Calculus I with Precalculus : A One-Year Course

by Larson, Ron; Hostetler, Robert P.; Edwards, Bruce H.

• ISBN13: 9780618568062
• ISBN10: 0618568069
• Edition: 2nd
• Format: Hardcover
• Copyright: 2008-06-09
• Publisher: Brooks Cole

Summary

Carefully developed for one-year courses that combine and integrate material from Precalculus through Calculus I, this text is ideal for instructors who wish to successfully bring students up to speed algebraically within precalculus and transition them into calculus. The Larson Calculus texts continue to offer instructors and students new and innovative teaching and learning resources. The Calculus series was the first to use computer-generated graphics, to include exercises involving the use of computers and graphing calculators, to be available in an interactive CD-ROM format, to be offered as a complete, online calculus course, and to offer this two-semester Calculus I with Precalculus text. Every edition of the series has made the mastery of traditional calculus skills a priority, while embracing the best features of new technology and, when appropriate, calculus reform ideas. Two primary objectives guided the authors in writing this book: to develop precise, readable materials for students that clearly define and demonstrate concepts and rules of calculus and to design comprehensive teaching resources for instructors that employ proven pedagogical techniques and saves the instructor time.

Table of Contents

Note: Each chapter concludes with Problem Solving

Prerequisites

Solving Equations Section Project: Projectile Motion

Solving Inequalities

Graphical Representation of Data

Graphs of Equations

Linear Equations in Two Variables

Functions and Their Graphs

Functions

Analyzing Graphs of Functions

Shifting, Reflecting, and Stretching Graphs

Combinations of Functions

Inverse Functions

Mathematical Modeling Section Project: Hooke's Law

Polynomial and Rational Functions

Quadratic Functions

Polynomial Functions of Higher Degree

Polynomial and Synthetic Division

Complex Numbers Section Project: The Mandelbrot Set

The Fundamental Theorem of Algebra

Rational Functions Section Project: Rational Functions

Limits and Their Properties

A Preview of Calculus

Finding Limits Graphically and Numerically

Evaluating Limits Analytically

Continuity and One-Sided Limits

Infinite Limits Section Project: Graphs and Limits of Functions Progressive Summary 1: Flowchart of Calculus

Differentiation

The Derivative and the Tangent Line Problem

Basic Differentiation Rules and Rates of Change

The Product and Quotient Rules and Higher-Order Derivatives

The Chain Rule

Implicit Differentiation Section Project: Optical Illusions

Related Rates

Applications of Differentiation

Extrema on an Interval

Rolle's Theorem and the Mean Value Theorem

Increasing and Decreasing Functions and the First Derivative Test

Concavity and the Second Derivative Test

Limits at Infinity

A Summary of Curve Sketching

Optimization Problems Section Project: Connecticut River

Differentials

Integration

Antiderivatives and Indefinite Integration

Area

Riemann Sums and Definite Integrals

The Fundamental Theorem of Calculus Section Project: Demonstrating the Fundamental Theorem

Integration by Substitution

Numerical Integration Progressive Summary 2: Flowchart of Calculus

Exponential and Logarithmic Functions

Exponential Functions and Their Graphs

Logarithmic Functions and Their Graphs

Using Properties of Logarithms

Exponential and Logarithmic Equations

Exponential and Logarithmic Models Section Project: Comparing Models

Exponential and Logarithmic Functions and Calculus

Exponential Functions: Differentiation and Integration

Logarithmic Functions and Differentiation Section Project: An Alternate Definition of ln x

Logarithmic Functions and Integration

Differential Equations: Growth and Decay Progressive Summary 3: Flowchart of Calculus

Trigonometric Functions

Radian and Degree Measure

Trigonometric Functions: The Unit Circle

Right Triangle Trigonometry

Trigonometric Functions of Any Angle

Graphs of Sine and Cosine Functions Section Project: Approximating Sine and Cosine Functions

Graphs of Other Trigonometric Functions

Inverse Trigonometric Functions

Applications and Models

Analytic Trigonometry

Using Fundamental Trigonometric Identities

Verifying Trigonometric Identities

Solving Trigonometric Equations Section Project: Modeling a Sound Wave

Sum and Difference Formulas

Multiple-Angle and Product-to-Sum Formulas

Trigonometric Functions and Calculus

Limits of Trigonometric Functions Section Project: Graphs and Limits of Trigonometric Functions

Trigonometric Functions: Differenti

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