Single Variable Calculus, Hybrid (with Enhanced WebAssign Homework and eBook LOE Printed Access Card for Multi Term Math and Science) / Edition 9by Ron Larson, Bruce H. Edwards
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 result--a briefer printed text that engages students online! The Larson… See more details below
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 result--a 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.
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. Rolle's 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. Newton's 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 Euler's 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, L'Hopital's 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 L'Hopital's Rule. Improper Integrals Review Exercises P.S. Problem Solving. 9. Infinite Series Sequences. Series and Convergence Section Project: Cantor's 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 Kepler's Laws Review Exercises P.S. Problem Solving. BOOK APPENDICES. A. Proofs of Selected Theorems. B. Integration Tables.
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