Calculus: Single Variable, 5th Edition
ISBN: 9780470089156 | 0470089156
Edition: 5thFormat: Paperback
Publisher: Wiley
Pub. Date: 12/1/2008
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Work more effectively and gauge your progress as you go along! This Student Study Guide is designed to accompany Hughes-Hallett's "Calculus: Single Variable, 4th Edition." It contains additional study aids for students that are tied directly to the text. Now in its Fourth Edition, Hughes-Hallett's Calculus: Single Variable reflects the strong consensus within the mathematics community for a balance between contemporary and traditional ideas. Building on previous work, it brings together the best of both new and traditional curricula in an effor... MORE
| 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 | |
| Theorems about Differentiable Functions | |
| Review Problems | |
| Check Your Understanding | |
| Projects: Rule of 70, Newtonâ s 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 hopitalâ s 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 s 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 s 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 s Formula and the Value of pi, Approximation the Derivative | |
| Differential Equations | |
| What Is a Differential Equation? | |
| Slope Fields | |
| Eulerâ s 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 s Law, Vibrations in a Molecule | |
| Table of Contents provided by Publisher. All Rights Reserved. |
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