When learning about the Fundamental Theorem of Calculus, I used mostly Inductive Learning, but a little of Deductive Learning. By looking at the theorem alone, I didn't understand it much and I didn't really know how to use it. However, after playing around with the theorem and using it to answer a few problems in the book, I grasped the concept to the point where I believe I understand it. I think the Fundamental Theorem of Calculus is fundamental because it connects the use of integrals and differentiation, and by doing so opens up more possibilities that I probably don't know about yet. In my mind, this theorem means basically that it's possible to find integrals and derivatives in a way that I wouldn't normally be able to find them, but it will probably mean more to me once I use it more. To me, it implies that all that we learned and all that we will learn will be connected in some way. Knowing this, or even just thinking about this, it's interesting and also scary. Both integrals and differentiation are mildly difficult things alone. Putting them together make them even harder, and if this theorem is put with something else we will learn later I can't imagine how hard it will be to use.
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February 2015
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