Calculus, Hybrid (with Enhanced WebAssign Homework and eBook LOE Printed Access Card for Multi Term Math and Science) / Edition 9 available in Paperback
- Pub. Date:
- Cengage Learning
Reflecting Cengage Learning's commitment to offering flexible teaching solutions and value for students and instructors, these new hybrid versions feature the instructional presentation found in the printed text while delivering end-of-section exercises online in Enhanced WebAssign. The resulta briefer printed text that engages students online! The Larson CALCULUS program has a long history of innovation in the calculus market. It has been widely praised by a generation of students and professors for its solid and effective pedagogy that addresses the needs of a broad range of teaching and learning styles and environments. Each title 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.
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 2014 William Holmes McGuffey Longevity Award for CALCULUS: EARLY TRANSCENDENTAL FUNCTIONS, the 2013 Text and Academic Authors Association Award for CALCULUS, 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 bestselling Calculus series published by Cengage.
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 Bogotá, 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. Professor Edwards has produced five mathematics courses for the Great Courses (The Teaching Company). He has also coauthored a wide range of award winning mathematics textbooks with Professor Ron Larson.
Table of Contents
1. PRELIMINARIES. Real Numbers and the Real Line. Lines, Circles, and Parabolas. Functions and Their Graphs. Identifying Functions; Mathematical Models. Combining Functions; Shifting and Scaling Graphs. Trigonometric Functions. Graphing with Calculators and Computers. 2. LIMITS AND DERIVATIVES. Rates of Change and Limits. Calculating Limits Using the Limit Laws. Precise Definition of a Limit. One-Sided Limits and Limits at Infinity. Infinite Limits and Vertical Asymptotes. Continuity. Tangents and Derivatives. 3. DIFFERENTIATION. The Derivative as a Function. Differentiation Rules. The Derivative as a Rate of Change. Derivatives of Trigonometric Functions. The Chain Rule and Parametric Equations. Implicit Differentiation. Related Rates. Linearization and Differentials. 4. APPLICATIONS OF DERIVATIVES. Extreme Values of Functions. The Mean Value Theorem. Monotonic Functions and the First Derivative Test. Concavity and Curve Sketching. Applied Optimization Problems. Indeterminate Forms and L'Hopital's Rule. Newton's Method. Antiderivatives. 5. INTEGRATION. Estimating with Finite Sums. Sigma Notation and Limits of Finite Sums. The Definite Integral. The Fundamental Theorem of Calculus. Indefinite Integrals and the Substitution Rule. Substitution and Area Between Curves. 6. APPLICATIONS OF DEFINITE INTEGRALS. Volumes by Slicing and Rotation About an Axis. Volumes by Cylindrical Shells. Lengths of Plane Curves. Moments and Centers of Mass. Areas of Surfaces of Revolution and The Theorems of Pappus. Work. Fluid Pressures and Forces. 7. TRANSCENDENTAL FUNCTIONS. Inverse Functions and their Derivatives. Natural Logarithms. The Exponential Function. ax and loga x. Exponential Growth and Decay. Relative Rates of Growth. Inverse Trigonometric Functions. Hyperbolic Functions. 8. TECHNIQUES OF INTEGRATION. Basic Integration Formulas. Integration by Parts. Integration of Rational Functions by Partial Fractions. Trigonometric Integrals. Trigonometric Substitutions. Integral Tables and Computer Algebra Systems. Numerical Integration. Improper Integrals. 9. FURTHER APPLICATIONS OF INTEGRATION. Slope Fields and Separable Differential Equations. First-Order Linear Differential Equations. Euler's Method. Graphical Solutions of Autonomous Equations. Applications of First-Order Differential Equations. 10. CONIC SECTIONS AND POLAR COORDINATES. Conic Sections and Quadratic Equations . Classifying Conic Sections by Eccentricity. Quadratic Equations and Rotations. Conics and Parametric Equations; The Cycloid. Polar Coordinates . Graphing in Polar Coordinates. Area and Lengths in Polar Coordinates. Conic Sections in Polar Coordinates. 11. INFINITE SEQUENCES AND SERIES. Sequences. Infinite Series. The Integral Test. Comparison Tests. The Ratio and Root Tests. Alternating Series, Absolute and Conditional Convergence. Power Series. Taylor and Maclaurin Series. Convergence of Taylor Series; Error Estimates. Applications of Power Series. Fourier Series. 12. VECTORS AND THE GEOMETRY OF SPACE. Three-Dimensional Coordinate Systems. Vectors. The Dot Product. The Cross Product. Lines and Planes in Space. Cylinders and Quadric Surfaces . 13. VECTOR VALUED FUNCTIONS AND MOTION IN SPACE. Vector Functions. Modeling Projectile Motion. Arc Length and the Unit Tangent Vector T. Curvature and the Unit Normal Vector N. Torsion and the Unit Binormal Vector B. Planetary Motion and Satellites. 14. PARTIAL DERIVATIVES. Functions of Several Variables. Limits and Continuity in Higher Dimensions. Partial Derivatives. The Chain Rule. Directional Derivatives and Gradient Vectors. Tangent Planes and Differentials. Extreme Values and Saddle Points. Lagrange Multipliers. Partial Derivatives with Constrained Variables. Taylor's Formula for Two Variables. 15. MULTIPLE INTEGRALS. Double Integrals. Areas, Moments and Centers of Mass. Double Integrals in Polar Form. Triple Integrals in Rectangular Coordinates. Masses and Moments in Three Dimensions. Triple Integrals in Cylindrical and Spherical Coordinates. Substitutions in Multiple Integrals. 16. INTEGRATION IN VECTOR FIELDS. Line Integrals. Vector Fields, Work, Circulation, and Flux. Path Independence, Potential Functions, and Conservative Fields. Green's Theorem in the Plane. Surface Area and Surface Integrals. Parametrized Surfaces. Stokes' Theorem. The Divergence Theorem and a Unified Theory. APPENDICES. Mathematical Induction. Proofs of Limit Theorems. Commonly Occurring Limits . Theory of the Real Numbers. Complex Numbers. The Distributive Law for Vector Cross Products. Determinants and Cramer's Rule. The Mixed Derivative Theorem and the Increment Theorem. The Area of a Parallelogram's Projection on a Plane.