I just made a video interviewing students on your campus! You should check it out!

(fyi...I graduated from UMKC this past May)

Your a great channel, keep it up.

Some comments on Calculus 24, and for the benefit of us all, anyone can read it here. We use the power rule, as an example of a hopefully simplier thinking. We do not take into consideration the "+C".

Differentiation is a SPLIT. One entity becomes two. It is easy to do, you go forwards in time, you get what you get, from a fixed raw-material, and by a fixed manipulation-formula (for example the power-rule: "you bring the power down, and you subtract 1 from it").

Rules simplified for derivation: 1. memorize power, 2. multiply coefficient with number memorized, and write result as new coefficient, 3. subtract 1 from number memorized, and seat it back to the top, as new power
i think IT IS EASIER TO BACKFLIP THIS, WRITTEN IN THIS FORM.

Backwards-differentiation (indefinite integration) is not so simple. Since the method is fixed, and must be played in reverse on a fixed end-result of a differentiation. IE. which is already there, but where did it come from....? Just like in communism, where they said: "comrades, only the future is certain!!" The starting point is blurred.

Rules simplified for backwards-derivation (indefinite integration):
1. the thing seated on the top (the power), had 1 subtracted from it - add 1, and you get a magic number, which wreaked havoc down below
2. the coefficient that you see, had ALREADY BEEN MULTIPLIED by the certain "magic number" - divide coeff by the magic number, and by this, you got an alignment..


Backwards-differentiation is a MERGE. Two entities become one. And to be able to perform it, we need a certain constellation. The coefficient ascends to the power, and once there, it merges with it, leaving only a "1" behind. The problem is, you dont always got the perfect case: coefficient = power+1.
If we have, say X^54, we cant just initiate a merge. Because the constellation means, we would need a 55*(X^54).

But we only have 1*(X^54). Important: What we can do, is BOUND BY THE METHOD, that we are trying to undo. The coeff is the soft part. It adopts. The power is more stubborn here. You cant say, lets make power = 0. Thus, coefficient can = power+1. NO-GO. And, more trouble, the power must be (the current power, +1). This is step1of2. Resupplying that "1", that had been taken away. Programmers would say: power = power+1. Thats what you start with. Here, we figure it out, that the merging point will be at power=55. This is our magic number right now. In which we merge. Once this is done, the coeff can start its ASCENSION, and it WILL LEAVE BEHIND A 1/magic numberTH PART of itself (as a new coeff). Here comes "wishful thinking", saying, that, that "1" IS ALREADY "magic number" UNITS of something. This is step2of2. This, in the language of mathematics is: 1 = 55units. What is a "unit"? It is 1/55. That will be the new coefficient.
And new the power already taken care of in step1.

Addendum. Here, we can manipulate the coefficient freely, we dont have to deal with measurement units. For ex. if we got meters, liters, watts, etc.. We would be in some deep trouble.. But we only work with plain numbers. They can be twisted, as long as the mathematician does not violate the laws of algebra, and the laws of whatever method e is working with.

Nice videos

Thanks for calculus 1 lectures, where are the calculus 2 lectures?

Looking forward to checking out more of your uploads!

Feel free to subscribe to the Edutopia channel, updated weekly, for more information for educators.