Just-In-Time Algebra and Trigonometry for Early Transcendentals Calculus

by Mueller, Guntram; Brent, Ronald I.

• ISBN13: 9780321320506
• ISBN10: 0321320506
• Edition: 3rd
• Format: Paperback
• Copyright: 2005-05-03
• Publisher: Pearson

Summary

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 offgiven by a graph, finding the inverse offgiven 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 arcsinx, the functions arctanxand arcsecx, 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. For all readers interested in algebra and trigonometry in early transcendentals calculus.

Table of Contents

Review of Basics
Numbers and Their Disguises
Multiplying and dividing fractions, adding and subtracting fractions, parentheses, exponents, roots, percent, scientific notation, calculators, rounding, intervals	1	(24)
Circles, Parabolas, etc.
Completing the Square
Completing the square in one and two variables	25	(5)
Equations
Solving Equations
Equations of degree 1 and 2, solving other types of equations, rational equations, the zero-factor property	30	(17)
Algebraic Functions and Graphs
Functions and Their Graphs
Introduction, equations of lines, power functions, shifting graphs, intersection of curves	47	(28)
Transcendental Functions
Cyclic Phenomena: The Six Basic Trigonometric Functions
Angles, definitions of the six trigonometric functions, basic identities, special angles, sum formulas	75	(20)
Exponential Functions
The family of exponential functions, the function ex	95	(6)
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	101	(12)
Logarithmic Functions
Definition of logarithms, logarithms as inverses of exponential functions, laws of logarithms, the natural logarithm	113	(13)
Inverse Trigonometric Functions
The definition of arcsin x, the functions arctan x and arcsec x, inverse trigonometric identities	126	(13)
Limits
Changing the Form of a Function
Factoring, canceling, long division, rationalizing, extracting a factor from under a root	139	(14)
Derivatives
Simplifying Algebraic Expressions
Working with difference quotients and rational functions, canceling common factors, rationalizing expressions	153	(7)
The Chain Rule
Decomposition of Functions
Inner, outer, and outermost functions, decomposing composite functions	160	(2)
Implicit Differentiation
Equations of Degree 1 Revisited
Solving linear equations involving derivatives	162	(4)
Related Rates, Applied Max-Min Problems
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	166	(12)
Integrating Trigonometric Functions
Trigonometric Identities
Rewriting trigonometric expressions using identities	178	(5)
Appendices (Use as needed)
The Binomial Theorem	183	(3)
Derivation of the Quadratic Formula	186	(3)
Answers to Odd-Numbered Exercises	189	(22)
Index	211