شرح دروس الرياضيات بالمجان شرح ماهو خط مماس أو خط الظل Tangent lines

Ahmad

الثلاثاء، 9 أكتوبر 2012

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هل ترغب في تعلم الرياضيات بسهولة؟ هل تجد صعوبة في فهم دروس الرياضيات في المدرسة؟ هل تجد شرح وتفسير المعلم مملا وغامضا وغير مفهوم في فهم دروس ودورات الرياضيات؟ إن كانت هذه هي مشاكلك وصعوباتك في الرياضيات سوف يفيدك هذا الفيديو, مجموعة من الدروس المجانية في تعلم الجبر والهندسة وحساب التفاضل والتكامل والمعادلات والدالات بأنواعها, سوف نقدم لك كل ما تحتاجه لاجتياز اختبارات الرياضيات في الباكالوريا والجامعة, لطلبة علوم الرياضيات والعلوم الأخرى المختلفة, كما سوف نشاهد دروس تعليم تقنيات حساب الأعداد الجمع الضرب الطرح والقسم الذهني, سوف تحسب مثل آلة حاسبة بسهولة دون تفكير. What happens to a polynumber when you translate it? For instance p[8,-5,4,-1] turns into p[6,3,6,-1] if you go from base alpha to say base alpha -1. Are these polynumbers still the same though they consist of different series of numbers? Or in other words, does is a polynumber not just defined by its list of numbers bur also bij the base we use? Does that Isn't p more like a vector than like a number? CorFortgens 8 months ago Hi, When we translate, we get a different polynumber. Two polynumbers are the same precisely when all their coefficients are the same. njwildberger in reply to CorFortgens 8 months ago So (x-1)^2+4(x-1)+4 and x^2+2x+1 are the same polynomials (they evaluate tot the same number), but they are 2 different polynumbers 1,4,4 and 1,2,1 since x or x-1 are just place holders. CorFortgens in reply to njwildberger 8 months ago Strictly speaking we do not have a polynomial until we have expanded/simplified into standard alpha form. So the first expression is not a polynomial, rather I would say it is a polynomial expression: something that can be evaluated to a polynomial. And technically I use alpha not x. njwildberger in reply to CorFortgens 8 months ago Thank you very much. Two minor questions. One. Aren't the Taylor series ausually being associated with expanding functions into infinite series Two: you did mention that the usual Taylor series has powers of the derivatives. What powers did you mean? CorFortgens in reply to njwildberger 8 months ago Hi, Yes often Taylor series are applied to ``infinite series" (whatever they might be!) but they apply also to polynomials, where the ideas are the same and the results also useful. I refer by powers of the derivative to mean: take the derivative of the derivative of the derivative---that is usually called the third power of the derivative, often denoted D^3. njwildberger in reply to CorFortgens 8 months ago see all All Comments (17) Sam Kamal Respond to this video... Well in a later video he does state exactly my intuition that I stated wrong earlier. The nth sub-derivative is not the nth derivative but the derivative of the prior (n-1th) derivative, divided by n. Doing the arithmetic in my head I merely thought "derivative" since that is what I was doing in my head, just on the D_(n-1) polynomial. But I think you are right, because that one will be a derivative of the derivative, etc. of the original polynomial, divided by the nth, (n-1)th, etc. value: n! Bryan Goodrich in reply to JPaulDiLucci (Show the comment) 3 months ago Darkwolf, I think the nth sub-derivative is the nth derivative divided by n! (that is, divided by n-factorial) JPaulDiLucci in reply to Bryan Goodrich (Show the comment) 3 months ago I haven't seen you discuss it yet, even though you mentioned the derivative, if I recall correctly, a scalar multiple of the sub derivative. I haven't worked out the general case yet, but (1) the examples you used the nth sub-derivative was the nth derivative divided by n. Is this true generally or is there a way to express that scalar generally? Furthermore, you expressed the Pascal array in binomial coefficients a video or two ago. Is there a general summation expression of p using this coef? This video introduces tangent lines and tangents conics of polynomials, using the very simple high school approach through polynumbers and bipolynumbers. We first define constant, linear, quadratic, cubic, quartic and quintic polynumbers in terms of the degree. Then we make some subtle shifts in the Taylor bipolynumber to find the Taylor expansion of a polynomial at a point c, and then using that to define the 1st tangent, 2nd tangent and so on. We will see how these are useful in computing approximations to the values of a polynomial. This lecture is part of the MathFoundations series, which tries to lay out proper foundations for mathematics, and will not shy away from discussing the serious logical difficulties entwined in modern pure mathematics. The full playlist is at http://www.youtube.com/playlist?list=PL5A714C94D40392AB&feature=view_all