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Gresty Academy
Singapore
Приєднався 18 тра 2020
Gresty Academy together with Anstey Maths - making learning maths slightly less painful or slightly more fun, depending on your viewpoint!
We are constantly uploading new maths videos and making more maths playlists..check them out at www.youtube.com/@grestyacademy/playlists
Anybody interested in us making a 'specialist' maths playlist that we don't currently have, please contact us by commenting on any relevant video and we will do our best to oblige.
For those who prefer to watch our videos in another language - go to the settings of the UA-cam video in question and click on 'Subtitles'. This will give you an auto generated English transcription of the audio. Then click on 'English Auto Generated' and there is option to 'Auto Translate' to any other language - hey presto you have a transcript of the audio in your own language.
We are constantly uploading new maths videos and making more maths playlists..check them out at www.youtube.com/@grestyacademy/playlists
Anybody interested in us making a 'specialist' maths playlist that we don't currently have, please contact us by commenting on any relevant video and we will do our best to oblige.
For those who prefer to watch our videos in another language - go to the settings of the UA-cam video in question and click on 'Subtitles'. This will give you an auto generated English transcription of the audio. Then click on 'English Auto Generated' and there is option to 'Auto Translate' to any other language - hey presto you have a transcript of the audio in your own language.
Finding ALL Solutions with the Lambert W Function
In this video we use the Lambert W function to find all three solutions of the equation x + 4 ln (x^2) = 6. Later in the video we show a second method which, if not very careful, provides only ONE of the solutions, missing the other two.
For those unfamiliar with the Lambert W Function, check out the video 'The Simple Guide to the Lambert W Function Graph' at ua-cam.com/video/wq2zAiuOJ_4/v-deo.html
For more videos on the Lambert W Function, check out our playlist 'Lambert W Function' at ua-cam.com/play/PLlX3COjsHPVApqLukQcbj2e9rDC5sRg_t.html
For those unfamiliar with the Lambert W Function, check out the video 'The Simple Guide to the Lambert W Function Graph' at ua-cam.com/video/wq2zAiuOJ_4/v-deo.html
For more videos on the Lambert W Function, check out our playlist 'Lambert W Function' at ua-cam.com/play/PLlX3COjsHPVApqLukQcbj2e9rDC5sRg_t.html
Переглядів: 535
Відео
How to Solve an Exponential Equation with the Lambert W Function
Переглядів 38221 годину тому
In this video we use the Lambert W function to find the general solution of the exponential equation a^x bx c=0. The Gresty Academy video that we mention when cross checking our general solution is entitled 'How to Solve 3^x = 2x 2' and can be found at ua-cam.com/video/DgU_hK3e_Pg/v-deo.html For those unfamiliar with the Lambert W Function, check out the video 'The Simple Guide to the Lambert W...
Reconciling Two Seemingly Completely Different Lambert W Solutions
Переглядів 675День тому
In this video we use the Lambert W function to solve the equation x^3 / 24 - ln(x) = 0 using two different methods, which seem to give completely different solutions. However, as we show in this video, the solutions, despite looking very different, are actually the same. For the video 'The Simple Guide to the Lambert W Function Graph' see ua-cam.com/video/wq2zAiuOJ_4/v-deo.html - those unfamili...
Solving Coin Toss Problems with Markov Chains
Переглядів 1,2 тис.21 день тому
In this video we examine two common questions, namely a) the expected number of coin tosses in order to get three consecutive heads, and b) the expected number of coin tosses in order to get EITHER three consecutive heads OR three consecutive tails. Important Note: At 1:10 the author should have said "and you get your three consecutive heads in three throws" rather than "and you get your three ...
GMAT / GRE 'Work' Word Problem with a Twist
Переглядів 122Місяць тому
GMAT / GRE 'Work' Word Problem with a Twist
Complex Line Integrals and the Fundamental Theorem of Calculus
Переглядів 137Місяць тому
Complex Line Integrals and the Fundamental Theorem of Calculus
Integrating Complex Valued Functions of a Real Variable
Переглядів 297Місяць тому
Integrating Complex Valued Functions of a Real Variable
Finding the Harmonic Conjugates of a Complex Differentiable Function
Переглядів 216Місяць тому
Finding the Harmonic Conjugates of a Complex Differentiable Function
Three Questions on Complex Differentiation and the Cauchy-Riemann Equations
Переглядів 215Місяць тому
Three Questions on Complex Differentiation and the Cauchy-Riemann Equations
Differentiating Trigonometric Identities Cos z and Sin z for Complex z
Переглядів 220Місяць тому
Differentiating Trigonometric Identities Cos z and Sin z for Complex z
Investigating Trigonometric Identities with Complex Numbers
Переглядів 127Місяць тому
Investigating Trigonometric Identities with Complex Numbers
Understanding Complex Solutions of sin (θ) = a
Переглядів 2412 місяці тому
Understanding Complex Solutions of sin (θ) = a
Understanding Complex Solutions of cos (θ) = a
Переглядів 2982 місяці тому
Understanding Complex Solutions of cos (θ) = a
Finding all Real and Complex Solutions of a Trigonometric Equation
Переглядів 2652 місяці тому
Finding all Real and Complex Solutions of a Trigonometric Equation
Absorbing Markov Chains Solved with Transition and Solution Matrices
Переглядів 1702 місяці тому
Absorbing Markov Chains Solved with Transition and Solution Matrices
Absorbing Markov Chains, Total Probabilities and Recursion
Переглядів 2772 місяці тому
Absorbing Markov Chains, Total Probabilities and Recursion
Three Typical Questions on Green's Theorem
Переглядів 1802 місяці тому
Three Typical Questions on Green's Theorem
Three Methods to Find the Area of an Ellipse (and One Method that Doesn't Work)
Переглядів 2973 місяці тому
Three Methods to Find the Area of an Ellipse (and One Method that Doesn't Work)
Double Integrals using Polar Coordinates
Переглядів 2363 місяці тому
Double Integrals using Polar Coordinates
Fundamental Theorem of Calculus for Line Integrals of Conservative Vector Fields F(x,y,z)
Переглядів 2694 місяці тому
Fundamental Theorem of Calculus for Line Integrals of Conservative Vector Fields F(x,y,z)
Finding the Potential Function f(x,y,z) of a Conservative Vector Field F(x, y, z)
Переглядів 3874 місяці тому
Finding the Potential Function f(x,y,z) of a Conservative Vector Field F(x, y, z)
Test if a Vector Field is Conservative
Переглядів 2874 місяці тому
Test if a Vector Field is Conservative
Line Integrals With Respect to dx, dy, and dz
Переглядів 1,4 тис.4 місяці тому
Line Integrals With Respect to dx, dy, and dz
Scalar Line Integrals and 'Wire/Spring' Questions
Переглядів 3064 місяці тому
Scalar Line Integrals and 'Wire/Spring' Questions
Using a Scalar Line Integral to Find the Area of a Vertical Fence along a Curve
Переглядів 3424 місяці тому
Using a Scalar Line Integral to Find the Area of a Vertical Fence along a Curve
Using a Double Integral to Find the Average Value of a Function z=f(x,y) Over a Region
Переглядів 1934 місяці тому
Using a Double Integral to Find the Average Value of a Function z=f(x,y) Over a Region
Useful Trick To Solve 'Infinitely Many Solutions' to System of Equations Questions
Переглядів 1954 місяці тому
Useful Trick To Solve 'Infinitely Many Solutions' to System of Equations Questions
Determinant of the Adjoint of a Matrix
Переглядів 1434 місяці тому
Determinant of the Adjoint of a Matrix
Good to see you present two solutions.
Yes thanks - I try to whenever I can for comparison purposes..it certainly helps with maths understanding I find.
For more Gresty Academy 'One Minute Teasers' and 'Weekend Workouts' see our playlist 'Miscellaneous Shorts' ua-cam.com/play/PLlX3COjsHPVB9MwWLYpVV5cLbFmBUayZY.html
Im learning this as a 9th grader Im not even in eastern Asia
Great - hope its helpful!
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For more videos on the Lambert W Function check out our playlist 'Lambert W Function' at ua-cam.com/play/PLlX3COjsHPVApqLukQcbj2e9rDC5sRg_t.html
For more Gresty Academy 'One Minute Teasers' and 'Weekend Workouts' see our playlist 'Miscellaneous Shorts' ua-cam.com/play/PLlX3COjsHPVB9MwWLYpVV5cLbFmBUayZY.html
For more videos on the Lambert W Function check out our playlist 'Lambert W Function' at ua-cam.com/play/PLlX3COjsHPVApqLukQcbj2e9rDC5sRg_t.html
But we still haven't proved that 2 and 4 are the only sols. There might ecist some weird decimal number s.t. the equation holds. I believe the best way to prove this limit is by considering a sequence s.t.: a_0=√2 a_n+1=(√2)^a_n Then with careful analysis, we have to bound it from above by 2 and show that it is increasing therefore the lim a_n = 2 As n -->∞
Great point - thanks for the comment
For more Gresty Academy 'One Minute Teasers' and 'Weekend Workouts' see our playlist 'Miscellaneous Shorts' ua-cam.com/play/PLlX3COjsHPVB9MwWLYpVV5cLbFmBUayZY.html
For more videos on the Lambert W Function check out our playlist 'Lambert W Function' at ua-cam.com/play/PLlX3COjsHPVApqLukQcbj2e9rDC5sRg_t.html
Thank You 🙂🙂
You're welcome 😊 - if you found it useful check out our 'Counting Identical/Distinct Distributions' playlist at ua-cam.com/play/PLlX3COjsHPVCFZNiawIWvdC_kj56USiEc.html
D
Correct!
@@grestyacademy your video is brilliant mate
Thanks! Nice to hear...if you like these types of 'one minute' teasers check out our FaceBook page where we upload a new teaser every day - it's at facebook.com/gresty.academy/ . Our UA-cam Channel has hundreds of lengthier videos - check out our playlists at www.youtube.com/@grestyacademy/playlists to get an idea of the subjects we cover...Enjoy!
For more Gresty Academy 'One Minute Teasers' and 'Weekend Workouts' see our playlist 'Miscellaneous Shorts' ua-cam.com/play/PLlX3COjsHPVB9MwWLYpVV5cLbFmBUayZY.html
I have a question sir, if a function gives 2 results for one x, hox could it be a func.? W(-1/4) W₀ or W₁
Great question and in fact it isnt a function for precisely the reasons you state - so the W0 and W1 are considered as two separate branches (ie the red line and the blue line), both of which ARE functions..hope this clarifies
@@grestyacademy ok thanks for answer 👍🏻👍🏻
You are most welcome!
For more Gresty Academy 'One Minute Teasers' and 'Weekend Workouts' see our playlist 'Miscellaneous Shorts' ua-cam.com/play/PLlX3COjsHPVB9MwWLYpVV5cLbFmBUayZY.html
I came across an equation. ln(x)=Wln5 Then x=ln5÷Wln5 x=1•609÷W(ln5) Then x=2•1293 Now for x to be equal to 2•1293, the value of W(ln5) has to be •7556 Could you please tell me how W(ln5) equals •7556
Hi there - starting with xe^x = a for some constant 'a' then by definition x=W(a) and so also by definition W(a)e^W(a)=a --- basically W(a) is simply the value of 'x' which solves xe^x = a. So given that 0e^0=0 and 0.5e^0.5~0.824 and 1e^1~2.71 and 2e^2~15 and 3e^3~60 (give or take) then W(0) = 0 and W(0.824)~0.5 and W(2.71)~1 and W(15)~2 and W(60)~3. Now ln(5)~1.61 (from a calculator) so W(ln 5)= W(~1.61)~0.75 interpolating between the values we can calculate easily W(0.824) and W(2.71). Hope this clarifies. Incidentally, letting y=ln(x) in your equation (to make the explanation easier) we have y=W(ln5) so from the definition ye^y=ln(5), ie ln(x)e^(lnx)=ln(5) and as e^lnx=x we have xln(x)=ln(5) ie ln(x^x)=ln5 ie x^x = 5 so the solution 'x' to the power of itself is 5 :)
For more Gresty Academy 'One Minute Teasers' and 'Weekend Workouts' see our playlist 'Miscellaneous Shorts' ua-cam.com/play/PLlX3COjsHPVB9MwWLYpVV5cLbFmBUayZY.html
Important Note: At 1:10 the author should have said "and you get your three consecutive heads in three throws" rather than "and you get your three consecutive heads". Then at 1:33 in the equation for 'E' the author erroneously omits to add "+1/8 x 3" at the end which is the probability of getting three heads in the first three throws. However in the line after at 1:44 he corrects this adding the "+3" at the end and from then on everything is correct.
For more videos on Markov Chains, check out the Gresty Academy playlist 'Markov Chains' at ua-cam.com/play/PLlX3COjsHPVDkTC3MENgdITlfCnKy3fxK.html
For more Gresty Academy 'One Minute Teasers' and 'Weekend Workouts' see our playlist 'Miscellaneous Shorts' ua-cam.com/play/PLlX3COjsHPVB9MwWLYpVV5cLbFmBUayZY.html
I did it using method 1 ..
Nice - thanks for the feedback!
if you had to calculate W(5) by hand; how would you go about it?
Hi there - interesting question. There are lots of online calculators around but if you consider 'excel' calculating by hand you could 'build' a Lambert W function calculator into that - for real 'hand' method I would suggest Newton Raphson iteration. Good luck!
@@grestyacademy in my mind's eye I can see how to undo multiplication by way of division: I can see how to square root a square . . . but what is happening when I w(5)? are you saying that it can't be done by hand? if it can't be done by hand then are you sure it's real? I can just graph it on Desmos and just ''tap'' the answer: however, what would they do before calculators? Imagin telling a machinist to cut something to a length of W(5)? or perhaps each point of datum is just a reflection across the line x=y and therefore there is no process?
Hi there, I am not saying it can't be done by hand - it can. Personally I consider it similar to logarithms in that they can be calculated without calculators (via log tables in previous times) but normally they don't need to be. So W(5) is just as real as log (5). W(5) = 1.3267 (approx) and all that means is that 1.3267 is the solution to xe^x = 5. So one way of doing it by hand would be to put random values of x into xe^x and then narrow them down (a basic Newton Raphson). So for example to find w(5) we could put x=1 into xe^x and that gives us 'e' (2.71 approx) so lets put x=2 and that gives us 2e^2 (14.7 approx) - so we know w(5) is between 1 and 2, so lets try 1.5 which gives us 1.5e^1.5 = 6.72 approx so we know w(5) is between 1 and 1.5 etc etc. So yes a machinist asked to cut something to length w(5) could (without a calculator) look up the value in a 'lambert W function table' (similar to a log table) and get the measurement 1.3267. Hope this helps
@@grestyacademy . . . let's try these two: if someone were to ask me ''what is the sine of 89.99999999 degrees?'', I would say to them "I don't know, but it must be close to one"; if theta is less than 10 degrees and I know the length of the Tangent line then I know that I can just use its length as an approx for the sine function, yet I would not swap them if the theta was 80 degrees. I can have these thoughts because I know what is really going on --the why of it--, yet if someone were to ask me in earnest ''what is W(5) approx?'', my thoughts would be empty. like the log tables sometimes one must play collect the dots until a wiggle graph appears, and hope that the wiggle can be reflected across the line x=y. thanks for the help.
Hi there I get your point. For me in a similar way that I can estimate in my head that log (to base 10) of 50 for example is somewhere slightly north of 1.5 because I know that log 10=1 and log 100 = 2, I can approximate W(50) for example in my head to somewhere in the region of 2.75 (its actually 2.86) because I know that w(e)=1 (e~2.71) and w(2e^2)=2 (2e^2~2*2.71*2,71~15 give or take)and w(3e^3)=3 (3e^3~3*2.71*2,71*2.71~ 60 give or take) etc ...so very very roughly as pointers w(2.71)~1 and w(15)~2 and w(60)~3...From that I can estimate that w(10)~1.75 , w(30)~2.4 etc etc which are not that far from their true values. Hope this helps
For more Gresty Academy 'One Minute Teasers' and 'Weekend Workouts' see our playlist 'Miscellaneous Shorts' ua-cam.com/play/PLlX3COjsHPVB9MwWLYpVV5cLbFmBUayZY.html
Is he confusing equations, functions and relations?
Hi there - if you think there is an error in the video feel free to detail the error, what it should say, and the time in the video the error occurred (ie at 5:35 or whatever). We check all our videos before publishing but there is always a possibility an error has somehow found its way through undetected. Thanks
Thanks 🎉
You are welcome!
For more Gresty Academy 'One Minute Teasers' and 'Weekend Workouts' see our playlist 'Miscellaneous Shorts' ua-cam.com/play/PLlX3COjsHPVB9MwWLYpVV5cLbFmBUayZY.html
For more Gresty Academy 'One Minute Maths Teasers' see our playlist 'Miscellaneous Shorts' ua-cam.com/play/PLlX3COjsHPVB9MwWLYpVV5cLbFmBUayZY.html
For more Gresty Academy 'One Minute Maths Teasers' see our playlist 'Miscellaneous Shorts' ua-cam.com/play/PLlX3COjsHPVB9MwWLYpVV5cLbFmBUayZY.html
Thanks a lot, this video really helped me out with interview prep
Nice to hear - thanks for the feedback and good luck! Note that there is a 'Part Two' to this video, entitled 'Absorbing Markov Chains Solved with Transition and Solution Matrices', which can be found at ua-cam.com/video/WxCBILZt_0U/v-deo.html
For more questions on GMAT/GRE check out the Gresty Academy playlist 'GMAT/GRE' at ua-cam.com/play/PLlX3COjsHPVBiCQNutKiU0bsPynBHJBca.html
For more on calculus of complex numbers see our playlist 'Calculus of Complex Numbers' at ua-cam.com/play/PLlX3COjsHPVC3950F2WhgxDR0-nyloONJ.html
For more Gresty Academy 'One Minute Maths Teasers' see our playlist 'Miscellaneous Shorts' ua-cam.com/play/PLlX3COjsHPVB9MwWLYpVV5cLbFmBUayZY.html
For more on calculus of complex numbers see our playlist 'Calculus of Complex Numbers' at ua-cam.com/play/PLlX3COjsHPVC3950F2WhgxDR0-nyloONJ.html
For more Gresty Academy 'One Minute Maths Teasers' see our playlist 'Miscellaneous Shorts' ua-cam.com/play/PLlX3COjsHPVB9MwWLYpVV5cLbFmBUayZY.html
For those who desire a clue - think 'Maths meets English'!😎
Jesus...
😂🙃
La fonction de LAMERT résosud bon nombre d'équations en matémathiques et sciences physiques Exemple : x^4 = 4.x. Equation facile. Equation plus compliquée : 4^x = 4.x. Non facile à résoudre. Utilser la fonction de 'LAMBERT W' dans ce cas.
Hi - we have a video on that - check it out at ua-cam.com/video/DgU_hK3e_Pg/v-deo.html (entitled 'How to Solve 3^x = 2x + 2')
For more on calculus of complex numbers see our playlist 'Calculus of Complex Numbers' at ua-cam.com/play/PLlX3COjsHPVC3950F2WhgxDR0-nyloONJ.html
For more on calculus of complex numbers see our playlist 'Calculus of Complex Numbers' at ua-cam.com/play/PLlX3COjsHPVC3950F2WhgxDR0-nyloONJ.html
For more on calculus of complex numbers see our playlist 'Calculus of Complex Numbers' at ua-cam.com/play/PLlX3COjsHPVC3950F2WhgxDR0-nyloONJ.html
For more videos on complex numbers check out the Gresty Academy playlist 'Complex Numbers' at ua-cam.com/play/PLlX3COjsHPVC9MnNSwdVOfFk6zALYYEAm.html
For more Gresty Academy 'One Minute Maths Teasers' see our playlist 'Miscellaneous Shorts' ua-cam.com/play/PLlX3COjsHPVB9MwWLYpVV5cLbFmBUayZY.html
thank you very much!
You are most welcome! Thanks for the support😎 We have an entire playlist covering the various question types at ua-cam.com/play/PLlX3COjsHPVCFZNiawIWvdC_kj56USiEc.html - enjoy!
For more Gresty Academy 'One Minute Maths Teasers' see our playlist 'Miscellaneous Shorts' ua-cam.com/play/PLlX3COjsHPVB9MwWLYpVV5cLbFmBUayZY.html
You ignore the convention that anything other than base 10 should be explicitly indicated, and 2 + 2 makes no sense in base 2.
It's a one minute teaser - just a bit of fun. We all know 2+2 only equals 4 in base 10
The video doesn't mention base 2
For more Gresty Academy 'One Minute Maths Teasers' see our playlist 'Miscellaneous Shorts' ua-cam.com/play/PLlX3COjsHPVB9MwWLYpVV5cLbFmBUayZY.html
For more Gresty Academy 'One Minute Maths Teasers' see our playlist 'Miscellaneous Shorts' ua-cam.com/play/PLlX3COjsHPVB9MwWLYpVV5cLbFmBUayZY.html
For more Gresty Academy 'One Minute Maths Teasers' see our playlist 'Miscellaneous Shorts' ua-cam.com/play/PLlX3COjsHPVB9MwWLYpVV5cLbFmBUayZY.html
For more Gresty Academy 'One Minute Maths Teasers' see our playlist 'Miscellaneous Shorts' ua-cam.com/play/PLlX3COjsHPVB9MwWLYpVV5cLbFmBUayZY.html
For more Gresty Academy 'One Minute Maths Teasers' see our playlist 'Miscellaneous Shorts' ua-cam.com/play/PLlX3COjsHPVB9MwWLYpVV5cLbFmBUayZY.html