12 years ago and I'm finding it useful now. God bless you

Very underrated, thank you sm!

Bro come back these videos are too good

Nice Video, I was Just curious, what do you know? Are you into corporate, or have you pursued teaching or something else.

Do you have any textvook references for this

2:35 i cant understand why costheta is cant be greater than 0. isnt it all about the angle of between two vectors? why the angle is cant be smaller than 90 degrees.

Thank you so much

👏🏻👏🏻👏🏻👏🏻👏🏻👏🏻 ❤❤❤❤❤❤

thanks a lot!! very clear and insightful; ❤❤

Thank you sir ❤

Can u teach in Hindi

Pls talk in Hindi

You’re a life saver man ❤️

Thank you so much for this

best handwriting ive ever seen

ECE 485 UofA

U=x²+xy+y²+3z² subject to contrain x+2y+4z=60 Using Lagrange method for optimization 🙏sir pls iska solution bta dijiye

Ive searched and searched for help with this , slicing it into planes is genius THANKS !

Your video is so helpful!! Thanks a lot, Sir!!

It's 9 year old video 👌👌👌

Thankyou for your videos, it helps 😄

Your lecture is absolutely amazing, sir. Thank you for that!

What is use of laws, when we use it.pls tell me 🙏

Thanks a lot sir.... u did a commendable job by makin these..... Ur videos helped me alot alot ..... I without any doubt herald that there's no maths teacher in my institution who teaches concepts like you teach....

1 semester of work condensed into a couple of minutes.... 😭😭 thank you so much!

I think so too -min should replace max in statement 3.

Can i send you a question based on this and you perhaps solve it sir

Thanks Sir🙏🏾 I am Indian

My tuition fees must go to you. University lecturers don't do anything

why is the r^2 ?

What is the best book to learn all this? What is the name of subject in mathematics?

Thank you very much. I know this is supposed to be some old stuff but it is of great benefits.

which program did you use for making this video?

Thanks sir

Thank you very much. You uploaded this in 2012 and it helped me in 2020 :) which is an indication that whatever good we do, let's just do it. We don't know at what time in life that good things will benefit people. Maybe the effect will appear long after we die. So let's not always try to see an immediate effect of the good we do in our life : )

Too bad the youtube algorithm doesn't promote this educational content. Thanks, from an engineering student!

I cant wait to finish all of these stupid math classes

shouldn't the second order condition be that the double derivative of the function is less than zero for a (strict) maximum and greater than zero for a (strict) minimum ? I think you got the signs wrong there.

I can see you like Simon and Blume :)

Hi. First of all, I just want to say thank you so much for this playlist. Secondly, I have a question. In this video, you show that if the upper left determinants of A are both positive for a (2,2) matrix, then the matrix is positive definite, and the equation X^T AX = f(X) (where X is some vector) will have a minimum at x=0. You did so by completing the square. However, how would we show that the upper determinant test also checks for positive definiteness for bigger matrices? I tried completing the square for X^T AX in the case that A was (3,3), and that was WAAAY too ugly. There's gotta be a better way! Thanks!

i got it bro thanks

Loved it! Greatly appreciated!

I love people who explain with a figure rather than definitions alone. Great video btw!

perfect explanation

nice video

hey man you're awesome, life saver

Good explanation of Basic Vector Algebra. When you wrote 2u - v = (2-2, 4-1) . Didn't you mean to write 2(u-v) ?

nice explantion, what program r u using to write? it seems very good

was the problem left incomplete ?

EUCLIDEAN SPACE References Geometry | Definition of Geometry by Merriam-Websterwww.merriam-webster.com/dictionary/geometry Definition of geometry for Students. : a branch of mathematics that deals with points, lines, angles, surfaces, and solids. Two-dimensional definition and meaning | Collins English Dictionarywww.collinsdictionary.com/dictionary/english/two-dimensional two-dimensional. A two-dimensional object or figure is flat rather than solid so that only its length and width can be measured. Three-dimensional definition and meaning | Collins English Dictionarywww.collinsdictionary.com/dictionary/english/three-dimensional A three-dimensional object is solid rather than flat, because it can be measured in three different directions, usually the height, length, and width. ... Rhetorical Questions 1. Are electromagnetic particles flat, or are they infinitesimal quanta’s of radiant energy that exist in the form of infinitesimal spheres of spinning and radiating particles of electromagnetic influence? 2. Are atoms flat or are they composites of infinitesimal quanta's of radiant energy orbiting around the central gravitational nucleus of an atom, within the limits of its gravitational field and its surrounding space? 3. Can anything of the physically apparent (macro-cosmic) cosmos be straight or flat, as all physical things of the macro-cosmic universe are constructed from composites of infinitesimal (microcosmic-quantum) electromagnetic (gravitational) particles, which spin and (centrifugally) radiate their spheres of electromagnetic influence outward into all sectors of their immediate surrounding space? 4. Given, that the space surrounding each of us, and our planet, are extents of voluminous emptiness. How in logic and in rationality can it be claimed, that the mathematical propositions of Euclid’s straight linear geometry, can be applied, to what is essentially directionless non-geometrical empty space? Euclidean Linear Definitions Euclid A line is a breadth-less length. Reality Only within the imagery of the mind’s eye e.g. the imaginary lines between the stars of the constellations, whereas the lines of linear drawn geometry possess both a length and a width of surface area to their presence. Euclid A point is that which has no part. Reality Only within the imagery of the mind’s eye. A point in linear drawn geometry, possesses an amount of surface area with a graphite particle or coloured pigment coverage. Euclid A straight line is a line which lies evenly on itself. Reality A straight line is a line which lies evenly *of* itself over an evenly straight flat surface. Euclid A surface is that which has length and breadth only. Reality A surface is that which has length breadth and depth. Euclid The Extremities of a surface are line. Reality The extremities of a surface relative its shape, is its naked edge. The extremities of surface to a solid, is governed by its volume. The volumes of ovoid’s and spheres do not have any extremities to the curvature of their surface. www.fromthecircletothesphere.net