Algebra and Trigonometry for Early Transcendental CalculusBook - 2006
Strong algebra and trigonometry skills are crucial to success in calculus. This text is designed to bolster these skills while readers study calculus. As readers make their way through the calculus course, this supplemental text shows them the relevant algebra or trigonometry topics and points out potential problem spots. The table of contents is organized so that the algebra and trigonometry topics are arranged in the order in which they are needed for calculus.
Numbers and Their Disguises: Multiplying and dividing fractions, adding and subtracting fractions, parentheses, exponents, roots, percent, scientific notation, calculators, rounding, intervals. Completing the Square: Completing the square in one and two variables. Solving Equations: Equations of degree 1 and 2, solving other types of equations, rational equations, the zero-factor property. Functions and Their Graphs: Introduction, equations of lines, power functions, shifting graphs, intersection of curves. Cyclic Phenomena: The Six Basic Trigonometric Functions: Angles, definitions of the six trigonometric functions, basic identities, special angles, sum formulas. Exponential Functions: The family of exponentials, the function. Composition and Inverse Functions: Composite functions, the idea of inverses, finding an inverse of f given by a graph, finding the inverse of f given by an expression. Logarithmic Functions: Definition of logarithms, logs as inverses of exponential functions, laws of logarithms, the natural logarithm. Inverse Trigonometric Functions: The definition of arcsin x, the functions arctan x and arcsec x, inverse trigonometric identities. Changing the Form of a Function: Factoring, canceling, long division, rationalizing, extracting a factor from under a root. Simplifying Algebraic Expressions: Working with difference quotients and rational functions, canceling common factors, rationalizing expressions. Decomposition of Functions: Inner, outer, and outermost functions, decomposing composite functions. Equations of Degree 1 Revisited: Solving linear equations involving derivatives. Word Problems, Algebraic and Transcendental: Algebraic word problems, the geometry of rectangles, circles and spheres, trigonometric word problems, right angle triangles, the law of sines and the law of cosines, exponential growth and decay. Trigonometric Identities: Rewriting trigonometric expressions using identities.