Calculus of a Single Variable: Early Transcendental Functions

Hardcover

ISBN 10: 0618606254 ISBN 13: 9780618606252

Publisher: Brooks Cole, 2006

Designed for the first two semesters of a three-semester engineering calculus course, Calculus of a Single Variable: Early Transcendental Functions, 4/e, continues to offer instructors and students innovative teaching and learning resources. Two primary objectives guided the authors in the revision of 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 save time. The Larson/Hostetler/Edwards Calculus program offers a solution to address the needs of any calculus course and any level of calculus student.Calculus of a Single Variable: Early Transcendental Functions, 4/e, contains Chapters 1-10 of the full Calculus: Early Transcendental Functions, 4/e, text. Every edition from the first to the fourth of Calculus: Early Transcendental Function, 4/e, 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 Fourth Edition is part of the first calculus program to offer algorithmic homework and testing created in Maple so that answers can be evaluated with complete mathematical accuracy.

About the Author:

Dr. Ron Larson is a professor of mathematics at The Pennsylvania State University, where he has taught since 1970. He received his Ph.D. in mathematics from the University of Colorado and is considered the pioneer of using multimedia to enhance the learning of mathematics, having authored over 30 software titles since 1990. Dr. Larson conducts numerous seminars and in-service workshops for math educators around the country about using computer technology as an instructional tool and motivational aid. He is the recipient of the 2013 Text and Academic Authors Association Award for CALCULUS, the 2012 William Holmes McGuffey Longevity Award for CALCULUS: AN APPLIED APPROACH, the 2011 William Holmes McGuffey Longevity Award for PRECALCULUS: REAL MATHEMATICS, REAL PEOPLE, and the 1996 Text and Academic Authors Association TEXTY Award for INTERACTIVE CALCULUS (a complete text on CD-ROM that was the first mainstream college textbook to be offered on the Internet). Dr. Larson authors numerous textbooks including the best-selling Calculus series published by Cengage Learning.

Review:

Note: Each chapter concludes with Review Exercises and P.S. Problem Solving. 1. Preparation for Calculus 1.1 Graphs and Models 1.2 Linear Models and Rates of Change 1.3 Functions and Their Graphs 1.4 Fitting Models to Data 1.5 Inverse Functions 1.6 Exponential and Logarithmic Functions 2. Limits and Their Properties 2.1 A Preview of Calculus 2.2 Finding Limits Graphically and Numerically 2.3 Evaluating Limits Analytically 2.4 Continuity and One-Sided Limits 2.5 Infinite Limits Section Project: Graphs and Limits of Trigonometric Functions 3. Differentiation 3.1 The Derivative and the Tangent Line Problem 3.2 Basic Differentiation Rules and Rates of Change 3.3 The Product and Quotient Rules and Higher-Order Derivatives 3.4 The Chain Rule 3.5 Implicit Differentiation Section Project: Optical Illusions 3.6 Derivatives of Inverse Functions 3.7 Related Rates 3.8 Newton's Method 4. Applications of Differentiation 4.1 Extrema on an Interval 4.2 Rolle's Theorem and the Mean Value Theorem 4.3 Increasing and Decreasing Functions and the First Derivative Test Section Project: Rainbows 4.4 Concavity and the Second Derivative Test 4.5 Limits at Infinity 4.6 A Summary of Curve Sketching 4.7 Optimization Problems Section Project: Connecticut River 4.8 Differentials 5. Integration 5.1 Antiderivatives and Indefinite Integration 5.2 Area 5.3 Riemann Sums and Definite Integrals 5.4 The Fundamental Theorem of Calculus Section Project: Demonstrating the Fundamental Theorem 5.5 Integration by Substitution 5.6 Numerical Integration 5.7 The Natural Logarithmic Function: Integration 5.8 Inverse Trigonometric Functions: Integration 5.9 Hyperbolic Functions Section Project: St. Louis Arch 6. Differential Equations 6.1 Slope Fields and Euler's Method 6.6 Differential Equations: Growth and Decay 6.7 Differential Equations: Separation of Variables 6.4 The Logistic Equation 6.5 First-Order Linear Differential Equations Section Project: Weight Loss 6.6 Predator-Prey Differential Equations 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'Hopital'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'Hopital'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 Appendices Appendix A Proofs of Selected Theorems Appendix B Integration Tables Appendix C Business and Economic Applications Additional Appendices The following appendices are available at the textbook website, on the HM mathSpace Student CD-ROM, and the HM ClassPrep with HM Testing CD-ROM. Appendix D Precalculus Review Appendix E Rotation and General Second-Degree Equation Appendix F Complex Numbers