A college algebra-and-trigonometry textbook by Robert F. Blitzer covering prerequisite review, equations and inequalities, functions and graphs, polynomial and rational functions, exponential/logarithmic functions, trigonometric functions, analytic trigonometry, additional topics in trigonometry, systems of equations and inequalities, matrices and determinants, conic sections and analytic geometry, and sequences/induction/probability. Sister volume of Blitzer Precalculus 7e with the Introduction to Calculus chapter removed and the equations/inequalities content from Blitzer Precalc Ch P.7-P.9 expanded into a full Chapter 1.
Review of foundational algebra concepts students need before college algebra: real numbers, exponents and scientific notation, radicals and rational exponents, polynomials, factoring, and rational expressions.
Solving linear equations, rational equations, quadratic equations, equations with radicals, and equations quadratic in form. Modeling with equations. Complex numbers. Solving linear and absolute value inequalities. (Blitzer Algebra and Trigonometry expands the equations content from Blitzer Precalculus Ch P.7-P.9 into a full chapter.)
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.