A college precalculus textbook by Robert F. Blitzer covering prerequisites, functions and graphs, polynomial and rational functions, exponential and logarithmic functions, trigonometry, analytic trigonometry, additional trig topics, systems and matrices, conic sections, sequences and induction, and an introduction to calculus. Known for application-rich pedagogy and pop-culture references.
Foundational algebra review: real numbers and properties, exponents and scientific notation, radicals and rational exponents, polynomials, factoring, rational expressions, equation solving, modeling with equations, linear and absolute value inequalities.
Coordinate plane and graphing utilities, function definition and notation, properties of functions, linear functions and slope, transformations, combining and composing functions, inverse functions, distance and circles, modeling with functions.
Complex number system, quadratic functions and modeling, polynomial functions and their graphs, polynomial division and zeros, rational functions and asymptotes, polynomial and rational inequalities, modeling using variation.
Exponential functions and the natural exponential, logarithmic functions and their graphs, properties of logarithms, exponential and logarithmic equations, applications including growth, decay, and data modeling.
Angles and radian measure, the trigonometric functions defined via the unit circle and via right triangles, evaluating trigonometric functions of any angle, graphs of all six trigonometric functions, inverse trigonometric functions, applications including bearings and harmonic motion.
Verifying identities, sum and difference formulas, double-angle, power-reducing, and half-angle formulas, product-to-sum and sum-to-product formulas, solving trigonometric equations.
Law of Sines and Law of Cosines, polar coordinates and graphs, complex numbers in polar form, DeMoivre's Theorem, vectors in the plane, dot product.
Systems of linear equations in two and three variables, solving nonlinear systems.
Matrix solutions of linear systems via row operations, matrix operations, multiplicative inverses and matrix equations, determinants and Cramer's Rule.
Standard equations and properties of the ellipse, hyperbola, and parabola.
Sequences and summation notation, arithmetic and geometric sequences and series, the Binomial Theorem.
A preview of calculus topics: limits via tables and graphs, properties of limits, continuity, and derivatives at a point. Cross-listed from M2231 Calculus 1 limits and derivatives content (same approach as C9 Sullivan Ch 14, Stewart Ch 12, and C10 Larson Limits Ch 11).