This laboratory manual/textbook complements the topics found in a traditional precalculus course by introducing topics that are generally bypassed in these courses but are effective in anticipating calculus. Topics--such as finding the turning points for polynomials of any degree, finding equations of tangent lines to polynomials, and solving elementary optimization problems--that are generally reserved for treatment in calculus are explored from a precalculus viewpoint. The textbook presumes access to Mathematica and introduces students to a set of Mathematica commands. The Graphing
add-on package used with the textbook includes several commands to create mathematically enhanced graphs for functions with singularities and helps clarify for students the location and behavior of functions at points of singularity.
An Introduction to Mathematica | Solving Linear Equations and Graphing Inequalities in 1D | Solving Polynomial Equations and Inequalities in 1D | Plotting Straight Lines and Circles and Defining Functions | Lines, Parabolas, and Cubics | Plotting and Graphing in 2D | Further Plotting and Graphing in 2D | Finding Turning Points of Polynomials; Optimization Problems | Tangent and Normal Lines to Polynomial Curves | Graphing Rational Functions | Graphing Exponential and Logarithmic Functions | Graphing Basic Trigonometric Functions | Behind the Scenes of the Plot
Command | Plotting in the Complex Plane | Index | Appendix
Calculus and Analysis