Mathematics causes problems but it is also very beautiful when you eventually understand it. With this channel, I want to show the bright side of mathematics and help you to understand it.
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Hello, In Papa Rudin, the basic definition of a measurable mapping is that of a function from a measurable space to a topological space. But he also says somewhere else that sometimes, measures can happen in spaces without topology. Does that mean that the definition you gave in this video is more general?
Well, I think it is very crucial for using motivating applications to build intuition before abstracting things away and once mastered so some degree, see how powerful the mathematics is in context.
Hello ! You Said that the set U ( set of all cos( k * x ) , sin( k *x) ) is linearly independant and that s not hard to show buuuut it’s seem kinda hard for me ^^ we need to show that if the linear combination of all elements is 0 that implies that all coefficient are 0. I tried evaluating the linear combination at different point but we have series here and infinately many coefficient ^^. Can you give me a hint pls ? :) Ty for reading and GREAT VIDEOS !!
Thank you sir for this wonderful lecture but i did not understand why the limit is SupM and also in case of (1+1/n)^n the limit is e how do we now this by conv. Criteria
What a nice introduction! It would be nice to have the sections you've explained at the beginning of the course in order to have a picture (like a book). Really useful video to order ideas and to summarize the course.
15:50 Lebesgue measure extends the two properties of volume and translation to arbitrary subsets. The power set cannot be chosen as the sigma-algebra for the Lebesgue measure, rather a smaller one is chosen, called the Borel sigma-algebra.
Hi sir I found a printing mistake in your real analysis book that is available on your website. on page no. 17 when you proved third statement i found there is written "Due to b>0" but it is always not possible. there should be |b|>0 that is also mentioned in below. this book is really has a good content for beginners.
10:55 Does the fact that surjective functions have a right inverse depend on the axiom of choice? To construct such a right inverse, we need to be able to choose an element from the preimage of f for every element in its codomain
never thought before of using pithagoras' theorem for splitting the orthogonal components. PS: in oncoming videos could you explain how the Fourier Transform and Fourier Series on closed intervals are related through Abel's summation formula?
It makes a lot of sense too because, by the definition we saw in a previous video, for a function f: A → B, f(x) = y and f(x) = ỹ means that y = ỹ, because you cannot have an x which maps to two different y. Likewise, the other way around, you have to have exactly one arrow, you cannot have more. I know that's probably common sense but I felt good coming onto that realization (boy will I be embarrassed if this is wrong), so yeah :)
In part a) the exp should contain C hence it becomes e^(t +C) which can be seperated as K.e^t. Otherwise if you substitute the initial value conditions K=x_0-1?
Absolut geniales Material! Hältst du dich bei diesem Kurs an eine bestimmte Literatur mit übereinstimmenden Definitionen, welche man als Hintergrund verwenden könnte?
When we talking about differentiability it is easy to under this is defined on an open interval because in the definition of derivative f(x+h) defined for only interior point but why we use closed interval in tge continuity definition. Same problem occour here also?
Please, as you know the matrix multiplied by x, gives us b, is a set of linear equations. Question 1: Do we mean that the matrix is injective or surjective? Or linear equations crystallized into functions? . Question 2: For example, a matrix consists of linear equations defined as functions. One of these functions is surjective, and the other is injective, meaning it is mixed. How do we distinguish the type of matrix in light of that? Thank you very much for your wonderful effort.
