18.100B Real Analysis
18.100B Real Analysis (Spring 2025, MIT OCW). Instructor: Prof. Tobias Holck Colding. This course gives an introduction to analysis, and the goal is twofold:
1. To learn how to prove mathematical theorems in analysis and how to write proofs.
2. To prove theorems in calculus in a rigorous way.
The course will start with real numbers, limits, convergence, series and continuity. We will continue on with metric spaces, differentiation and Riemann integrals. After that, we will move on to differential equations.
(from ocw.mit.edu)
| Lecture 15 - Derivatives; Laws of Differentiation |
We define what it means for a function to be differentiable. We show that if a function is differentiable at a point, then it is also continuous. We then establish the basic algebraic laws for differentiation. Those include Leibniz's rule, the quotient rule, and the chain rule. Once we have that, we prove Rolle’s lemma and use it to show the mean value theorem.
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