
Typical
Syllabus for Math 127: Precalculus at Lycoming College
Note: This is a typical
syllabus for this course. Each semester a semesterspecific syllabus will
be distributed, which will spell out in addition to the topics
administrative details such as information about grading, homework, tests,
labs, etc.
Precalculus attempts to prepare students for calculus
in two general ways:
(1) by remedying the mathematical prerequisites in the
algebra and geometry of the elementary functions, and
(2) by introducing students to Mathematica, a
computer algebra system that will be used throughout the calculus curriculum.
More specifically, we address
 The analytical geometry of the
Cartesian plane (distance, slope, lines, circles, parabolas, ellipses,
hyperbolas, their intercepts, vertices, centers, radii, major and minor
axes, foci, and tangents),
 The algebra of polynomials and
rational functions (zeros, factoring, remainder theorem, asymptotes, intercepts,
sketching, multiplicity, complex roots, algebra of the complex numbers,
inverses of polynomial and rational functions; onetoone, onto functions;
composition)
 Exponential functions and logarithms
(the laws of exponents and logarithms, solving exponential and
logarithmic equations, applications to population, radioactive decay,
Newton's law of heat transfer, etc)
 Circular functions and their inverses
(definitions of the six circular functions, special values, modeling
with the sine and cosine, right triangle trigonometry, trigonometric
identities, solving trigonometric equations, the inverse trigonometric
functions)
 Systems
of 2 nonlinear equations in two unknowns, especially pairs of linked quadratic
equations. (This is a skill needed in calculus 3.)
Mathematica provides a typical example of the capabilities
of a computer algebra system. At the Precalculus
level, it can be used to plot the graphs of a great variety of polynomials, rational
functions and conics, as well as to elegantly solve modeling problems
involving the sine and the exponential.
Geometer's Sketchpad is used, where possible, to illustrate
certain properties of the circular functions.
