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MATH 221 { 1st SEMESTER CALCULUS LECTURE NOTES VERSION 2.0 (fall 2009) This is a self contained set of lecture notes for Math 221. The notes were written by Sigurd Angenent, starting from an extensive collection of notes and problems compiled by Joel Robbin. The LATEX and Python les
Differential Calculus finds Function .2/ from Function .1/. We recover the speedometer information from knowing the trip distance at all times. Integral Calculus goes the other way. The “integral” adds up small pieces, to get the total distance traveled. That integration brings back Function .1/.
Integral Calculus provides methods for calculating the total effect of such changes, under the given conditions. The phrase rate of change mentioned above stands for the actual rate of
Introduction These notes are intended to be a summary of the main ideas in course MATH 214-2: Integral Calculus. I may keep working on this document as the course goes on, so these notes will not be completely finished until the end of the quarter. The textbook for this course is Stewart: Calculus, Concepts and Contexts (2th ed.), Brooks/Cole ...
Integrals. This chapter is about the idea of integration, and also about the technique of integration. We explain how it is done in principle, and then how it is done in practice. Integration is a problem of adding up infinitely many things, each of which is infinitesimally small. Doing the addition is not recommended.
• Be familiar with the definition of the definite integral as the limit of a sum; • Understand the rule for calculating definite integrals; • Know the statement of the Fundamental Theorem of the Calculus and understand
This chapter is about the idea of integration, and also about the technique of integ- ration. We explain how it is done in principle, and then how it is done in practice.
