Calculus I with Precalculus : A One-Year Course

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  • Edition: 2nd
  • Format: Hardcover
  • Copyright: 2008-06-09
  • Publisher: Brooks Cole
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Supplemental Materials

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  • The New copy of this book will include any supplemental materials advertised. Please check the title of the book to determine if it should include any access cards, study guides, lab manuals, CDs, etc.


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
Solving Equations Section Project: Projectile Motion
Solving Inequalities
Graphical Representation of Data
Graphs of Equations
Linear Equations in Two Variables
Functions and Their Graphs
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
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
Antiderivatives and Indefinite Integration
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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