Math 127: Precalculus - Syllabus

Typical Syllabus for Math 127: Precalculus at Lycoming College

Note: This is a typical syllabus for this course.  Each semester a semester-specific 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; one-to-one, 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 non-linear 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.