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Calculus of a Single Variable Ron Larson

Calculus of a Single Variable By Ron Larson

Calculus of a Single Variable by Ron Larson


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Summary

Suitable for students and professors, this title addresses the needs of a broad range of teaching and learning styles and environments. It is just one component in a comprehensive calculus course program that carefully integrates and coordinates print, media, and technology products for successful teaching and learning.

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Calculus of a Single Variable Summary

Calculus of a Single Variable by Ron Larson

For the 9th edition of CALCULUS, the authors analyzed the copious student usage data they receive from their website. The authors analyzed student downloads to completely revise and refined the exercise sets based on this analysis. The result is the only calculus book on the market that uses real data about its exercises to address student needs.

About Ron Larson

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 2014 William Holmes McGuffey Longevity Award for CALCULUS: EARLY TRANSCENDENTAL FUNCTIONS, the 2014 Text and Academic Authors Association TEXTY Award for PRECALCULUS, the 2012 William Holmes McGuffey Longevity Award for CALCULUS: AN APPLIED APPROACH, 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. Dr. Bruce H. Edwards is Professor of Mathematics at the University of Florida. Professor Edwards received his B.S. in Mathematics from Stanford University and his Ph.D. in Mathematics from Dartmouth College. He taught mathematics at a university near Bogota, Colombia, as a Peace Corps volunteer. While teaching at the University of Florida, Professor Edwards has won many teaching awards, including Teacher of the Year in the College of Liberal Arts and Sciences, Liberal Arts and Sciences Student Council Teacher of the Year, and the University of Florida Honors Program Teacher of the Year. He was selected by the Office of Alumni Affairs to be the Distinguished Alumni Professor for 1991-1993. Professor Edwards has taught a variety of mathematics courses at the University of Florida, from first-year calculus to graduate-level classes in algebra and numerical analysis. He has been a frequent speaker at research conferences and meetings of the National Council of Teachers of Mathematics. He has also coauthored a wide range of award winning mathematics textbooks with Professor Ron Larson.

Table of Contents

P. PREPARATION FOR CALCULUS. Graphs and Models. Linear Models and Rates of Change. Functions and Their Graphs. Fitting Models to Data Review Exercises P.S. Problem Solving. 1. 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 Trigonometric Functions Review Exercises P.S. Problem Solving. 2. 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 Review Exercises P.S. Problem Solving. 3. APPLICATIONS OF DIFFERENTIATION. Extrema on an Interval. Rolles Theorem and the Mean Value Theorem. Increasing and Decreasing Functions and the First Derivative Test Section Project: Rainbows. Concavity and the Second Derivative Test. Limits at Infinity. A Summary of Curve Sketching. Optimization Problems Section Project: Connecticut River. Newtons Method. Differentials Review Exercises P.S. Problem Solving. 4. 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 Review Exercises P.S. Problem Solving. 5. LOGARITHMIC, EXPONENTIAL, AND OTHER TRANSCENDENTAL FUNCTIONS. The Natural Logarithmic Function: Differentiation. The Natural Logarithmic Function: Integration. Inverse Functions. Exponential Functions: Differentiation and Integration. Bases Other than e and Applications Section Project: Using Graphing Utilities to Estimate Slope. Inverse Trigonometric Functions: Differentiation. Inverse Trigonometric Functions: Integration. Hyperbolic Functions Section Project: St. Louis Arch Review Exercises P.S. Problem Solving. 6. Differential Equations Slope Fields and Eulers Method. Differential Equations: \\Growth and Decay. Separation of Variables and the Logistic Equation. First-Order Linear Differential Equations Section Project: Weight Loss Review Exercises P.S. Problem Solving. 7. Applications of Integration Area of a Region Between Two Curves. Volume: The Disk Method. Volume: The Shell Method Section Project: Saturn. Arc Length and Surfaces of Revolution. Work Section Project: Tidal Energy. Moments, Centers of Mass, and Centroids. Fluid Pressure and Fluid Force Review Exercises P.S. Problem Solving. 8. Integration Techniques, LHopitals Rule, and Improper Integrals Basic Integration Rules. Integration by Parts. Trigonometric Integrals Section Project: Power Lines. Trigonometric Substitution. Partial Fractions. Integration by Tables and Other Integration Techniques. Indeterminate Forms and LHopitals Rule. Improper Integrals Review Exercises P.S. Problem Solving. 9. Infinite Series Sequences. Series and Convergence Section Project: Cantors Disappearing Table. The Integral Test and p-Series Section Project: The Harmonic Series. Comparisons of Series Section Project: Solera Method. Alternating Series. The Ratio and Root Tests. Taylor Polynomials and Approximations. Power Series. Representation of Functions by Power Series. Taylor and Maclaurin Series Review Exercises P.S. Problem Solving. 10. CONICS, PARAMETRIC EQUATIONS, AND POLAR COORDINATES. Conics and Calculus. Plane Curves and Parametric Equations Section Project: Cycloids. Parametric Equations and Calculus. Polar Coordinates and Polar Graphs Section Project: Anamorphic Art. Area and Arc Length in Polar Coordinates. Polar Equations of Conics and Keplers Laws Review Exercises P.S. Problem Solving. BOOK APPENDICES. A. Proofs of Selected Theorems. B. Integration Tables. ONLINE APPENDICES. C. Precalculus Review (please visit URL to come) C.1 Real Numbers and the Real Number Line C.2 The Cartesian Plane C.3 Review of Trigonometric Functions. D. Rotation and the General Second-Degree Equation (please visit URL to come). E. Complex Numbers (please visit URL to come). F. Business and Economic Applications (please visit URL to come).

Additional information

CIN0547209983VG
9780547209982
0547209983
Calculus of a Single Variable by Ron Larson
Used - Very Good
Hardback
Cengage Learning, Inc
20081101
912
N/A
Book picture is for illustrative purposes only, actual binding, cover or edition may vary.
This is a used book - there is no escaping the fact it has been read by someone else and it will show signs of wear and previous use. Overall we expect it to be in very good condition, but if you are not entirely satisfied please get in touch with us

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