College mathematics : algebra, discrete mathematics, precalculus, calculus / Frank Ayres, Jr., Philip A. Schmidt

Includes index

Revised edition of: Schaum's outline of theory and problems of college mathematics / Frank Ayres, Jr., Philip A. Schmidt. 3rd ed. c2003

Includes bibliographical references and index

Part I. Review of algebra -- Elements of algebra -- Functions -- Graphs of functions -- Linear equations -- Simultaneous linear equations -- Quadratic functions and equations -- Inequalities -- The Locus of an equation -- The Straight line -- Families of straight lines -- The Circle -- Part II. Topics in discrete mathematics -- Arithmetic and geometric progressions -- Infinite geometric series -- Mathematical induction -- The Binomial theorem -- Permutations -- Combinations -- Probability -- Determinants of orders two and three -- Determinants of order n -- Systems of linear equations -- Part III. Topics in precalculus -- Angles and arc length -- Trigonometric functions of a general angle -- Trigonometric functions of an acute angle -- Reduction to functions of positive acute angles -- Graphs of the trigonometric functions -- Fundamental relations and identities -- Trigonometric functions of two angles -- Sum, difference, and product formulas -- Oblique triangles -- Inverse trigonometric functions -- Trigonometric equations -- Complex numbers

The Conic sections -- Transformation of coordinates -- Points in space -- Simultaneous equations involving quadratics -- Logarithms -- Power, exponential, and logarithmic curves -- Polynomial equations, rational roots -- Irrational roots of polynomial equations -- Graphs of polynomials -- Parametric equations -- Part IV. Calculus -- The Derivative -- Differentiation of algebraic expressions -- Applications of derivatives -- Integration -- Polar, spherical, and cylindrical coordinate systems -- Multivariate calculus -- Infinite sequences -- Infinite series -- Power series -- Appendix A. Introduction to the graphing calculator -- Appendix B. The Number system of algebra -- Appendix C. Mathematical modeling -- Appendix D. Integration by parts -- Index