Fundamentals for Calculus: Functions and Equations
This course is expected to run but has not yet been scheduled.
The aim of this course is to reinforce fundamental concepts and techniques that a student preparing to enter a first calculus or pre-calculus class will need for success. To this end, we will focus on those topics introduced in algebra courses that most often pose difficulties for students down the road. Along the way, for enrichment and depending on student interest, we may explore some ideas that fall outside the standard curriculum but can nevertheless help students to master the core material.
We will investigate the basic operations and functions that play a starring role in calculus and pre-calculus classes, as well as the rules and techniques for manipulating them to produce clear solutions to commonly encountered problems. Specific topics include polynomials, rational functions, exponents, and basic trigonometry. Special attention will be devoted to working with absolute values, inequalities, and logarithms, since these tend to present stumbling blocks for many students in calculus courses. As much as possible, emphasis will be adjusted to meet students' background and interests, but it should be noted that this course is intended as preparation for future study of calculus rather than being itself an introduction to the methods of calculus; that is, we will study the fundamentals FOR calculus instead of the fundamentals OF calculus.
By the end of the course, students will have a solid command of the fundamentals of algebra needed for success in a future calculus or pre-calculus course. In particular, students will have acquired a firm conceptual grasp of the following mathematical objects as well as facility manipulating them to solve problems: logarithms, absolute values, inequalities, exponents, polynomials, rational functions, sine, cosine, and tangent.
To get the most out of Fundamentals for Calculus, students should enter with two years of background in algebra and at least a little trigonometry. Pre-calculus is not a prerequisite, but the class should also be valuable to students who have already taken such a course.