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slcmath@pc
Canada
Приєднався 7 вер 2013
Visit my course web page to download for free course packs about a variety of courses. The course packs contain PDF transcripts of the videos, exercise sheets to allow you to test your understanding by solving a large number of problems of varying complexity, and class notes ranging from minimal for some courses to extremely detailed for others. I hope that this material allows you to gain a deeper understanding and appreciation of certain advanced topics in mathematics. Cheers!
Proof of the Technique of U-Substitution: - 2/3
Course Web Page: sites.google.com/view/slcmathpc/home
CORRECTION: At 8:20, I of course meant to write u_n=g(b), but instead mistakenly wrote u_n=b.
CORRECTION: At 8:20, I of course meant to write u_n=g(b), but instead mistakenly wrote u_n=b.
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Відео
Proof of the Technique of U-Substitution: - 3/3
Переглядів 1178 місяців тому
Course Web Page: sites.google.com/view/slcmathpc/home
Proof of the Technique of U-Substitution: - 1/3
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Course Web Page: sites.google.com/view/slcmathpc/home
Differentials and Explicit Error Bound
Переглядів 768 місяців тому
Course Web Page: sites.google.com/view/slcmathpc/home
Complex Numbers & Special Trigonometric Integrals - Part 4/4
Переглядів 5992 роки тому
Course Web Page: sites.google.com/view/slcmathpc/home This is part 4 of 4 of an application of Euler's identity where our objective is to find the exact value of a class of real trigonometric integrals.
Complex Numbers & Special Trigonometric Integrals - Part 3/4
Переглядів 2452 роки тому
Course Web Page: sites.google.com/view/slcmathpc/home This is part 3 of 4 of an application of Euler's identity where our objective is to find the exact value of a class of real trigonometric integrals.
Complex Numbers & Special Trigonometric Integrals - Part 2/4
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Course Web Page: sites.google.com/view/slcmathpc/home This is part 2 of 4 of an application of Euler's identity where our objective is to find the exact value of a class of real trigonometric integrals.
Complex Numbers & Special Trigonometric Integrals - Part 1/4
Переглядів 2752 роки тому
Course Web Page: sites.google.com/view/slcmathpc/home This is part 1 of 4 of an application of Euler's identity where our objective is to find the exact value of a class of real trigonometric integrals.
Complex Numbers & the Exact Value of Two Famous Infinite Series - Part 6/6
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Course Web Page: sites.google.com/view/slcmathpc/home This is part 6 of 6 of an application of Euler's identity where our objective is to find the exact value of two classic infinite trigonometric series. For complete technical details about the limit, check out problem 5 of the following document: drive.google.com/file/d/11pF7wzcSDN1GNO521qdKCrRQA_i2qApk/view?usp=sharing
Complex Numbers & the Exact Value of Two Famous Infinite Series - Part 5/6
Переглядів 1252 роки тому
Course Web Page: sites.google.com/view/slcmathpc/home This is part 5 of 6 of an application of Euler's identity where our objective is to find the exact value of two classic infinite trigonometric series. For complete details on integration and differentiation of power series, check out the following document: drive.google.com/file/d/11qj77w_KyhJSbiLO3WUcrhAkTsNnbpyJ/view?usp=sharing For fundam...
Complex Numbers & the Exact Value of Two Famous Infinite Series - Part 4/6
Переглядів 1162 роки тому
Course Web Page: sites.google.com/view/slcmathpc/home This is part 4 of 6 of an application of Euler's identity where our objective is to find the exact value of two classic infinite trigonometric series. For a complete proof of Dirichlet's test, check out problems 1 and 3 of the following document: drive.google.com/file/d/11pF7wzcSDN1GNO521qdKCrRQA_i2qApk/view?usp=sharing
Complex Numbers & the Exact Value of Two Famous Infinite Series - Part 3/6
Переглядів 1252 роки тому
Course Web Page: sites.google.com/view/slcmathpc/home This is part 3 of 6 of an application of Euler's identity where our objective is to find the exact value of two classic infinite trigonometric series.
Complex Numbers & the Exact Value of Two Famous Infinite Series - Part 2/6
Переглядів 1332 роки тому
Course Web Page: sites.google.com/view/slcmathpc/home This is part 2 of 6 of an application of Euler's identity where our objective is to find the exact value of two classic infinite trigonometric series.
Complex Numbers & the Exact Value of Two Famous Infinite Series - Part 1/6
Переглядів 1722 роки тому
Course Web Page: sites.google.com/view/slcmathpc/home This is part 1 of 6 of an application of Euler's identity where our objective is to find the exact value of two classic infinite trigonometric series.
The Definition of the Derivative - Slick Solution 6
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Course Web Page: sites.google.com/view/slcmathpc/home This is an example of how to find the derivative of a function from the definition while doing as little algebraic manipulation as possible, hence the use of the term "slick". The goal is to factor a multiple of Δx from Δy by doing as little work as possible.
The Definition of the Derivative - Slick Solution 5
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The Definition of the Derivative - Slick Solution 5
The Definition of the Derivative - Slick Solution 4
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The Definition of the Derivative - Slick Solution 4
The Definition of the Derivative - Slick Solution 3
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The Definition of the Derivative - Slick Solution 3
The Definition of the Derivative - Slick Solution 2
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The Definition of the Derivative - Slick Solution 2
The Definition of the Derivative - Slick Solution 1
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The Definition of the Derivative - Slick Solution 1
Deriving Summation Formulas for the Sum of Consecutive Powers - Part 4 (k ≥ 3)
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Deriving Summation Formulas for the Sum of Consecutive Powers - Part 4 (k ≥ 3)
Deriving Summation Formulas for the Sum of Consecutive Powers - Part 3 (k=2)
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Deriving Summation Formulas for the Sum of Consecutive Powers - Part 3 (k=2)
Deriving Summation Formulas for the Sum of Consecutive Powers - Part 2 (k=1)
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Deriving Summation Formulas for the Sum of Consecutive Powers - Part 2 (k=1)
Deriving Summation Formulas for the Sum of Consecutive Powers - Part 1 (k=0)
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Deriving Summation Formulas for the Sum of Consecutive Powers - Part 1 (k=0)
NYB_13_3_b - A Rigorous Proof of the General Formula for the Area of an Ellipse
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NYB_13_3_b - A Rigorous Proof of the General Formula for the Area of an Ellipse
Such a clear derivation. Realy amazing.
I can t hear you
thank you dear sir for this demonstration. It helped me review my studies. Have a great day.
Thanks Man for the great proof! minor correction at 1:20 (you wrote + said (AB) is a P x M matrix. I think you meant (AB)^T is a P x M matrix. (It's still definitely clear what you mean btw)
you said cube root of negative is negative so why did you write x not -x
Because x is negative. ;-)
Where did you get those figures 7,10,15 and 22 because when I square matrix a Am getting those figures
Excellent!! From Nigeria, thank you.
bro does not get enough credit
Me the question is not stated befor sloving how i meant going to understand
Very clear and well explained Thank you very much🙏
Amazing. Helped me with my Uni assignment. Much love.
Well explanation
Ya bro, it was really nice to understand this basic problem. Thank you so much to describe this in easy and brief manner. Just keep it up.😊
Thanks for the simplification
I am starting to hate school especially when math is included
Explained a 3hr lecture in less than 1hr
Thank you so much for such a detailed and easy-to-follow explanation!
This is the first time I understood this thank you, it’s been 2 months since my professor taught it.
in final step, is the tangent line slope calculation mean to say f(x)dx /g(x) dx evaluated at c (not the derivatives) thank you
It is indeed f'(x)dx/g'(x)dx evaluated at x=c.
What if you have x and x squared in the equations? If you define x squared to be... lets say... "a", then the non-squared x turns into a square root and it's still non-linear?
Not every non-linear system can be effectively turned into a linear one; it only works for "slightly non-linear" systems. Of course, in your example, you could let a=x and b=x^2, and if the system can then become linear, you can solve it, but at the end, you would have to check that the values of a and b obtained are consistent with the fact that b=a^2.
@@slcmathpc Thank you for the feedback, my example system is: (1) x²+y²=125 and (2) x+y=15... we can already see that it's {x=10,y=5} and vice versa. But I fail to find a nice way to turn it into a linear system, even tho the answer already seems so obvious/simple. My best hope was: let a=a+y, b=xy and take the binomial form of (1) which is (3) (x+y)²-2xy. Then we will have as a result: a²-2b=125 and a=15 and if you solve that you get {a=15, b=50} which is correct since a=x+y=10+5=15 and b=x*y=10*5=50. Still not linearly solvable... maybe it's an example of a non-slightly non-linear system? Lol
Great explanation. Thanks
Real Goat
this video was gonna make me question the things i know about this topic, I don't recommend this video
Hi, My understanding for series to diverge is when "nth divergence test" must also meet this criteria lim n→∞ aₙ = lim n→∞+1 aₙ ......= lim n→∞+∞ aₙ ≠ 0 else they would either Diverge (don't summed up to a real number) or Undefined (if all summed up to zero and infinitely repeating). Example for aₙ terms that are lim n→∞ (-1)^n or lim n→∞ sin(n) is Undefined. And for your case above lim n→∞ |aₙ| = ∞ ⇒ lim n→∞ aₙ ≠ 0 it may not meet lim n→∞ aₙ = lim n→∞+1 aₙ because lim n→∞ aₙ and n→∞+1 aₙ could also be +- aside from ++ or -- according to the ratio test |aₙ₊₁/aₙ| > 1. It Diverge only because the terms didn't summed up to zero. What do you think sir?
Ten/ten video, helps out a ton! Props for putting in the work to make this video's explanation perfectly comprehensible.
thanks
i was like WTF ?!? when i saw she is a male then i realized that he said we should correct it with "person" lol
but after a 10 years , thanks a lot ! you made me understand this topic which other 5 videos failed to do :D
thank you boss
Thanks very good example👍💖💚
A great video!
Did somebody call my name?
Appreciate you g
Great vid
absolute legend
Nice content, was a great refresher for me!
best vedio on this topic
flawless vid
I found your derivation to be very helpful.....but I have just one question..... The graph a displacemnt-time graph right?
Yes, you should think of f(t) as the position of an object moving in a linear fashion as a function of time. :-)
So that means the position of the object is in a continuous function of time.....like for example for a free falling body changing its postion or accelerating uniformly in the influence of gravity.....with change in time.....
Yep, those are valid examples!
Thank u:-)
Thank you prof for the wonderful explanation. I study in Stanford; according to people our faculties are world class. However, I could not understand 1/10th of what I understood here.
Very good. Thanks
I know that he said that finding the generic formula for i^k is supposed to be an exercise, but I have gotten stuck at (n+1)sum((2i-1)^(k/2)) - sum(i(2i-1)^(k/2)), so what is it? I haven't been able to find anything online so far
The idea that I have presented in these videos only allows one to find the summation formula for i^k recursively, so you can find that of i^3, then i^4, then i^5, and so on, but you cannot jump to say i^20, without first finding the formula for all of the powers lower than 20. Hope this clarifies things. :-)
God I swear this helped me understand the concept better thanks so much.
Thanks sir
Thanks a lot. You explained ALL tests for convergence flawlessly and clearly.
Man, that was a crystal clear explanation. My respect!
wait did the accent start from indian turn to british to american?
Thank you so much
Thank you for this lesson. I am grateful
what is the name of this method
Helpful. Thanks.