Synopses & Reviews
A leader in the field through six editions, Calculus has achieved this status by providing a wide variety of teaching and learning techniques, allowing professors to teach the way they want to teach. Designed for the three-semester course for math and science majors, the Larson/Hostetler/Edwards series continues its tradition of success by being the first to offer both an Early Transcendental version as well as a new Calculus with Precalculus text. This was also the first calculus text 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), and to be offered as a complete, online calculus course (Sixth Edition). 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. The text's evolving range of conceptual, technological, and creative tools has always allowed each professor to choose the best, most effective way to teach his or her calculus course. The Seventh Edition also expands its support package with an all-new set of text-specific videos.Known for its diverse and flexible exercise sets, the text now contains nearly 10,000 carefully graded exercises, each set progressing from skill-development problems to more rigorous problems involving applications and proofs.New! P.S. Problem-Solving Sections, an additional set of thought-provoking exercises added to the end of each chapter, require students to use a variety of problem-solving skills and provide a challenging arena for students to work withcalculus concepts.New! Getting at the Concept Exercises added to each section exercise set check students' understanding of the basic concepts. Located midway through the exercise set, they are both boxed and titled for easy reference.New! Review Exercises at the end of each chapter have been reorganized to provide students with a more effective study tool. The exercises are now grouped and correlated by text section, enabling students to target concepts requiring review.New! The icon IC in the text identifies examples that appear in the Interactive Calculus 3.0 CD-ROM and Internet Calculus 2.0 web site with enhanced opportunities for exploration and visualization using the program itself and/or a Computer Algebra System.Think About It conceptual exercises require students to use their critical-thinking skills and help them develop an intuitive understanding of the underlying theory of the calculus.Modeling Data multi-part questions ask students to find and interpret mathematical models to fit real-life data, often through the use of a graphing utility.Section Projects, extended applications that appear at the end of selected exercise sets. may be used for individual, collaborative, or peer-assisted assignments.Writing exercises throughout help develop students' reasoning skills and make them comfortable with discussing mathematical concepts.True or False? Exercises, included toward the end of many exercises sets, help students understand the logical structure of calculus and highlight concepts, common errors, and the correct statements of definitions and theorems.A wealth and variety of applications, many using current real data, clearly demonstrate the relevance of calculus.All real data in exercises and examples has been updated.Answers to all odd-numbered exercises are included in the back of the text.Technology is integrated thoughtfully (although not required) throughout the text, allowing for optimal flexibility in teaching and learning. When appropriate in examples, exercises, and applications, students are encouraged to use a graphing utility or computer algebra system as a tool for exploration, discovery, and problem-solving. To facilitate and clarify technology use, a graphing utility icon identifies all exercises that specifically instruct students to use a graphing utility or a computer algebra system.Explorations are optional boxed projects that help students discover selected concepts on their own before being exposed to them in the text.Motivating the Chapter sections opening each chapter present data-driven applications that explore the concepts to be covered in the context of a real-world setting.More than 1000 examples in the Seventh Edition enhance the text's usefulness as a study tool for all types of learners. Each example is titled for easy reference and many provide detailed solutions (many with side comments) that are presented graphically, analytically, and/or numerically to provide further insight into mathematical concepts.
Synopsis
Designed for the three-semester calculus course for math and science majors, Calculus continues to offer instructors and students new and innovative teaching and learning resources. This was the first calculus text 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 a 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. 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.
About the Author
Ron Larson received his Ph.D. in mathematics from the University of Colorado and has been a professor of mathematics at The Pennsylvania State University since 1970. He has pioneered the use of multimedia to enhance the learning of mathematics, having authored over 30 software titles since 1990. Dr. Larson has also conducted numerous seminars and in-service workshops for math teachers around the country about using computer technology as a teaching tool and motivational aid. His INTERACTIVE CALCULUS (a complete text on CD-ROM) received the 1996 Texty Award for the most innovative mathematics instructional material at the college level, and was the first mainstream college textbook to be offered on the Internet.The Pennsylvania State University, The Behrend College Bio: Robert P. Hostetler received his Ph.D. in mathematics from The Pennsylvania State University in 1970. He has taught at Penn State for many years and has authored several calculus, precalculus, and intermediate algebra textbooks. His teaching specialties include remedial algebra, calculus, and math education, and his research interests include mathematics education and textbooks.Bruce Edwards has been a mathematics professor at the University of Florida since 1976. Dr. Edwards majored in mathematics at Stanford University, graduating in 1968. He then joined the Peace Corps and spent four years teaching math in Colombia, South America. He returned to the United States and Dartmouth in 1972, and he received his PhD. in mathematics in 1976. Dr. Edwards' research interests include the area of numerical analysis, with a particular interest in the so-called CORDIC algorithms used by computers and graphing calculators to compute function values. His hobbies include jogging, reading, chess, simulation baseball games, and travel.
Table of Contents
Note: Each chapter includes Review Exercises and Problem Solving. P. Preparation for Calculus P.1 Graphs and Models P.2 Linear Models and Rates of Change P.3 Functions and Their Graphs P.4 Fitting Models to Data 1. Limits and Their Properties 1.1 A Preview of Calculus 1.2 Finding Limits Graphically and Numerically 1.3 Evaluating Limits Analytically 1.4 Continuity and One-Sided Limits 1.5 Infinite Limits Section Project: Graphs and Limits of Trigonometric Functions 2. Differentiation 2.1 The Derivative and the Tangent Line Problem 2.2 Basic Differentiation Rules and Rates of Change 2.3 The Product and Quotient Rules and Higher-Order Derivatives 2.4 The Chain Rule 2.5 Implicit Differentiation Section Project: Optical Illusions 2.6 Related Rates 3. Applications of Differentiation 3.1 Extrema on an Interval 3.2 Rolle's Theorem and the Mean Value Theorem 3.3 Increasing and Decreasing Functions and the First Derivative Test Section Project: Rainbows 3.4 Concavity and the Second Derivative Test 3.5 Limits at Infinity 3.6 A Summary of Curve Sketching 3.7 Optimization Problems Section Project: Connecticut River 3.8 Newton's Method 3.9 Differentials 4. Integration 4.1 Antiderivatives and Indefinite Integration 4.2 Area 4.3 Riemann Sums and Definite Integrals 4.4 The Fundamental Theorem of Calculus Section Project: Demonstrating the Fundamental Theorem 4.5 Integration by Substitution 4.6 Numerical Integration 5. Logarithmic, Exponential, and Other Transcendental Functions 5.1 The Natural Logarithmic Function: Differentiation 5.2 The Natural Logarithmic Function: Integration 5.3 Inverse Functions 5.4 Exponential Functions: Differentiation and Integration 5.5 Bases Other Than e and Applications Section Project: Using Graphing Utilities to Estimate Slope 5.6 Inverse Trigonometric Functions: Differentiation 5.7 Inverse Trigonometric Functions: Integration 5.8 Hyperbolic Functions Section Project: St. Louis Arch 6. Differential Equations 6.1 Slope Fields and Euler's Method 6.2 Differential Equations: Growth and Decay 6.3 Separation of Variables and the Logistic Equation 6.4 First-Order Linear Differential Equations Section Project: Weight Loss 7. Applications of Integration 7.1 Area of a Region Between Two Curves 7.2 Volume: The Disk Method 7.3 Volume: The Shell Method Section Project: Saturn 7.4 Arc Length and Surfaces of Revolution 7.5 Work Section Project: Tidal Energy 7.6 Moments, Centers of Mass, and Centroids 7.7 Fluid Pressure and Fluid Force 8. Integration Techniques, L'H?pital's Rule, and Improper Integrals 8.1 Basic Integration Rules 8.2 Integration by Parts 8.3 Trigonometric Integrals Section Project: Power Lines 8.4 Trigonometric Substitution 8.5 Partial Fractions 8.6 Integration by Tables and Other Integration Techniques 8.7 Indeterminate Forms and L'H?pital's Rule 8.8 Improper Integrals 9. Infinite Series 9.1 Sequences 9.2 Series and Convergence Section Project: Cantor's Disappearing Table 9.3 The Integral Test and p-Series Section Project: The Harmonic Series 9.4 Comparisons of Series Section Project: Solera Method 9.5 Alternating Series 9.6 The Ratio and Root Tests 9.7 Taylor Polynomials and Approximations 9.8 Power Series 9.9 Representation of Functions by Power Series 9.10 Taylor and Maclaurin Series 10. Conics, Parametric Equations, and Polar Coordinates 10.1 Conics and Calculus 10.2 Plane Curves and Parametric Equations Section Project: Cycloids 10.3 Parametric Equations and Calculus 10.4 Polar Coordinates and Polar Graphs Section Project: Anamorphic Art 10.5 Area and Arc Length in Polar Coordinates 10.6 Polar Equations of Conics and Kepler's Laws 11. Vectors and the Geometry of Space 11.1 Vectors in the Plane 11.2 Space Coordinates and Vectors in Space 11.3 The Dot Product of Two Vectors 11.4 The Cross Product of Two Vectors in Space 11.5 Lines and Planes in Space Section Project: Distances in Space 11.6 Surfaces in Space 11.7 Cylindrical and Spherical Coordinates 12. Vector-Valued Functions 12.1 Vector-Valued Functions Section Project: Witch of Agnesi 12.2 Differentiation and Integration of Vector-Valued Functions 12.3 Velocity and Acceleration 12.4 Tangent Vectors and Normal Vectors 12.5 Arc Length and Curvature 13. Functions of Several Variables 13.1 Introduction to Functions of Several Variables 13.2 Limits and Continuity 13.3 Partial Derivatives Section Project: Moire Fringes 13.4 Differentials 13.5 Chain Rules for Functions of Several Variables 13.6 Directional Derivatives and Gradients 13.7 Tangent Planes and Normal Lines Section Project: Wildflowers 13.8 Extrema of Functions of Two Variables 13.9 Applications of Extrema of Functions of Two Variables Section Project: Building a Pipeline 13.10 Lagrange Multipliers 14. Multiple Integration 14.1 Iterated Integrals and Area in the Plane 14.2 Double Integrals and Volume 14.3 Change of Variables: Polar Coordinates 14.4 Center of Mass and Moments of Inertia Section Project: Center of Pressure on a Sail 14.5 Surface Area Section Project: Capillary Action 14.6 Triple Integrals and Applications 14.7 Triple Integrals in Cylindrical and Spherical Coordinates Section Project: Wrinkled and Bumpy Spheres 14.8 Change of Variables: Jacobians 15. Vector Analysis 15.1 Vector Fields 15.2 Line Integrals 15.3 Conservative Vector Fields and Independence of Path 15.4 Green's Theorem Section Project: Hyperbolic and Trigonometric Functions 15.5 Parametric Surfaces 15.6 Surface Integrals Section Project: Hyperboloid of One Sheet 15.7 Divergence Theorem 15.8 Stokes's Theorem Section Project: The Planimeter Appendices A. Proofs of Selected Theorems B. Integration Tables C. Additional Topics in Differential Equations (Web only) C.1 Exact First-Order Equations C.2 Second-Order Homogeneous Linear Equations C.3 Second-Order Nonhomogeneous Linear Equations C.4 Series Solutions of Differential Equations D. Precalculus Review (Web only) D.1 Real Numbers and the Real Number Line D.2 The Cartesian Plane D.3 Review of Trigonometric Functions E. Rotation and the General Second-Degree Equation (Web only) F. Complex Numbers (Web only) G. Business and Economic Applications (Web only)