July 24, 2008. Self-made, based on Image:Right_hand_cross_product.png. http://commons.wikimedia.org/wiki/File:Right_hand_rule_cross_product.svg.
Zureks. English: Schematic Representation of Earth's Magnetic Field Lines, January 12, 2012. Own work. http://commons.wikimedia.org/wiki/File:Earth%27s_magnetic_field,_schematic.png.

Views: 557201
Bozeman Science

Jukin Media Verified (Original)
* For licensing / permission to use: Contact - licensing(at)jukinmediadotcom
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
The Man behind the video camera:
Instagram: http://instagram.com/ThatGuyBlev
Twitter: https://twitter.com/ThatGuyBlev
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
Me:
Instagram: http://instagram.com/astrosnack

Views: 13334952
AstrosnacK

054 - Angular Momentum
In this video Paul Andersen explains rotating object have angular momentum. The angular momentum of a point object is the product of the distant from the center of rotation and the linear momentum. The angular momentum of an extended object is a product of the rotational inertia and the angular velocity. The change in angular momentum is equal to the product of the net torque and the change in time.
Do you speak another language? Help me translate my videos:
http://www.bozemanscience.com/translations/
Music Attribution
Title: String Theory
Artist: Herman Jolly
http://sunsetvalley.bandcamp.com/track/string-theory
All of the images are licensed under creative commons and public domain licensing:
“Angular Momentum.” Wikipedia, the Free Encyclopedia, September 7, 2014. http://en.wikipedia.org/w/index.php?title=Angular_momentum&oldid=623981729.
“Bicycle.” Wikipedia, the Free Encyclopedia, September 8, 2014. http://en.wikipedia.org/w/index.php?title=Bicycle&oldid=624655868.
DarKobra. Tango Icon for RocketDock., April 17, 2008. http://darkobra.deviantart.com/art/Tango-Rocket-Dock-Icon-83118394. http://commons.wikimedia.org/wiki/File:Blue-rocket.svg.
de.wikipedia, Original uploader was Schorschi2 at. Deutsch: Rechte-Daumen-Regel, February 28, 2006. Transferred from de.wikipedia (Original text : Eigene Zeichnung). http://commons.wikimedia.org/wiki/File:Right_hand_rule_simple.png.
“Introduction to Angular Momentum.” Wikipedia, the Free Encyclopedia, August 24, 2014. http://en.wikipedia.org/w/index.php?title=Introduction_to_angular_momentum&oldid=579141427.

Views: 275199
Bozeman Science

vector dot product in calculator.calculation of dot product of vector using calculator.
after watching this video you will able to calculate dot product of vector using calculator.using calculator 991es you will solve dot product of vector product easily.vector product in calculator,

Views: 10148
Arohan kumar

In this video I have discussed how to construct the minimal DFA which accepts set of all strings over {a,b} such that second symbol from L.H.S is 'a' and 3rd symbol from LHS is 'a' respectively.

Views: 85439
Gate Lectures by Ravindrababu Ravula

How to find the components of the cross product (by formula and by finding the determinant of a 3 x 3 matrix).

Views: 1485
Math Videos from Heather

Recorded: 2014-12-19
Playlist: https://www.youtube.com/watch?v=leb1hMPC274&list=PLC-qVSnsyc7-6MXt0ZakH4s4EDOINGiOl&index=4
A discussion of the use of an outer product.
0:30 The difference between an outer product and inner (dot) product depends on whether you put the vertical matrix followed by the horizontal matrix, or vice versa.
1:50 The outer product, sometimes denoted $\vec A \otimes \vec B$, ends up being a 3x3 matrix (a rank 2 tensor).
2:35 Sarrus' rule for doing a cross product. (which I'm not terribly good at, and it takes me a long time.)
5:45 A physical interpretation of the cross product. Magnitude according to the area of a parallelogram. Direction according to the right-hand-rule.
7:00 Magnitude = A*B*sin(\theta)
8:10 Using the outer product and Levi-Cevita to help us do the cross product.
9:10 I need to make up a new notation for a sum of the products.
10:00 The dot product of two vectors is the TRACe of the outer product of the two vectors.
10:45 I make a surprising number of mistakes in taking this outer product.
11:30 Finally it's correct.
12:00 Now I'm trying to get the outer product to do the work of a cross product.
13:55 Re-writing this outer-product method of getting the cross product.
15:10 Using the Levi Cevita symbol to do the cross-product.
16:00 Fixing my equation to show that it's not really a matrix multiplication.
16:30 Enshrining these formulas into LaTeX.
17:30 Equation 4 has this outer-product term... So I thought it was important before figuring how to do a transformation of an outer product, it might be nice to figure out what the outer product was for in the first place.
19:15 Oh, this thing $\delta_{mn}$ is called a Kroeniker Delta function... Not the Dirac Delta function

Views: 1902
Jonathan Doolin

You probably see a dollar bill every day, but do you ever really look at one?
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Virgil Photo by Giorces, http://commons.wikimedia.org/wiki/File:GiorcesBardo42.jpg
LINKS!
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BuzzFeed is the world's first true social news organization. Featuring tasty, short, fun, inspiring, funny, edgy, interesting videos from theBuzzFeed. /BuzzFeedVideo is BuzzFeed's original YouTube Channel, with a focus on producing great short-form BuzzFeed videos for YouTube (and the world!). BuzzFeed Video will entertain, educate, spark conversation, inspire and delight. Subscribe to BuzzFeedVideo today and check us out at http://buzzfeed.com

Views: 3900403
BuzzFeedVideo

067 - The Vector Properties of Angular Quantities
In this video Paul Andersen explains how a rotating system will have several quantities; including torque, angular velocity, angular acceleration and angular momentum. Each of these quantities have a vector property that can be discovered through by using the right-hand rule.
Do you speak another language? Help me translate my videos:
http://www.bozemanscience.com/translations/
Music Attribution
Title: String Theory
Artist: Herman Jolly
http://sunsetvalley.bandcamp.com/track/string-theory
All of the images are licensed under creative commons and public domain licensing:
Credner, Till. English: Photography of the Constellation Ursa Minor, the Little Bear, August 8, 2004. Own work: AlltheSky.com. http://commons.wikimedia.org/wiki/File:UrsaMinorCC.jpg.
Inc, Google. English: A Material Design Icon, October 15, 2014. GitHub. http://commons.wikimedia.org/wiki/File:Ic_directions_walk_48px.svg.
USA, Steve Ryan from Groveland, CA. I Took a Somewhat Similar Shot at the Time of the Leonid Meteor Shower, but Wanted to Repeat It with the North Star in the View. This Was Taken with a Nearly Full Moon Which Lit up the Trees and Added Background Light to the Sky, but a Reasonable Number of Stars Were Still Visible., December 3, 2006. Stars around Polaris - Day 62. http://commons.wikimedia.org/wiki/File:Steve_Ryan_-_Stars_around_Polaris_-_Day_62_(by-sa).jpg.

Views: 24623
Bozeman Science

This course will continue on Patreon at http://bit.ly/PavelPatreon
Textbook: http://bit.ly/ITCYTNew
Solutions: http://bit.ly/ITACMS_Sol_Set_YT Errata: http://bit.ly/ITAErrata
McConnell's classic: http://bit.ly/MCTensors
Weyl's masterpiece: http://bit.ly/SpaceTimeMatter Levi-Civita's classic: http://bit.ly/LCTensors Linear Algebra Videos: http://bit.ly/LAonYT
Table of Contents of http://bit.ly/ITCYTNew
Rules of the Game
Coordinate Systems and the Role of Tensor Calculus
Change of Coordinates
The Tensor Description of Euclidean Spaces
The Tensor Property
Elements of Linear Algebra in Tensor Notation
Covariant Differentiation
Determinants and the Levi-Civita Symbol
The Tensor Description of Embedded Surfaces
The Covariant Surface Derivative
Curvature
Embedded Curves
Integration and Gauss’s Theorem
The Foundations of the Calculus of Moving Surfaces
Extension to Arbitrary Tensors
Applications of the Calculus of Moving Surfaces
Index:
Absolute tensor
Affine coordinates
Arc length
Beltrami operator
Bianchi identities
Binormal of a curve
Cartesian coordinates
Christoffel symbol
Codazzi equation
Contraction theorem
Contravaraint metric tensor
Contravariant basis
Contravariant components
Contravariant metric tensor
Coordinate basis
Covariant basis
Covariant derivative
Metrinilic property
Covariant metric tensor
Covariant tensor
Curl
Curvature normal
Curvature tensor
Cuvature of a curve
Cylindrical axis
Cylindrical coordinates
Delta systems
Differentiation of vector fields
Directional derivative
Dirichlet boundary condition
Divergence
Divergence theorem
Dummy index
Einstein summation convention
Einstein tensor
Equation of a geodesic
Euclidean space
Extrinsic curvature tensor
First groundform
Fluid film equations
Frenet formulas
Gauss’s theorem
Gauss’s Theorema Egregium
Gauss–Bonnet theorem
Gauss–Codazzi equation
Gaussian curvature
Genus of a closed surface
Geodesic
Gradient
Index juggling
Inner product matrix
Intrinsic derivative
Invariant
Invariant time derivative
Jolt of a particle
Kronecker symbol
Levi-Civita symbol
Mean curvature
Metric tensor
Metrics
Minimal surface
Normal derivative
Normal velocity
Orientation of a coordinate system
Orientation preserving coordinate change
Relative invariant
Relative tensor
Repeated index
Ricci tensor
Riemann space
Riemann–Christoffel tensor
Scalar
Scalar curvature
Second groundform
Shift tensor
Stokes’ theorem
Surface divergence
Surface Laplacian
Surge of a particle
Tangential coordinate velocity
Tensor property
Theorema Egregium
Third groundform
Thomas formula
Time evolution of integrals
Torsion of a curve
Total curvature
Variant
Vector
Parallelism along a curve
Permutation symbol
Polar coordinates
Position vector
Principal curvatures
Principal normal
Quotient theorem
Radius vector
Rayleigh quotient
Rectilinear coordinates
Vector curvature normal
Vector curvature tensor
Velocity of an interface
Volume element
Voss–Weyl formula
Weingarten’s formula
Applications: Differenital Geometry, Relativity

Views: 23729
MathTheBeautiful

Original post on our site with additional information, plans, questions & comments: http://www.thewoodwhisperer.com/videos/fixing-common-woodworking-mistakes/
The Wood Whisperer is education and entertainment for the modern woodworker! Find more at http://thewoodwhisperer.com & don't forget to subscribe to our YouTube channel! http://www.youtube.com/subscription_center?add_user=thewoodwhisperer
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Whether we like to admit it or not, mistakes will happen. Knowing how to repair them may make the difference between a nerve-wracking build and a relaxed one. So in this demo (recorded live), I'll show you some of the most common mistakes and errors I encounter and the various ways I like to fix them.
What You'll Need
CA Glue - Cyanoacrylate is a quick-drying adhesive that makes it easy to re-attach small bits of wood. Used with a quick-set activator, it's an incredibly ally in the battle of repairs. http://www.rockler.com/quick-set-glue-2-5-oz?sid=AFN86
Wood Filler - While many folks poo poo wood filler, there are just some flaws that call for the stuff. Getting the right color is the key and knowing a few tricks to give the appearance of real wood is also a big help. The stuff I like to use is Timbermate Wood Filler. http://www.amazon.com/gp/product/B003FWK5BO/ref=as_li_tl?ie=UTF8&camp=1789&creative=390957&creativeASIN=B003FWK5BO&linkCode=as2&tag=thewoodwhispe-20&linkId=NV43SE2G3NTBIPJQ
Clothes Iron - Sometimes the best solution is a little heat and moisture. A household iron will help us steam out dents and scratches. http://www.amazon.com/gp/product/B000M4D96G/ref=as_li_tl?ie=UTF8&camp=1789&creative=390957&creativeASIN=B000M4D96G&linkCode=as2&tag=thewoodwhispe-20&linkId=WKY73BXFVOXEHM3R
Repairing Tearout With Filler
In some cases, a gnarly bit of tearout is best repaired with filler. A good quality filler that won't shrink and accepts stain will give you the best chance of a good match. Since fillers are typically colored to match the primary background color of the wood, it can sometimes help to use a colored pencil to draw in the missing wood grain. Though I only resort to that for large/obvious repairs where the missing grain would be an eyesore.
Misplaced Mortise
A mortise is nothing more than a big hole, so filling it with wood is usually the best and most reliable fix. Be sure to orient the grain so that the repair is in line with the grain of the workpiece. This provides the best visual match and in many cases makes the repair all but invisible. Cut the repair piece a little bit longer than the size of the hole and use sandpaper to create a slight taper at each end. This ensures a nice tight fit at each end where the repair is likely to be most visible.
Repairing Chipout with Recovered Piece
On occasion, fortune smiles upon you and a chipped out piece of wood is recovered. This is a good thing since the piece will most likely nest right back into position without any visible gaps. So all you need to do is use a little CA glue and re-attach the piece. Once the glue cures, sand the area thoroughly and you should have a nearly flawless fix.
Repairing Chipout with a Patch
When you can't find the chipped out piece (or it has been disintegrated by the Woodworking Gods) and you don't want to use filler, a patch is often the most appropriate course of action. Since chipout/tearout is never a pretty sight, you'll need to work the affected area with a plan or chisel to create a flat area for the repair. This is one case where you actually need to make the flaw bigger for the greater good. Once a nice flat area is established, simply glue in a small scrap of wood using CA glue. Plane, saw, scrape, or chisel away the excess stock and sand smooth.
Steaming Dents & Scratches
Blunt force trauma is a common occurrence in the wood shop. Whether you drop a workpiece on the floor or something drops onto the workpiece, you'll often be confronted with dents that are too deep to just sand away. Fortunately, dents are nothing more than aggressively compressed fibers. Since wood fibers expand with moisture, we can steam the dents using a wet towel and a household clothes iron. With a few seconds of treatment, the wood fibers expand to fill the dented areas. Of course this will only work on shallow dents but it can still be used to lessen the impact of deeper dents. The same theory applies to scratches in solid wood and plywood.

Views: 1290488
The Wood Whisperer

Cartesian Product (or Cross Product) Construction Example
Recorded Sp2014 for CSE355 at Arizona State University to supplement Sipser Section 0

Views: 766
Erin Lanus

SOLIDWORKS ELECTRICAL: GETTING STARTED
Creating Detailed Schematic Symbols
Learn how SOLIDWORKS Electrical enables you to create detailed schematic symbols using the "symbol manager" tool. Save time by creating a symbol ONCE and reusing the symbol via your symbol library.

Views: 4308
PrismEngineering

Some people say this is "how the Japanese multiply." Others say this is "Vedic Math." I'm not sure of the origin, but this is a visual way to multiply two numbers and it does work. The video also shows how to use the same method to multiply algebraic expressions like (x + 2)(x + 3).
Here's a blog post I wrote on this: http://mindyourdecisions.com/blog/2012/01/27/multiplicating-with-lines-math-trick-how-it-works/
Many people asked me to write a reference guide. So I wrote a book "Multiply Numbers By Drawing Lines." https://www.amazon.com/gp/product/1500866148/
I've made a few follow-up videos you might like.
Multiply by lines (advanced examples)
https://www.youtube.com/watch?v=DUop79ZKxmc
Multiply by lines (why it works)
https://www.youtube.com/watch?v=bL5eUQIMaek
Multiply by lines (the rotation trick)
https://www.youtube.com/watch?v=scCfeJhJ2TA
If you like my videos, you can support me at Patreon: http://www.patreon.com/mindyourdecisions
Connect on social media. I update each site when I have a new video or blog post, so you can follow me on whichever method is most convenient for you.
My Blog: http://mindyourdecisions.com/blog/
Twitter: http://twitter.com/preshtalwalkar
Facebook: https://www.facebook.com/pages/Mind-Your-Decisions/168446714965
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Tumblr: http://preshtalwalkar.tumblr.com/
Instagram: https://instagram.com/preshtalwalkar/
Patreon: http://www.patreon.com/mindyourdecisions
Newsletter (sent about 2 times a year): http://eepurl.com/KvS0r
My Books
"The Joy of Game Theory" shows how you can use math to out-think your competition. (rated 4/5 stars on 23 reviews) https://www.amazon.com/gp/product/1500497444
"The Irrationality Illusion: How To Make Smart Decisions And Overcome Bias" is a handbook that explains the many ways we are biased about decision-making and offers techniques to make smart decisions. (rated 5/5 stars on 1 review) https://www.amazon.com/gp/product/1523231467/
"Math Puzzles Volume 1" features classic brain teasers and riddles with complete solutions for problems in counting, geometry, probability, and game theory. Volume 1 is rated 4.5/5 stars on 11 reviews. https://www.amazon.com/gp/product/1517421624/
"Math Puzzles Volume 2" is a sequel book with more great problems. https://www.amazon.com/gp/product/1517531624/
"Math Puzzles Volume 3" is the third in the series. https://www.amazon.com/gp/product/1517596351/
"40 Paradoxes in Logic, Probability, and Game Theory" contains thought-provoking and counter-intuitive results. (rated 4.9/5 stars on 7 reviews) https://www.amazon.com/gp/product/1517319307/
"The Best Mental Math Tricks" teaches how you can look like a math genius by solving problems in your head (rated 4.7/5 stars on 3 reviews) https://www.amazon.com/gp/product/150779651X/
"Multiply Numbers By Drawing Lines" This book is a reference guide for my video that has over 1 million views on a geometric method to multiply numbers. (rated 5/5 stars on 1 review) https://www.amazon.com/gp/product/1500866148/

Views: 2059055
MindYourDecisions

Watch the next lesson: https://www.khanacademy.org/science/physics/torque-angular-momentum/torque-tutorial/v/constant-angular-momentum-when-no-net-torque?utm_source=YT&utm_medium=Desc&utm_campaign=physics
Missed the previous lesson? https://www.khanacademy.org/science/physics/torque-angular-momentum/torque-tutorial/v/rolling-without-slipping-problems?utm_source=YT&utm_medium=Desc&utm_campaign=physics
Physics on Khan Academy: Physics is the study of the basic principles that govern the physical world around us. We'll start by looking at motion itself. Then, we'll learn about forces, momentum, energy, and other concepts in lots of different physical situations. To get the most out of physics, you'll need a solid understanding of algebra and a basic understanding of trigonometry.
About Khan Academy: Khan Academy offers practice exercises, instructional videos, and a personalized learning dashboard that empower learners to study at their own pace in and outside of the classroom. We tackle math, science, computer programming, history, art history, economics, and more. Our math missions guide learners from kindergarten to calculus using state-of-the-art, adaptive technology that identifies strengths and learning gaps. We've also partnered with institutions like NASA, The Museum of Modern Art, The California Academy of Sciences, and MIT to offer specialized content.
For free. For everyone. Forever. #YouCanLearnAnything
Subscribe to Khan Academy’s Physics channel: https://www.youtube.com/channel/UC0oGarQW2lE5PxhGoQAKV7Q?sub_confirmation=1
Subscribe to Khan Academy: https://www.youtube.com/subscription_center?add_user=khanacademy

Views: 433278
Khan Academy

handout: https://www.dropbox.com/s/bd3hiwlhfsem0dv/C%26P102.5Ht.pdf?dl=0
smartnotes: https://www.dropbox.com/s/nloyqjk60nrz49n/LAC2014-102-Day05.pdf?dl=0
Today we finished Packet 102 on 3D Vectors with a discussion of Torque!
HTH,
A. Jorge Garcia
Applied Math, Physics & CS
http://shadowfaxrant.blogspot.com
http://www.youtube.com/calcpage2009

Views: 159
calcpage2009

3.4.1 Matrix-vector multiplication via dot product

Going step by step, I'll be explaining the easiest way to solve the Rubik's Revenge!
For business inquiries:
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Noah Richardson
P.O. Box 183
Moline, IL 61266
PayPal: [email protected]
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I promised you all a 4x4 video and what better day is there to share this with you than on Thanksgiving?! I just want to say that I am very thankful for you and all the support you guys have given me by watching, commenting, liking and subscribing!
Here is the cube I used in this video: http://www.amazon.com/gp/product/B004UVJG7I/ref=oh_aui_detailpage_o00_s00?ie=UTF8&psc=1
If you have any questions or comments, feel free to post them or send me a PM!
Subscribe and follow me on Twitter for video updates and for GIVEAWAYS! https://twitter.com/richardson_noah
2x2 https://www.youtube.com/watch?v=bRYAhYtqL84
3x3 https://www.youtube.com/watch?v=rmnSpUgOvyI
Intro to F2L https://www.youtube.com/watch?v=sEQNC0s1NTg
Mirror Cube https://www.youtube.com/watch?v=VYOkh3j0GCw
1 Cor. 10:31, "So whether you eat or drink or whatever you do, do it all for the glory of God."

Views: 6349000
Noah Richardson

Scalar product of two vectors is an operation on two vectors of the same dimensionality with the result being a real number (that is, scalar, that's why this operation is called scalar product). Other names for this operation are dot product and inner product.
Symbolically, the scalar product of two vectors a and b is denoted as
a · b
(with a dot in between, that's why it's called dot product).
The same symbol of operation - dot - is used for multiplication of numbers, numbers and vectors and scalar product of two vectors. Hopefully, the context will be sufficiently clear to differentiate them. At the same time, the rules of these operations are in many ways similar (like the commutative, associative and distributive laws), which makes usage of the same symbol for these different operations justifiable.
Since vectors have a geometric interpretation as a directed segment and an algebraic interpretation as an ordered set of real numbers (a tuple), the scalar product also can be interpreted geometrically and algebraically. Before giving a formal definition of the scalar product using these two interpretations, let's suggest certain reasonable requirements it should satisfy to be rightfully called a "product".
Rule 1 - independence law
Scalar product of two vectors depends only on their lengths and relative position (an angle between their directions). It does not depend on any other object, including a system of coordinates.
Rule 2 - multiplication by a null-vector
a · 0 = 0
Rule 3 - multiplication of a unit vector by itself
1 · 1 = 1
Rule 4 - commutative law
a · b = b · a
Rule 5 - associative with multiplication by a constant law
(K·a) · b = K·(a · b) and
a · (K·b) = K·(a · b)
Rule 6 - distributive law
(a+b) · c = a · c + b · c
The rules presented above seem to be quite natural. Based on these rules, let's derive the algebraic expression of the scalar product in a tuple representation and in geometric terms.
Consider for simplicity a two-dimensional case and two vectors in tuple representation (a1,a2) and (b1,b2). How would their scalar product look like if we want to satisfy all the rules above?
First of all, we can simplify our job by replacing vector (a1,a2) with an expression
a1·(1,0)+a2·(0,1)
Their equality follows from the rules of multiplication of the vector by a constant and addition of vectors presented in the lecture on vector arithmetic.
Similarly, we can represent a vector (b1,b2):
(b1,b2) = b1·(1,0)+b2·(0,1)
Now the scalar product of vectors (a1,a2) and (b1,b2) equals to the scalar product
[a1·(1,0)+a2·(0,1)] · [b1·(1,0)+b2·(0,1)]
Using the commutative, associative and distributive laws, we can open the brackets and get the following expression for our scalar product:
a1·b1·(1,0)·(1,0) + a1·b2·(1,0)·(0,1) + a2·b1·(0,1)·(1,0) + a2·b2·(0,1)·(0,1)
Both scalar products (1,0)·(1,0) and (0,1)·(0,1) are equal to 1 by the above rule about unit vectors multiplied by themselves.
Situation with (1,0)·(0,1) and (0,1)·(1,0) is a little more complicated.
First of all, these two scalar products equal to each other because of the commutative law.
Secondly, one of the rules above states that a scalar product should depend only on the lengths of the vectors participating in it and an angle between them. According to this rule, the scalar product of (1,0) and (0,1) should be the same as a scalar product of (−1,0) and (0,1) since in both cases the lengths are the same and the angle between the participating vectors is the right angle of 90°. On the other hand, the latter scalar product equals to (−1)·(1,0)·(0,1). Therefore, we have an equality:
(1,0)·(0,1) = (−1)·(1,0)·(0,1)
from which follows that (1,0)·(0,1) equals to 0.
Using this, the final algebraic expression of the scalar product of two vectors in tuple form (a1,a2) and (b1,b2) is
(a1,a2) · (b1,b2) = a1·b1 + a2·b2
Similarly, in three dimensional case the formula for a scalar product is:
(a1,a2,a3) · (b1,b2,b3) =
a1·b1 + a2·b2 + a3·b3
Derivation of this expression is based on the representation of a vector (a1,a2,a3) in a form
a1·(1,0,0) + a2·(0,1,0) + a3·(0,0,1),
a vector (b1,b2,b3) in a form
b1·(1,0,0) + b2·(0,1,0) + b3·(0,0,1) and equalities for scalar products
(1,0,0) · (1,0,0) = 1
(0,1,0) · (0,1,0) = 1
(0,0,1) · (0,0,1) = 1
(1,0,0) · (0,1,0) = 0
(1,0,0) · (0,0,1) = 0
(0,1,0) · (0,0,1) = 0
and their commutative equivalents.
Notice that, instead of formal definition of a scalar product as formulas above, we have derived these formulas based on some reasonable assumptions about properties of a scalar product.

Views: 481
Zor Shekhtman

Learn how to make your own tie dye cross t-shirt using Tulip One-Step Tie Dye! This is a perfect tie dye project for church camp or Vacation Bible School! For more fun tie dye videos SUBSCRIBE: http://youtube.com/duncancrafts

Views: 64202
iLoveToCreate

Get it here: http://themoonlightshop.com/products/the-solstice-solar-cross-necklace
Transcript:
Hi... This is Hjalte from The Moonlight Shop and in this video, I will show you the beautiful and highly detailed Solstice Solar Cross Necklace from our shop.
The Solar Cross is an ancient celtic symbol that has been used to celebrate and worship the sun for many, many years.
It consists of the cross and a circle behind it and is closely related to the 4 season and the suns movement throughout the year.
The four parts of the cross symbolizes the 2 solstices and the 2 Equinoxes.
The circle behind the cross symbolizes the year which is divided into 4 seasons.
As you can see, there are celtic spirals and knot patterns which are highly detailed and stands out.
In the middle of the cross is a birthstone crystal. This necklace here has the birthstone for June. The Lavender Tanzanite.
Besides getting it with your own personal birthstone, you can also get this necklace with the Black Onyx stone or a Rainbow stone.
I really like this necklace because it is very non threatening for other people. If you can't or won't wear your pentacle for some reason, but you still want to have some meaningful and empowering jewelry on you, the Solstice Solar Cross is the perfect choice.
The solar cross gives you energy from the sun and the combination with the powers from the birthstone, makes this a very powerful pendant.
The necklace itself is made from lead and nickel free pewter, which makes it very durable and allergy friendly, so even if you are usually allergic to most jewelry, you should be able to wear this just fine.
The pendant has a good size and weight to it. It measures just around 1.5 inch across and a little more from top to bottom because of the loop.
It has a nice weight to it. You can feel that this is a quality necklace. This is a piece of jewelry that will last for many many years of daily use.
The pendant comes with an 18 inch leather cord with a lobster clasp that allows you to adjust the length with around 2 inches. If you'd rather put it on something else, there's plenty of room in the loop to do that.
So, to conclude, this is a very beautiful and powerful necklace. The birthstone in the middle makes is very fashionable and unique.
If you are into paganism or wicca and are looking for a necklace with meaning and power that you can use every day and in every occasion, this is the obvious choice.
Thank you for watching and blessed be.

Views: 1520
The Moonlight Shop

Multicoloured LEDs with integral WS2811 control chips, prewired into sets of 50.
In this episode, the LEDs are fixed into black plastic panels to create several illuminated name signs. (Part 1: http://youtu.be/XEy_IMT2WoU)
Panels are 3mm black foamex (foamed PVC sign board).
Paper templates created in CorelDraw.
LEDs: http://www.aliexpress.com/item/100x-WS2811-5V-12mm-LED-Module-Black-Green-White-Crystal-RGB-Wire-50-pixels-string-Christmas/32216500548.html
Controller: http://www.aliexpress.com/item/Free-Shipping-1x-24-Key-IR-Remote-Controller-WS2811-WS2812B-200-Change-Max-1000-Pixel-LED/1547147534.html
Power supply: http://cpc.farnell.com/ideal-power/25hk-ab-050a400-d5-1/psu-desktop-5v-4a-3-pin-iec/dp/PW03335
► Support this channel:
Patreon: https://www.patreon.com/jwflame
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► Social Media:
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► Contact info, sending stuff in: etc.:
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► Website - More on this video and many other subjects
Website: https://www.flameport.com
Page for this video: http://xo4.uk/?lpp

Views: 135212
John Ward

We can expect a very intense and transformative period beginning in 2014: In a way we are changing to a brand new car on a collective level. The Grand Cross in cardinal signs tests us on three levels: Our identity, our collective wound and how we act.
I have elaborated on this in this article: http://whitebull.dk/GrandCrossApril2014.pdf
.. and here a version in danish: http://whitebull.dk/StorkorsetApril2014.pdf
Facebook note (part 1): https://www.facebook.com/notes/johan-tino-frederiksen/astrology-for-april-2014-part-1-a-new-balance-between-male-and-female-energies/756094661109785
This lecture about the Grand Cross by Tom K. Lescher can also be recommended: http://newparadigmastrology.com/products-page/recorded-talks/astrology-of-2014-mexico-recording

Views: 1008
Johan Tino Frederiksen

-- Created using PowToon -- Free sign up at http://www.powtoon.com/ . Make your own animated videos and animated presentations for free. PowToon is a free tool that allows you to develop cool animated clips and animated presentations for your website, office meeting, sales pitch, nonprofit fundraiser, product launch, video resume, or anything else you could use an animated explainer video. PowToon's animation templates help you create animated presentations and animated explainer videos from scratch. Anyone can produce awesome animations quickly with PowToon, without the cost or hassle other professional animation services require.

Views: 651
Aizun Arifin

The Mediatwist Group and Team 2Xtreme Racing are helping one of the most adrenaline fueled rock-stars in the world, cross another item off of his infamous Bucket List. Follow along as we join Zoltan and his band, Five Finger Death Punch, backstage at Carolina Rebellion, the biggest outdoor rock festival in North Carolina. Watch as Zoltan signs with one of the premiere companies in motor sports, Simpson Racing Products. All of this brings us one step closer to the day of the test drive, where Zoltan, with the guidance of Monster Jam Freestyle World Champion, Jimmy Creten, will strap in behind the wheel of a 10,000lb monster, Knucklehead. Follow @mediatwist for project updates.

Views: 7775
The Mediatwist Group

Howdy, this is a sped up video of me folding up a Peace Symbol on the front of a shirt and a Mandala or 8 pointed star on the back of the shirt. I then show how to dye it.
Enjoy, please like and subscribe for more videos!
Original video:http://youtu.be/ZOsUaNwg1-E
http://www.RoslynRags.com
[email protected]
http://www.facebook.com/RoslynRags
http://www.dharmatrading.com/dyes/dharma-fiber-reactive-procion-dyes.html?lnav=dyes.html

Views: 3810
Roslyn Rags

DVD now available to order! Go to http://josephsmithfoundation.org/store/product/statesmen-symbols-prelude-to-the-restoration-dvd/ to get your copy today!
"Statesmen & Symbols: Prelude to the Restoration" Interviewees: Vicki Jo Anderson, Tim Ballard, Scott N. Bradley, Kay M. Godfrey, J. Ruel Haymond, Rod L. Meldrum, Amberli G. Nelson, V. Lauri Updike, L. Hannah Stoddard, James F. Stoddard III
Watch the Trailer! https://www.youtube.com/watch?v=gXNrqb-2cbU
Are inverted pentagrams occult symbols or do they have a sacred, nearly forgotten meaning?
Watch another clip! "Satanists and the Occult Desecrate Holy Symbols" https://www.youtube.com/watch?v=7vjWD6P7ZA0
The DVD, Statesmen & Symbols: Prelude to the Restoration includes two documentaries:
Part 1: Sacred Symbols
Compass, Square, Octagon, Inverted Pentagram, Joseph Smith & Masonry, Early Christian Ceremonies, Ouroboros
Why are some of the sacred symbols used by the Founding Fathers, also found on tapestries in China that date to the time of the flood?
Why do we find the same symbols revealed to the Prophet Joseph Smith, as part of the Restoration, used as well by the early Christians?
Are inverted pentagrams occult symbols or do they have a sacred, nearly forgotten meaning?
Part 2: Covenant Land
Hopewell Civilization, Ohio's East Fork/"Hanukkiah" Earthworks, Adams & Jefferson Letters, 50 Year Jubilee
Why are many of the Masonic symbols used by the American Founding Fathers identical to those revealed by Joseph Smith?
Do sacred symbols tie the Book of Mormon, the Hopewell civilization of North America and the American founding together?
What do LDS temples have in common with the Great Pyramid of Giza, Stonehenge and the Hopewell mounds in North America?
What is the significance in the deaths of Thomas Jefferson and John Adams on July 4th, fifty years to the day of the signing of the Declaration of Independence?
What are the details of American Founding Father Benjamin Rush's vision concerning Thomas Jefferson and John Adams? How was the vision fulfilled?
Did some of the American Founding Fathers understand the need for a Restoration and in many ways anticipate the work of Joseph Smith?
Why did Benjamin Franklin work to bring Freemasonry to America? Was Freemasonry in America a prelude to the Restoration?

Views: 63713
Joseph Smith Foundation

Could you be in the afterlife without realizing that you're there? And how much of our personality do we take with us to the other side? Join us, along with guest award-winning author Peter Rhodes, as we read through Swedenborg's accounts of his spiritual experiences, and what he learned through them.
Topics include:
-Why some people don't realize that they've died
-How our five senses translate into the spiritual world
-How heaven's light affects our minds
You can download the book that we'll be going through for free as an ebook or pdf here: http://www.swedenborg.com/product/life-death/?utm_source=facebook&utm_medium=event&utm_campaign=HHpost
Donate here: https://www.paypal.com/cgi-bin/webscr?cmd=_s-xclick&hosted_button_id=ZADSY8EZ62QLU

Views: 303510
offTheLeftEye

Describes symbols used in and rules for writing chemical equations

Views: 3884
Marci Harvey

One woman's global Photoshop experiment yielded stunning results
Post to Facebook: http://on.fb.me/1mGUwqc
Like BuzzFeedVideo on Facebook: http://on.fb.me/1ilcE7k
Post to Twitter: http://bit.ly/TG2DrA
Music:
Beauty and Magic
Music Licensed Via Warner Chappell Production Music Inc.
Credits:
All photos courtesy of Esther Honig
"Before & After"
http://www.estherhonig.com/
free_high_res_texture_259
http://www.flickr.com/photos/calebkimbrough/4131730141/
free_high_res_texture_260
http://www.flickr.com/photos/calebkimbrough/4132495368/
light-texture
http://www.flickr.com/photos/alicepopkorn/6372299829/
free_high_res_texture_262
https://www.flickr.com/photos/calebkimbrough/4151249534
Sources:
http://www.huffingtonpost.com/2012/03/20/women-makeup-free-stressful-first-date-job-interview_n_1366541.html
http://www.babtac.com/news-article/?id=105
http://www.womenshealthmag.com/beauty/beach-beauty
http://www.cosmeticsdesign-europe.com/Market-Trends/German-consumers-spend-most-on-cosmetics-in-Europe
http://www.bradleyfarless.com/the-standard-of-beauty-in-the-philippines/
Based on this BuzzFeed Post by Ashley Perez:
http://www.buzzfeed.com/ashleyperez/global-beauty-standards

Views: 10961398
As/Is

Views: 4255
MATH 1151

January Download: http://www.inclusiveastrology.com/collections/new-products/products/january-2014-live-webinar-registration
Weekly Tarot/Astro SHS House Music Show Link: http://www.youtube.com/watch?v=XYT9BKPltjg
Daily Inspirational Astrology Horoscope: January 7 2014 Moon In Aries Cardinal Cross
From beyond the dimensions of time and space, a King rises from the past and has come back from the future, to brighten up the dawning of a new age on Earth. Using his charm, ancient tool bag and positive energy, the Leo King reclaims his throne and sets on his quest to lead the new world into illuminating its individual and collective consciousness.
The Leo King's quest takes him on a journey of brightening up the world with his music, astrology and inspirational speeches in order to change your life and bring you into spiritual ecstasy.
Check out my new astrology readings! Book an astrology reading at my store.
http://www.inclusiveastrology.com
When you purchase a reading from Inclusive Astrology, be prepared to have your soul rocked! The reading will consist of David going through your natal chart and using his spiritual channel to interpret what is happening in your life, what he sees in your future and will answer your questions regarding love, work, your spiritual journey and more! David's channel is very sharp and will pick up on the energy you are going through and more importantly, he will guide you using the message spirit wants to direct you in. David uses state of the art chart systems and will run all astrology charts that are used in today's advanced chart programs. David will give you a deep and advanced look into spirit that you have never had access to before!
David has been reading charts and souls professionally for over 5 years and has been featured as the top astrologer in America on Yahoo!, E! Television, ABC, MTV, Style Network, National Enquirer, People Magazine and Reality Weekly!
Reading will be done via a phone call to a number provided or on skype. The reading will be recorded on an mp3 and will be delivered as soon as possible.
http://www.theleoking.com
http://spiritualhousemusic.com
http://www.david-palmer.com
http://www.starhearts.com
http://www.imdb.com/name/nm3926465/
http://dj.beatport.com/theleoking
http://inclusiveastrology.com
http://twitter.com/theleokingdom
http://soundcloud.com/djdavidpalmer
http://www.modelmayhem.com/palmer
Inclusive Astrology sets to Illuminate the Collective Consciousness http://www.inclusiveastrology.com
Follow us on twitter! @InclusiveAstro @theleokingdom
David is an esoteric astrologer.

Views: 4350
The Leo King

CIAAAOOO!
Nuova review by CHOIES!
T-shirt "Galaxy", modello unisex aderente full color + simboli.
Per ultra cyber look! inoltre reagisce benissimo alla wood lamp!
Enjoy & Dance!
Di seguito i links correlati:
La maglietta:
http://www.choies.com/product/new-look-galaxy-unisex-t-shirt-with-symbol-print?cid=5047margaret
Sito di CHOIES:
http://www.choies.com/?cid=5047margaret
Sito di IWANTWIG (extensions)
http://www.iwantwig.com/?cid=23margaret
Le altre reviews:
http://youtu.be/xBfqDy6zexw
http://youtu.be/BA0xdDuxGHo
http://youtu.be/KuxjHY60vUo

Views: 1555
MISTEROUGE

In this tutorial we will show you how to work with text that is displayed dynamically and written to graphics in InRoads Survey.
We will look at the InRoads Survey Options dialog box and the Edit View options compared to the Edit Text options and how the Text Scale factor is applied. Then we will look at the why the Survey Symbol for InRoads Survey does not snap to the center and how to correct that.

Views: 7158
envisioncad

The prevalent conduct of war on the Western Front of the First World War is unmistakably trench warfare. The trenches with knee deep mud are a war theatre as well as home to the soldiers. But how does it look like inside a trench? How is it constructed?
Indy took a look and explains why and how the trenches could be the base for a war between 1914 and 1918 and how life was inside a trench.
But how did the Trench Warfare start?: http://bit.ly/11PqXLp
Click here for the "Maconochi Stew Recipe": http://bit.ly/1r2vLtc
» HOW CAN I SUPPORT YOUR CHANNEL?
You can support us by sharing our videos with your friends and spreading the word about our work.You can also support us financially on Patreon: https://www.patreon.com/thegreatwar
Patreon is a platform for creators like us, that enables us to get monthly financial support from the community in exchange for cool perks.
» MORE HISTORY?
Check out our sister channel IT’S HISTORY: http://youtube.com/itshistory
» WHERE CAN I GET MORE INFORMATION ABOUT WORLD WAR I AND WHERE ELSE CAN I FIND YOU?
We’re offering background knowledge, news, a glimpse behind the scenes and much more on:
reddit: http://bit.ly/TheGreatSubReddit
Facebook: http://bit.ly/WW1FB
Twitter: http://bit.ly/WW1Series
Instagram: http://bit.ly/ZpMYPL
» CAN I EMBED YOUR VIDEOS ON MY WEBSITE?
Of course, you can embed our videos on your website. We are happy if you show our channel to your friends, fellow students, classmates, professors, teachers or neighbours. Or just share our videos on Facebook, Twitter, Reddit etc.
We are also happy to get your feedback, criticism or ideas in the comments. If you have interesting historical questions, just post them and we will answer in our OUT OF THE TRENCHES videos. You can find a selection of answers to the most frequently asked questions here: http://bit.ly/OOtrenches
» CAN I SHOW YOUR VIDEOS IN CLASS?
Of course! Tell your teachers or professors about our channel and our videos. We’re happy if we can contribute with our videos. If you are a teacher and have questions about our show, you can get in contact with us on one of our social media presences.
» WHAT ARE YOUR SOURCES?
Videos: British Pathé
Pictures: Mostly Picture Alliance
Background Map: http://d-maps.com/carte.php?num_car=6030&lang=en
Literature (excerpt):
Gilbert, Martin. The First World War. A Complete History, Holt Paperbacks, 2004.
Hart, Peter. The Great War. A Combat History of the First World War, Oxford University Press, 2013.
Hart, Peter. The Great War. 1914-1918, Profile Books, 2013.
Stone, Norman. World War One. A Short History, Penguin, 2008.
Keegan, John. The First World War, Vintage, 2000.
Hastings, Max. Catastrophe 1914. Europe Goes To War, Knopf, 2013.
Hirschfeld, Gerhard. Enzyklopädie Erster Weltkrieg, Schöningh Paderborn, 2004
Michalka, Wolfgang. Der Erste Weltkrieg. Wirkung, Wahrnehmung, Analyse, Seehamer Verlag GmbH, 2000
Leonhard, Jörn. Die Büchse der Pandora: Geschichte des Ersten Weltkrieges, C.H. Beck, 2014
If you want to buy some of the books we use or recommend during our show, check out our Amazon Store: http://bit.ly/AmazonTGW
NOTE: This store uses affiliate links which grant us a commission if you buy a product there.
» WHAT IS “THE GREAT WAR” PROJECT?
THE GREAT WAR covers the events exactly 100 years ago: The story of World War I in realtime. Featuring: The unique archive material of British Pathé. Indy Neidell takes you on a journey into the past to show you what really happened and how it all could spiral into more than four years of dire war. Subscribe to our channel and don’t miss our new episodes every Thursday.
» WHO IS REPLYING TO MY COMMENTS? AND WHO IS BEHIND THIS PROJECT?
Most of the comments are written by our social media manager Florian. He is posting links, facts and backstage material on our social media channels. But from time to time, Indy reads and answers comments with his personal account, too.
The Team responsible for THE GREAT WAR is even bigger:
- CREDITS -
Presented by: Indiana Neidell
Written by: Indiana Neidell
Director: David Voss
Sound & DoP: Toni Steller
Sound Design: Bojan Novic
Editing: Toni Steller & Ole-Sten Haufe
Research by: Indiana Neidell
Fact checking: Latoya Wild & David Voss
A Mediakraft Networks Original Channel
Based on a concept by Spartacus Olsson
Author: Indiana Neidell
Visual Concept: Astrid Deinhard-Olsson
Executive Producer: Astrid Deinhard-Olsson and Spartacus Olsson
Producer: David Voss
Social Media Manager: Florian Wittig
Contains licenced Material by British Pathé
All rights reserved - © Mediakraft Networks GmbH, 2014

Views: 1139275
The Great War

Sterling Silver Celtic Cross Pendant - handcrafted by Lee Allin of Handcrafted Symbolic Jewellery UK.
The Celtic Cross is a symbol that combines a cross with a ring surrounding the intersection. The symbol is associated with Celtic Christianity, although it has older, pre-Christian origins. Such crosses form a major part of Celtic art. A standing Celtic cross, made of stone and often richly ornamented, is called a high cross or Irish Cross.
Celtic crosses may also have origins in the early Coptic church. The similarity between the ankh, symbol of "life" and variations of the cross or ankh with a circle on Coptic stella and textiles from as early as the 5th century clearly show that the combination of circle and cross were used in early Christian Egypt. Although some experts say that they were originally carved horizontally on stone, their Geometrical ring construction and the fact that the lights in east-facing high crosses can be seen to refract early morning sunlight is indicative of vertical construction.
In Ireland, it is a popular myth that the Celtic cross was introduced to the island by Saint Patrick or possibly Saint Declan during his time converting the pagan Irish. It is believed that Saint Patrick combined the symbol of Christianity, a cross, with the symbol of the sun (or possibly the moon), to give pagan followers an idea of the importance of the cross by linking it with the idea of the life-giving properties of the sun.
http://www.handcraftedsymbolicjewellery.co.uk/page18/index.htm

Views: 370
Symbolic Jewellery UK

I have included all the project files on my github page.
Here's the link: https://github.com/sharath1231/Character-Recognition-using-OCR/tree/master
For the templates you can use MATLAB OCR templates: http://www.mathworks.com/matlabcentral/fileexchange/18169-optical-character-recognition--ocr-/all_files

Views: 55056
Sharath Kumar

This course will continue on Patreon at http://bit.ly/PavelPatreon
Textbook: http://bit.ly/ITCYTNew
Solutions: http://bit.ly/ITACMS_Sol_Set_YT Errata: http://bit.ly/ITAErrata
McConnell's classic: http://bit.ly/MCTensors
Weyl's masterpiece: http://bit.ly/SpaceTimeMatter Levi-Civita's classic: http://bit.ly/LCTensors Linear Algebra Videos: http://bit.ly/LAonYT
Table of Contents of http://bit.ly/ITCYTNew
Rules of the Game
Coordinate Systems and the Role of Tensor Calculus
Change of Coordinates
The Tensor Description of Euclidean Spaces
The Tensor Property
Elements of Linear Algebra in Tensor Notation
Covariant Differentiation
Determinants and the Levi-Civita Symbol
The Tensor Description of Embedded Surfaces
The Covariant Surface Derivative
Curvature
Embedded Curves
Integration and Gauss’s Theorem
The Foundations of the Calculus of Moving Surfaces
Extension to Arbitrary Tensors
Applications of the Calculus of Moving Surfaces
Index:
Absolute tensor
Affine coordinates
Arc length
Beltrami operator
Bianchi identities
Binormal of a curve
Cartesian coordinates
Christoffel symbol
Codazzi equation
Contraction theorem
Contravaraint metric tensor
Contravariant basis
Contravariant components
Contravariant metric tensor
Coordinate basis
Covariant basis
Covariant derivative
Metrinilic property
Covariant metric tensor
Covariant tensor
Curl
Curvature normal
Curvature tensor
Cuvature of a curve
Cylindrical axis
Cylindrical coordinates
Delta systems
Differentiation of vector fields
Directional derivative
Dirichlet boundary condition
Divergence
Divergence theorem
Dummy index
Einstein summation convention
Einstein tensor
Equation of a geodesic
Euclidean space
Extrinsic curvature tensor
First groundform
Fluid film equations
Frenet formulas
Gauss’s theorem
Gauss’s Theorema Egregium
Gauss–Bonnet theorem
Gauss–Codazzi equation
Gaussian curvature
Genus of a closed surface
Geodesic
Gradient
Index juggling
Inner product matrix
Intrinsic derivative
Invariant
Invariant time derivative
Jolt of a particle
Kronecker symbol
Levi-Civita symbol
Mean curvature
Metric tensor
Metrics
Minimal surface
Normal derivative
Normal velocity
Orientation of a coordinate system
Orientation preserving coordinate change
Relative invariant
Relative tensor
Repeated index
Ricci tensor
Riemann space
Riemann–Christoffel tensor
Scalar
Scalar curvature
Second groundform
Shift tensor
Stokes’ theorem
Surface divergence
Surface Laplacian
Surge of a particle
Tangential coordinate velocity
Tensor property
Theorema Egregium
Third groundform
Thomas formula
Time evolution of integrals
Torsion of a curve
Total curvature
Variant
Vector
Parallelism along a curve
Permutation symbol
Polar coordinates
Position vector
Principal curvatures
Principal normal
Quotient theorem
Radius vector
Rayleigh quotient
Rectilinear coordinates
Vector curvature normal
Vector curvature tensor
Velocity of an interface
Volume element
Voss–Weyl formula
Weingarten’s formula
Applications: Differenital Geometry, Relativity

Views: 33974
MathTheBeautiful

In April 2014, there will be three celestial events occurring: April 15 lunar eclipse, April 23/24 grand cardinal cross, and April 28 solar eclipse. What does psychic Douglas James Cottrell predict will happen at this time?
Be sure to check out Douglas's latest prediction regarding upcoming changes: http://www.douglasjamescottrell.com/products-page/earthchanges/earth-changes-prediction-april-2014-north-south-america/

Views: 5614
Douglas James Cottrell

(48) Calculate the magnitude and direction of the torque associated with a given force.

Views: 29690
Andrew Bennett

Traffic reporter Kevin Brennan said goodbye to the EyeOpener on Friday.

Views: 1858
WCVB Channel 5 Boston

https://MamaNatural.com 🔅 Griffin stages of crawling: http://youtu.be/f3xWaOkXCSQ
Cute baby in mirror: http://youtu.be/yXOt9agvIPg
Catch up with me on Facebook - I post tons of great natural recipes and inspiration!
http://fb.com/MamaNatural
See what I'm pinning:
http://www.pinterest.com/mamanaturalblog/
Let's connect on Instagram:
http://instagram.com/mamanatural
Pregnant? Check out my baby registry checklist:
http://www.mamanatural.com/baby-registry-checklist/
Here are all my fav products for natural living:
http://www.mamanatural.com/amazon/
Curious about the equipment we use to make these videos?
http://www.mamanatural.com/video-equipment/
THANK YOU FOR WATCHING AND SUBSCRIBING!
,
❤️❤️❤️
Genevieve Howland, aka Mama Natural
Bestselling author of The Mama Natural Week-by-Week Guide to Pregnancy & Childbirth ➡️ https://amzn.to/2Pf6Pfe
Co-Founder of https://www.mamanatural.com
FB: http://fb.com/MamaNatural
IG: https://www.instagram.com/mamanatural/
Pin: https://www.pinterest.com/mamanatural/

Views: 1196060
Mama Natural

LG Electronics and Google have signed a cross-licensing agreement... that will give both companies access to each other′s patents.
The deal will include existing patents,... as well as ones that are registered up until the year 2023.
Through the agreement,... LG will gain access to Google′s software patents, such as data processing and information security,... while Google gets the right to use LG′s hardware devices.
The two companies say... the deal will boost their relationship... and allow them to focus more on developing products and services together.

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