A college precalculus textbook by Lial, Hornsby, Schneider, and Daniels covering equations and inequalities, graphs and functions, polynomial/rational/exponential/logarithmic functions, trigonometry, identities and equations, applications of trigonometry, systems and matrices, analytic geometry (conics), and further topics in algebra (sequences, series, counting, probability). The 7e expands Chapter R (Review of Basic Concepts) with additional foundational content.
A review of basic algebra fundamentals before precalculus topics begin. Expanded in 7e to include foundational concepts that often challenge students.
Solving linear equations, complex numbers, quadratic equations, other equation types, inequalities, and absolute value equations and inequalities.
Coordinate plane, circles, functions, linear functions, equations of lines, basic function graphs, graphing techniques, and function operations.
Quadratic functions, synthetic division, zeros of polynomials, polynomial graphs, rational functions and graphs, polynomial and rational inequalities, variation.
Inverse functions, exponential functions, logarithmic functions, change-of-base, exponential and logarithmic equations, and applications of growth and decay.
Angles, trigonometric functions and quadrantal angles, trigonometric function values, and right triangle solutions.
Radian measure, the unit circle and circular functions, graphs of sine and cosine, translations, graphs of tangent, cotangent, secant, cosecant, and harmonic motion.
Fundamental identities, verifying identities, sum and difference identities, double-angle and half-angle identities, inverse trig functions, trig equations.
Law of Sines, Law of Cosines, vectors (geometric and algebraic), polar form of complex numbers, De Moivre's Theorem, polar equations, and parametric equations.
Systems of linear equations, matrix solutions, determinants, nonlinear systems, properties of matrices, and matrix inverses.
Conic sections: parabolas, ellipses, hyperbolas, and a summary of conics.
Sequences and series, arithmetic and geometric sequences and series, the Binomial Theorem, mathematical induction, counting theory, and probability.