Calculus, 3rd Edition, Single Variable, Student Solutions Manual, 3rd Edition
by Deborah Hughes-Hallett (Univ. of Arizona); Andrew M. Gleason (Harvard Univ.); Daniel E. Flath (Univ. of South Alabama); Patti Frazer Lock (St. Lawrence Univ.); Sheldon P. Gordon (SUNY at Framingdale); David O. Lomen (Univ. of Arizona); David LovelocEdition: 3rd
Format: Paperback
Pub. Date: 2002-01-01
Publisher(s): Wiley
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Summary
The new edition exhibits the same strengths from earlier editions including the Rule of Four, an emphasis on modeling, exposition that students can read and understand and a flexible approach to technology. The conceptual and modeling problems, praised for their creativity and variety, continue to motivate and challenge students.
Table of Contents
| A Library of Functions | |
| Functions and Chang | |
| Material from former | |
| And 1.2 | |
| Exponential Functions Material from former | |
| And 1.7 | |
| New Functions from Old Material from former | |
| And 1.8 | |
| Logarithmic Functions Material from former | |
| And 1.7 | |
| Trigonometric Functions Former 1.9 | |
| Powers, Polynomials, and Rational Functions Material from former | |
| And 1.10 | |
| Introduction to Continuity Former | |
| Including Intermediate Value Theorem | |
| The Binomial Theorem is now a section available on the web site | |
| Key Concept: The Derivative | |
| How Do We Measure Speed? | |
| Limits NEW section from former Focus on Theory section | |
| The Derivative at a Point | |
| The Derivative Function | |
| Interpretations of the Derivative | |
| The Second Derivative | |
| Continuity and Differentiability NEW section from former Focus on Theory section | |
| Short-Cuts to Differentiation | |
| Powers and Polynomials | |
| The Exponential Function | |
| The Product and Quotient Rules | |
| The Chain Rule | |
| The Trigonometric Functions | |
| Applications of the Chain Rule | |
| Implicit Functions | |
| Parametric Equations NEW: Material on Motion and Parametric Curves and Differentiation based on Appendix F and G and 16.1 | |
| Linear Approximations and the Derivative NEW: Material on Estimating the Error in the Approximation and theory on Differentiability and Local Linearity included | |
| Using Local Linearity to Find Limits Includes L"Hopital"s rule | |
| New | |
| Using the Derivative | |
| Using First and Second Derivatives | |
| Families of Curves | |
| Optimization | |
| Applications to Marginality | |
| More Optimization: Introduction to Modeling | |
| Hyperbolic Functions | |
| Theorems about Continuous and Differentiable Functions NEW | |
| Extreme Value Theorem, Local Extrema and Critical Points, Mean Value Theorem, Increasing Function Theorem, Constant Function Theorem, Racetrack Principle | |
| Key Concept: The Definite Integral | |
| How Do We Measure Distance Traveled? | |
| The Definite Integral Now includes general Riemann sum | |
| Interpretations of the Definite Integral Material about integrating rates of change is now in this section | |
| Theorems About Definite Integrals | |
| Constructing Antiderivatives | |
| Antiderivatives Graphically and Numerically | |
| Constructing Antiderivatives Analytically | |
| Differential Equations | |
| Second Fundamental Theorem of Calculus | |
| The Equations of Motion Former Focus on Modeling Section | |
| Integration | |
| Integration by Substitution | |
| Integration by Parts | |
| Tables of Integrals | |
| Algebraic Identities and Trigonometric Substitutions | |
| NEW section including partial factions and trigonometric substitutions involving completing the square | |
| Approximating Definite Integrals | |
| Approximating Errors and Simpson"s Rule | |
| Improper Integrals | |
| More on Improper Integrals | |
| Using the Definite Integral | |
| Areas and Volumes | |
| More accessible introduction to setting up integrals focusing on basic concepts | |
| Applications to Geometry | |
| Section simplified and made easier to use | |
| Density and Center of Mass Material on Center of Mass expanded | |
| Applications to Physics | |
| Applications to Economics | |
| Distribution Functions | |
| Probability and More on Distributions Note | |
| And 10 replace | |
| In the 2nd edition | |
| The material has been expanded and extensively reorganized and rewritten | |
| All sections have new problems | |
| Material is clearly divided between series and convergence (Chapter 9) and approximations of functions (Chapter 10) for users who wish to emphasize one or the other | |
| Series | |
| Geometric Series Former 9.4 | |
| Convergence of Sequences and Series NEW section from former Focus on Theory | |
| New material on integral test added | |
| Tests for Convergence From Focus on Theory section with substantial new material on integral test, ratio test, and alternating series added | |
| Power Series Material from former | |
| With substantial new material on intervals and radius of convergence added | |
| Approximating Functions | |
| Taylor Polynomials First part of former 9.1 | |
| Taylor Series Second part of former | |
| And 9.2 | |
| Finding and Using Series Former 9.3 | |
| The Error in Taylor Polynomial Approximations Former Focus on Theory section, substantially rewritten | |
| Fourier Series | |
| Differential Equations | |
| What Is a Differential Equation? | |
| Slope Fields | |
| Euler"s Method | |
| Separation of Variables | |
| Growth and Decay | |
| Applications and Modeling | |
| Models of Population Growth | |
| Systems of Differential Equations | |
| Analyzing the Phase Plane | |
| Second-Order Differential Equations: Oscillations | |
| Linear Second-Order Differential Equations | |
| Functions of Several Variables | |
| Functions of Two Variable? | |
| Former | |
| And 11.2 | |
| Graphs of Functions of Two Variables | |
| Contour Diagrams | |
| Linear Functions | |
| Functions of More than Two Variables | |
| Limits and Continuity | |
| NEW section from former Focus on Theory section | |
| A Fundamental Tool: Vectors | |
| Displacement Vectors | |
| Vectors in General | |
| The Dot Product | |
| The Cross Product | |
| Differentiating Functions of Many Variables | |
| The Partial Derivative | |
| Computing Partial Derivatives Algebraically | |
| Local Linearity and the Differential | |
| Gradients and Directional Derivatives in the Plane | |
| Gradients and Directional Derivatives in Space | |
| The Chain Rule | |
| Second Order Partial Derivatives | |
| Differentiability and Error Bounds | |
| Optimization: Local and Global Extrema | |
| Local Extrema | |
| Global Extrema:Unconstrained Optimization | |
| Constrained Optimization: Lagrange Multipliers | |
| Integrating Functions of Many Variables | |
| The Definite Integral of a Function of Two Variables | |
| Iterated Integrals | |
| Triple Integrals | |
| Double Integrals in Polar Coordinates | |
| Integrals in Cylindrical and Spherical Coordinates | |
| Applications of Integrationto Probability | |
| Change of Variables in a Multiple Integral NEW section from former Focus on Theory section | |
| Parameterized Curves and Vector Fields | |
| Parameterized Curves | |
| Motion, Velocity, and Acceleration | |
| Vector Fields | |
| The Flow of a Vector Field | |
| Line Integrals | |
| The Idea of a Line Integral | |
| Computing Line Integrals Over Parameterized Curves | |
| Gradient Fields and Path-Independent Fields | |
| Path-Independent Vector Fields and Green"s Theorem | |
| Proof of Green"s Theorem | |
| NEW section from former Focus on Theory section | |
| Flux Integrals | |
| The Idea of a Flux Integral | |
| Flux Integrals for Graphs, Cylinders, and Spheres | |
| Table of Contents provided by Publisher. All Rights Reserved. |
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