Explore >> Select a destination
|
You are here 
|
math.andrej.com | ||
| | | | |
mathscholar.org
|
|
| | | | | [AI summary] The text presents a detailed, self-contained proof of the Fundamental Theorem of Calculus (FTC) using basic principles of calculus and real analysis. It breaks the proof into two parts: Part 1 establishes that the integral of a continuous function defines a differentiable function whose derivative is the original function, and Part 2 shows that the definite integral of a continuous function can be computed as the difference of an antiderivative evaluated at the endpoints. The proof relies on lemmas about continuity, differentiability, and the properties of integrals, avoiding advanced techniques. The text is structured to provide a clear, step-by-step derivation of the FTC for readers familiar with calculus fundamentals. | |
| | | | |
xorshammer.com
|
|
| | | | | Nonstandard Analysis is usually used to introduce infinitesimals into the real numbers in an attempt to make arguments in analysis more intuitive. The idea is that you construct a superset $latex \mathbb{R}^*$ which contains the reals and also some infinitesimals, prove that some statement holds of $latex \mathbb{R}^*$, and then use a general "transfer principle"... | |
| | | | |
mathenchant.wordpress.com
|
|
| | | | | There are mathematical operations of all kinds with the property that doing the operation twice is tantamount to not doing anything at all. Such operations are called involutions, and you can find them all over the place in math: taking the negative of a number, taking the reciprocal of a number, rotating an object by... | |
| | | | |
fourdeeroak.wordpress.com
|
|
| | | There is pleasure in the pathless woods, there is rapture in the lonely shore, there is society where none intrudes, by the deep sea, and music in its roar; I love not Man the less, but Nature more. ~Byron | ||
