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

by: Mueller, Guntram; Brent, Ronald I.

ISBN: 9780321320506 | 0321320506

Edition: 3rd
Format: Paperback
Publisher: Pearson
Pub. Date: 5/3/2005

Newer Edition Available

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Summary Table of Contents

Designed for Students taking calculus with Early Transcendentals. Strong Algebra and Trigonometry skills are crucial to success in calculus. This text is designed to bolster these skills while students study calculus. As students 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.

... MORE="width:100%" />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.

Review of Basics

Numbers and Their Disguises

Multiplying and dividing fractions, adding and subtracting fractions, parentheses, exponents, roots, percent, scientific notation, calculators, rounding, i... MORE

(24)

Circles, Parabolas, etc.

Completing the Square

Completing the square in one and two variables

(5)

Equations

Solving Equations

Equations of degree 1 and 2, solving other types of equations, rational equations, the zero-factor property

(17)

Algebraic Functions and Graphs

Functions and Their Graphs

Introduction, equations of lines, power functions, shifting graphs, intersection of curves

(28)

Transcendental Functions

Cyclic Phenomena: The Six Basic Trigonometric Functions

Angles, definitions of the six trigonometric functions, basic identities, special angles, sum formulas

(20)

Exponential Functions

The family of exponential functions, the function ex

(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