November 13, 2008

These Single Variable Calculus lecture notes cover:

- The Two Fundamental Theorems of Calculus: Statement and explanation of the First and Second Fundamental Theorems, with examples.
- The Second Fundamental Theorem: Continuous Functions Have Antiderivatives: Explanation of the implications and applications of the Second Fundamental Theorem, including an example.
- Defining New Functions: Using the Second Fundamental Theorem to define the natural logarithm function and the error function, including diagrams and examples.
- Proof of the Two Fundamental Theorems: An intuitive argument justifying the Second Fundamental Theorem and a complete proof of the First Fundamental Theorem, inluding remarks about these theorems as they relate to definite and indefinite integrals.

Course: 18.01 Single Variable Calculus, Fall 2006

Instructor: Prof. David Jerison

Prof. David Jerison, 18.01 Single Variable Calculus, Fall 2006. (Massachusetts Institute of Technology: MIT OpenCourseWare), http://ocw.mit.edu (Accessed October 28, 2008). License: Creative Commons BY-NC-SA

http://ocw.mit.edu/OcwWeb/web/terms/terms/index.htm#cc http://creativecommons.org/licenses/by-nc-sa/3.0/us/legalcode

- Mathematics > General
- Mathematics > Calculus

- Grade 9
- Grade 10
- Grade 11
- Grade 12