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Calculus I - With Precalculus, One Year Course

Calculus I - With Precalculus, One Year Course - 2nd edition

Calculus I - With Precalculus, One Year Course - 2nd edition

ISBN13: 9780618568062

ISBN10: 0618568069

Calculus I - With Precalculus, One Year Course by Ron Larson, Robert P. Hostetler and Bruce H. Edwards - ISBN 9780618568062
Edition: 2ND 06
Copyright: 2006
Publisher: Houghton Mifflin Harcourt
International: No
Calculus I - With Precalculus, One Year Course by Ron Larson, Robert P. Hostetler and Bruce H. Edwards - ISBN 9780618568062

ISBN13: 9780618568062

ISBN10: 0618568069

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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 (Third Edition), to include exercises involving the use of computers and graphing calculators (Fourth Edition), to be available in an interactive CD-ROM format (Fifth Edition), to be offered as a complete, online calculus course (Sixth Edition), and to offer this two-semester Calculus I with Precalculus text. Every edition of the book has made the mastery of traditional calculus skills a priority, while embracing the best features of new technology and, when appropriate, calculus reform ideas. Now, the Eighth Edition is the first calculus program to offer algorithmic homework and testing created in Maple so that answers can be evaluated with complete mathematical accuracy.

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. The Eighth Edition continues to provide an evolving range of conceptual, technological, and creative tools that enable instructors to teach the way they want to teach and students to learn they way they learn best. The Larson program offers a variety of options to address the needs of any calculus course and any level of calculus student, enabling the greatest number of students to succeed.

  • The explanations, theorems, and definitions have been thoroughly and critically reviewed. When necessary, changes have been made to ensure that the text is pedagogically sound, mathematically precise, and comprehensible.
  • The exercise sets have been carefully and extensively examined to ensure they cover all calculus topics appropriately. Many new exercises have been added at the suggestion of a number of calculus instructors.
  • A variety of exercise types are included in each exercise set. Questions involving skills, writing, critical thinking, problem-solving, applications, and real-data applications are included throughout the text. Exercises are presented in a variety of question formats, including matching, free response, true/false, modeling, and fill-in the blank.
  • The Eduspace online resources have been integrated into a comprehensive learning system that combines numerous dynamic calculus resources with online homework and testing materials.
  • The Integrated Learning System addresses the changing needs of today's instructors and students. Recognizing that the calculus course is presented in a variety of teaching and learning environments, the program resources are available in print, CD-ROM, and online formats.
  • Eduspace, powered by Blackboard provides instructors with online courses and content in multiple disciplines. By pairing the widely recognized tools of Blackboard with quality, text-specific content from Houghton Mifflin (HMCo), Eduspace makes it easy for instructors to create all or part of a course online. Homework exercises, quizzes, tests, tutorials, and supplemental study materials all come ready-to-use. Instructors can choose to use the content as is, modify it, or even add their own. Eduspace with eSolutions combines all the features of Eduspace with an electronic version of the textbook exercises and the complete solutions to the odd-numbered text exercises, providing students with a convenient and comprehensive way to do homework and view the course materials.
  • SMARTHINKING online tutoring brings students real-time, online tutorial support when they need it most.

Table of Contents

Table of Contents

Note: Each chapter concludes with Problem Solving.

P. Prerequisites

P.1 Solving Equations
Section Project: Projectile Motion
P.2 Solving Inequalities
P.3 Graphical Representation of Data
P.4 Graphs of Equations
P.5 Linear Equations in Two Variables

1. Functions and their Graphs

1.1 Functions
1.2 Analyzing Graphs of Functions
1.3 Shifting, Reflecting, and Stretching Graphs
1.4 Combinations of Functions
1.5 Inverse Functions
1.6 Mathematical Modeling
Section Project: Hooke's Law

2. Polynomial and Rational Functions

2.1 Quadratic Functions
2.2 Polynomial Functions of Higher Degree
2.3 Polynomial and Synthetic Division
2.4 Rational Functions
Section Project: Rational Functions

3. Limits and Their Properties

3.1 A Preview of Calculus
3.2 Finding Limits Graphically and Numerically
3.3 Evaluating Limits Analytically
3.4 Continuity and One-Sided Limits
3.5 Infinite Limits
Section Project: Graphs and Limits of Functions
Progressive Summary 1: Flowchart of Calculus

4. Differentiation

4.1 The Derivative and the Tangent Line Problem
4.2 Basic Differentiation Rules and Rates of Change
4.3 The Product and Quotient Rules and Higher-Order Derivatives
4.4 The Chain Rule
4.5 Implicit Differentiation
Section Project: Optical Illusions
4.6 Related Rates

5. Applications of Differentiation

5.1 Extrema on an Interval
5.2 Rolle's Theorem and the Mean Value Theorem
5.3 Increasing and Decreasing Functions and the First Derivative Test
5.4 Concavity and the Second Derivative Test
5.5 Limits at Infinity
5.6 A Summary of Curve Sketching
5.7 Optimization Problems
Section Project: Connecticut River
5.8 Differentials

6. Integration

6.1 Antiderivatives and Indefinite Integration
6.2 Area
6.3 Riemann Sums and Definite Integrals
6.4 The Fundamental Theorem of Calculus
Section Project: Demonstrating the Fundamental Theorem
6.5 Integration by Substitution
6.6 Numerical Integration
Progressive Summary 2: Flowchart of Calculus

7. Exponential and Logarithmic Functions

7.1 Exponential Functions and Their Graphs
7.2 Logarithmic Functions and Their Graphs
7.3 Using Properties of Logarithms
7.4 Exponential and Logarithmic Equations
7.5 Exponential and Logarithmic Models
Section Project: Comparing Models

8. Exponential and Logarithmic Functions and Calculus

8.1 Exponential Functions: Differentiation and Integration
8.2 Logarithmic Functions and Differentiation
Section Project: An Alternate Definition of ln x
8.3 Logarithmic Functions and Integration
8.4 Differential Equations: Growth and Decay
Progressive Summary 3: Flowchart of Calculus

9. Trigonometric Functions

9.1 Radian and Degree Measure
9.2 Trigonometric Functions: The Unit Circle
9.3 Right Triangle Trigonometry
9.4 Trigonometric Functions of Any Angle
9.5 Graphs of Sine and Cosine Functions
Section Project: Approximating Sine and Cosine Functions
9.6 Graphs of Other Trigonometric Functions
9.7 Inverse Trigonometric Functions
9.8 Applications and Models

10. Analytic Trigonometry

10.1 Using Fundamental Identities
10.2 Verifying Trigonometric Identities
10.3 Solving Trigonometric Equations
Section Project: Modeling a Sound Wave
10.4 Sum and Difference Formulas
10.5 Multiple-Angle and Product-Sum Formulas

11. Trigonometric Functions and Calculus

11.1 Limits of Trigonometric Functions
Section Project: Graphs and Limits of Trigonometric Functions
11.2 Trigonometric Functions: Differentiation
11.3 Trigonometric Functions: Integration
11.4 Inverse Trigonometric Functions: Differentiation
11.5 Inverse Trigonometric Functions: Integration
11.6 Hyperbolic Functions
Section Project: St. Louis Arch
Progressive Summary 4: Flowchart of Calculus

12. Topics in Analytic Geometry

12.1 Introduction to Conics: Parabolas
12.2 Ellipses and Implicit Differentiation
12.3 Hyperbolas and Implicit Differentiation
12.4 Parametric Equations
12.5 Polar Coordinates
12.6 Graphs of Polar Coordinates
12.7 Polar Equations of Conics
Section Project: Polar Equations of Planetary Orbits
Progressive Summary 5: Flowchart of Calculus

13. Additional Topics in Trigonometry

13.1 Law of Sines
13.2 Law of Cosines
13.3 Vectors in the Plane
Section Project: Adding Vectors Graphically
13.4 Vectors and Dot Products
13.5 Complex Numbers and Zeros.
Section Project: The Mandelbrot Set.
13.6 Trigonometric Form of a Complex Number

14. Systems of Equations and Matrices

14.1 Systems of Linear Equations in Two Variables
14.2 Multivariable Linear Systems
14.3 Systems of Inequalities
Section Project: Area Bounded by Concentric Circles
14.4 Matrices and Systems of Equations
14.5 Operations with Matrices
14.6 The Inverse of a Square Matrix
14.7 The Determinant of a Square Matrix
Section Project: Cramer's Rule


A. Proofs of Selected Theorems
B. Applications of Integration
Perforated Tear out Nutshells
1. Algebraic Functions.
2. Limits of Algebraic Functions.
3. Differentiation of Algebraic Functions.
4. Calculus of Algebraic Functions.
5. Calculus of Exponential and Log Functions.
6. Trigonometric Functions.
7. Calculus of Trig and Inverse Trig.