Course Outline: MA460, Honors Precalculus Text: Richard Brown, Advanced Mathematics, Houghton Mifflin, 2003 1. Polar coordinates and Complex Numbers. (continued from MA450) • Multiplying complex numbers in trigonometric form • Powers and Roots of complex numbers: DeMoivre's Theorem 2. Exponential and Logarithmic Functions. • Definitions, domain and range • Graphs of exponential and logarithmic functions • Euler's number e and the function x ! ex • Exponential growth and decay • Compound interest—discrete and continuous • Laws of Exponents and Logarithms • Change of base formulas • Exponential and logarithmic equations 3. Vectors in the Plane and Parametric Equations. • Geometric representation of vectors • Algebraic representation of vectors • Geometry problems with vectors • Applications to navigation and physics problems • Vector and parametric equations • Direction vectors and unit vectors • Parametric representation of lines (interpretation as a particle moving along a line with constant velocity) • Parametric representation of conic sections (tracing out a circle or ellipse in a fixed amount of time or with a fixed velocity.) • Miscellaneous curves defined parametrically • The dot product and orthogonality • Vectors in three dimensions • Equations of spheres 4. Sequences and Series. • Arithmetic and geometric sequences and series • Explicit and recursive definitions of sequences • Limits of infinite sequences • Series and sigma notation • Telescoping sums • Infinite series (geometric and telescoping series) • Interval of convergence of geometric function series • Binomial Theorem and Pascal’s Triangle • Mathematical induction5. Limits and Continuity • Definition of limit of a function at a and at infinity • Techniques for evaluating limits • Special trigonometric limits • Definition of continuity of a function at a • Types of discontinuity: point, jump, infinite, miscellaneous • Graphs of rational functions: intercepts; horizontal, vertical, and slant asymptotes; holes in graphs (how these are found by evaluating appropriate limits) Some Calculator Skills. 1. Plot graphs in function mode and analyze. Trace. Zoom in and out. Find intercepts and max/min values. 2. Plot graphs in parametric mode and analyze. 3. Calculate terms of a sequence that is defined recursively or in closed form (sequence mode, iteration on the home screen, etc.) 4. Calculate partial sums of a series. 5. Locate special functions (factorial function, combination function, floor function) quickly. 6. Link with someone to send or receive