These Single Variable Calculus lecture notes cover:
- The Problem of Areas: Riemann integrals are introduced as a concept using the example of finding the area of a circle from the areas of N-sided polygons inscribed in the circle. Signed area (positive above the x-axis, negative below) is introduced.
- Partitions: Interval partitions are defined, including the concepts of mesh size and fine vs. coarse partitions.
- Riemann Sums: Definition, including a discussion of partition choices when computing these sums.
- The Riemann Integral: Definite integrals are defined. Includes an example using the function f(x) = x.
Course: 18.01 Single Variable Calculus, Fall 2005
Instructor: Prof. Jason Starr
Prof. Jason Starr, 18.01 Single Variable Calculus, Fall 2005. (Massachusetts Institute of Technology: MIT OpenCourseWare), http://ocw.mit.edu (Accessed October 28, 2008). License: Creative Commons BY-NC-SA
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Keywords:MIT AP Calculus AP Calculus math mathematics Riemann sum rate of change interval integrals
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