Calculus: Single Variable, 5th Edition
by Deborah Hughes-Hallett; Andrew M. Gleason (Harvard Univ.); William G. McCallum (Univ. of Arizona); David O. Lomen (Univ. of Arizona); David Lovelock (Univ. of Arizona); Jeff Tecosky-Feldman (Haverford College); Thomas W. Tucker (Colgate Univ.); DanieEdition: 5th
Format: Hardcover
Pub. Date: 2008-12-01
Publisher(s): Wiley
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Summary
Calculus teachers recognize Calculus as the leading resource among the "reform" projects that employ the rule of four and streamline the curriculum in order to deepen conceptual understanding. The fifth edition uses all strands of the "Rule of Four" graphical, numeric, symbolic/algebraic, and verbal/applied presentations to make concepts easier to understand. The book focuses on exploring fundamental ideas rather than comprehensive coverage of multiple similar cases that are not fundamentally unique. Readers will also gain access to WileyPLUS, an online tool that allows for extensive drills and practice. Calculus teachers will build on their understanding in the field and discover new ways to present concepts to their students.
Table of Contents
| A Library Of Functions | |
| Functions and Change | |
| Exponential Functions | |
| New Functions from Old | |
| Logarithmic Functions | |
| Trigonometric Functions | |
| Powers, Polynomials, and Rational Functions | |
| Introduction to Continuity | |
| Limits | |
| Review Problems | |
| Check Your Understanding | |
| Projects: Matching Functions to Data, Which Way Is the Wind Blowing? | |
| Key Concept: The Derivative | |
| How Do We Measure Speed? | |
| The Derivative at a Point | |
| The Derivative Function | |
| Interpretations of the Derivative | |
| The Second Derivative | |
| Differentiability | |
| Review Problems | |
| Check Your Understanding | |
| Projects: Hours of Daylight as a Function of Latitude, US Population | |
| Short-Cuts To Differentiation | |
| Powers and Polynomials | |
| The Exponential Function | |
| The Product and Quotient Rules | |
| The Chain Rule | |
| The Trigonometric Functions | |
| The Chain Rule and Inverse Functions | |
| Implicit Functions | |
| Hyperbolic Functions | |
| Linear Approximation and the Derivative | |
| Review Problems | |
| Check Your Understanding | |
| Projects: Rule of 70, Newtonâ Ös Method | |
| Using The Derivative | |
| Using First and Second Derivatives | |
| Optimization | |
| Families of Functions | |
| Optimization, Geometry, and Modeling | |
| Applications to Marginality | |
| Rates and Related Rates | |
| Lâ Öhopitalâ Ös Rule, Growth, and Dominance | |
| Parametric Equations | |
| Review Problems | |
| Check Your Understanding | |
| Projects: Building a Greenhouse, Fitting a Line to Data, Firebreaks | |
| Key Concept: The Definite Integral | |
| How Do We Measure Distance Traveled? | |
| The Definite Integral | |
| The Fundamental Theorem and Interpretations | |
| Theorems about Definite Integrals | |
| Review Problems | |
| Check Your Understanding | |
| Projects: The Car and the Truck, An Orbiting Satellite | |
| Constructing Antiderivatives | |
| Antiderivatives Graphically and Numerically | |
| Constructing Antiderivatives Analytically | |
| Differential Equations | |
| Second Fundamental Theorem of Calculus | |
| The Equations of Motion | |
| Review Problems | |
| Check Your Understanding | |
| Projects: Distribution of Resources, Yield from an Apple Orchard, Slope Fields | |
| Integration | |
| Integration by Substitution | |
| Integration by Parts | |
| Tables of Integrals | |
| Algebraic Identities and Trigonometric Substitutions | |
| Approximating Definite Integrals | |
| Approximation Errors and Simpsonâ Ös Rule | |
| Improper Integrals | |
| Comparison of Improper Integrals | |
| Review Problems | |
| Check Your Understanding | |
| Projects: Taylor Polynomial Inequalities | |
| Using The Definite Integral | |
| Areas and Volumes | |
| Applications to Geometry | |
| Area and Arc Length in Polar Coordinates | |
| Density and Center of Mass | |
| Applications to Physics | |
| Applications to Economics | |
| Distribution Functions | |
| Probability, Mean, and Median | |
| Review Problems | |
| Check Your Understanding | |
| Projects: Volume Enclosed by Two Cylinders, Length of a Hanging Cable, Surface Area of an Unpaintable Can of Paint, Maxwellâ Ös Distribution of Molecular Velocities | |
| Sequences And Series | |
| Sequences | |
| Geometric Series | |
| Convergence of Series | |
| Tests for Convergence | |
| Power Series and Interval of Convergence | |
| Review Problems | |
| Check Your Understanding | |
| Projects: A Definition of e, Probability of Winning in Sports, Prednisone | |
| Approximating Functions Using Series | |
| Taylor Polynomials | |
| Taylor Series | |
| Finding and Using Taylor Series | |
| The Error in Taylor Polynomial Approximations | |
| Fourier Series | |
| Review Problems | |
| Check Your Understanding | |
| Projects: Shape of Planets, Machinâ Ös Formula and the Value of pi, Approximation the Derivative | |
| Differential Equations | |
| What Is a Differential Equation? | |
| Slope Fields | |
| Eulerâ Ös Method | |
| Separation of Variables | |
| Growth and Decay | |
| Applications and Modeling | |
| The Logistic Model | |
| Systems of Differential Equations | |
| Analyzing the Phase Plane | |
| Second-Order Differential Equations: Oscillations | |
| Linear Second-Order Differential Equations | |
| Review Problems | |
| Check Your Understanding | |
| Projects: SARS Predictions for Hong Kong, A S-I-R Model for SARS, Paretoâ Ös Law, Vibrations in a Molecule | |
| Table of Contents provided by Publisher. All Rights Reserved. |
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