Precalculus - Unit 9
Introduction to Calculus
By the beginning of the 17th century, algebra and geometry had developed to the point where physical behavior could be modeled both algebraically and graphically, each type of representation providing deeper insights into the other. New discoveries about the solar system had opened up fascinating questions about gravity and its effects on planetary motion, so that finding the mathematical key to studying motion became the scientific quest of the day. The analytic geometry of René Descartes (1596–1650) put the final pieces into place, setting the stage for Isaac Newton (1642–1727) and Gottfried Leibniz (1646–1716) to stand “on the shoulders of giants” and see beyond the algebraic boundaries that had limited their predecessors. With geometry showing them the way, they created the new form of algebra that would come to be known as the calculus.
In this unit you look at the two central problems of motion much as Newton and Leibniz did, connecting them to geometric problems involving tangent lines and areas. You will see how the obvious geometric solutions to both problems led to algebraic dilemmas, and how the algebraic dilemmas led to the discovery of calculus. The language of limits, which is used in this brief introduction to describe asymptotes, end behavior, and continuity, will prepare students for future studies.
Lessons
- Lesson 1: Parametric Functions
- Lesson 2: Introduction to Limits
- Lesson 3: Limit of a Sequence and Limits at infinity
Resources - Limits
The following are links to resources for Matrices:
The following are other free resources:
- GeoGebra - Free online math tools
- Desmos - Free online graphing calculator
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