Precalculus

Overview

This course builds on a strong algebra foundation to explore further implications of the function concept, starting with graph transformations of the functions we already know. We draw on geometry knowledge to develop the circular functions, which enjoy a beautiful connection to the exponential function by way of the complex numbers and infinite series. Armed with these tools, we then consider polar coordinates, vector-valued functions (AKA parametric equations), and the algebra of vectors in Cartesian coordinates.

Selected learning outcomes

• analyze 2D and 3D geometric constructions using the language of vector algebra.
• build and interpret models of periodic phenomena using the circular functions.
• solve trigonometric equations and prove trigonometric identities.
• develop sequences and series to model discrete-time phenomena.
• apply laws of exponents and logarithms to solve transcendental equations.
• graph by hand rational and polynomial equations.
• find (complex) roots of algebraic equations and (real) solution sets of algebraic inequalities.

Resources

Course structure and syllabus excerpts

Program-level objectives to align with standards-based grading

The (underappreciated) diagrammatic approach to functions

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