MA 115 Course Description

MA115 PRECALCULUS (4 Cr.)

COURSE DESCRIPTION

Applies toward the division III liberal studies requirement.

Prerequisite: MA 111, or B- or better in MA 104, or satisfactory score on the Math Placement Exam. A graphing calculator or equivalent software is required.

Offered: Fall, Winter

General Introduction and Goals

MA115 is for students who plan to study calculus. It may also be taken by those whose curriculum currently requires MA106 (but note the prerequisites); and by those seeking Liberal Studies credit who wish to assess their desire to study calculus. Credit cannot be earned for both MA106 and MA115, except by written permission from the Mathematics Department.

The content includes trigonometry, analytic geometry (including an introduction to three-dimensional analytic geometry), and topics from algebra (sequences, series, limits.)

Course Content

  1. The Graphing Calculator
    • Using the graphing utility to draw graphs, solve equations, determine extrema, etc.
    • Using other utilities: the solver, evaluating functions, solving systems of equations
  2. Trigonometry
    • Review of geometry: right triangles, similarity
    • Angles and their measures: degrees, radians
    • Definition of the trig functions for acute angles
    • Right triangle trigonometry, including applications
  3. Analytic Trigonometry
    • Trig functions of any angle or number
    • Graphs of the trig functions
    • Transformations of trigonometric graphs
    • Finding an equation to fit an empirically-derived graph
    • Inverse trig functions and their graphs
    • Solving trigonometric equations analytically and graphically
    • Trigonometric identities: The basic identities and using these to derive others
  4. Other Topics in Trigonometry
    • Laws of Sines and Cosines
    • Polar coordinates and graphs of polar equations
  5. Conic Sections
    • Geometric definitions of parabola, ellipse and hyperbola
    • Equations of the conics
    • Applications
  6. Other Topics in Analytic Geometry
    • Graphs of algebraic and transcendental functions
    • Vectors
    • Parametric equations, motion in the plane
    • Analytic characteristics of functions and their graphs: monotonicity, continuity, etc.
  7. Solid Analytic Geometry
    • Three-dimensional coordinate system
    • Graphs of equations in three variables
    • Vector (parametric) equations for lines
    • Parametric description of motion in three-space
  8. Topics in Algebra
    • Sequences and an introduction to the limit of a sequence
    • Geometric series, finite and infinite, and applications thereof
    • Counting, permutations and combinations
    • Mathematical induction