MATH 1P01 Lecture Notes - Lecture 1: Differential Calculus, The Tangent, Stock Market

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erinrabbit736

20 Oct 2018

School

Brock University

Department

Mathematics and Statistics

Course

MATH 1P01

Professor

William B. Ralph

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Document Summary

Calculus is a branch of mathematics that deals with the finding and properties of derivatives and integrals. It was originally developed to find an answer to questions involving infinitesimally small differences. Calculus is humanity"s answer to the two great problems of mathematics: The branch of integral calculus is concerned with this problem. The primary issue was finding the area under a curve. An approximation could be done by using rectangles and calculating their area, but that would not be an exact measurement. The branch of differential calculus is concerned with this problem. The primary issue was finding the slope of a tangent that caresses a curve. The issue was that there was only one point for the slope of the line to be computed from. Any attempts to solve this equation was hindered by two problems: We need two points to solve a line, but we only have one.

Related Questions

. Find a formal definition for the derivative as we use it in calculus. Then unpack and explain that definition in your own words. Your explanation should connect the limit of the difference quotient, the slope of tangent lines, and the instantaneous rate of change.

5. One of our ideas about Integrals is that they give the âarea under the curveâ. Another idea is that we use an antiderivative in the process to compute an integral. Why are these really the same thing? Iâm NOT looking for you to tell me what the fundamental theorem of calculus is here; mentioning the FTC means EXPLAINING why the FTC works and does what it does. There are other ways to go with this problem, too.