Columbia Home
Precalculus Sample Syllabus

All sections refer to James Stewart, Lothar Redlin, Saleem Watson Precalculus: Mathematics for Calculus, 7th edition.

 Class Material Sections 1 Real numbers, powers. §1.1, 1.2 2 Algebraic expressions, rational expressions. §1.3, 1.4 3 More on rational expressions, equations. §1.4, 1.5 4 Modeling with equations (word problems), inequalities, coordinate geometry. §1.7, 1.8, 1.9 5 Functions, graphs. §2.1, 2.2, 2.3 6 Average rate of change, linear functions. §2.4, 2.5 7 Transformations of functions. §2.6 8 Review. 9 Midterm 1. 10 Combining functions. §2.7 11 One-to-one functions and inverses. §2.8 12 Quadratic functions. Polynomial functions. §3.1, 3.2 13 Dividing polynomials, real roots. §3.3, 3.4 14 Complex numbers, fundamental theorem of algebra, rational functions. §1.6, 3.5, 3.6 15 Exponential functions and logarithms. §4.1, 4.2, 4.3 16 Properties of logarithms, equations with exponents and logs, applications. §4.4, 4.5, 4.6 17 Trigonometric functions via the unit circle §5.1, 5.2 18 Graphs of trigonometric functions. §5.3, 5.4 19 Inverse trig functions, applications. §5.5, 5.6 20 Trigonometric functions via right angles. §6.1, 6.2, 6.3 21 Inverse trig functions, laws of sines and cosines. §6.4, 6.5, 6.6 22 Review. 23 Midterm 2. 24 Trigonometric identities. §7.1, 7.2 25 More identities. Working with equations involving trig functions. §7.3, 7.4, 7.5 26 More equations with trig functions. §7.5, 7.6 27 Polar coordinates. §8.1, 8.2, 8.3 28 Review.