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ISBN-10: 1305266633

ISBN-13: 9781305266636

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**Assessment Book for Single Variable Calculus, 8th Edition, by James Stewart, ISBN-10: 1305266633, ISBN-13: 9781305266636**

**Table of Contents**

Preface.

Addressed to the Student.

Diagnostic Assessments.

Previewing Calculus.

1. FUNCTIONS AND LIMITS.

4 Approaches to Represent a Function.

Numerical Models: A List of Essential Functions.

New Functions derived from Existing Functions.

The Slope and Speed Problems.

The Boundary of a Function.

Compute Limits Using the Boundary Laws.

The Precise Description of a Limit.

Continuity.

Review.

Principles of Problem Solving.

2. DERIVATIVES.

Differentiation and Rates of Change.

Writing Assignment: Early Approaches to Finding Tangents.

The Derivative as a Function.

Differentiation Formulas.

Applied Problem: Constructing a Better Roller Coaster.

Derivatives of Trigonometric Functions.

The Chain Rule.

Applied Problem: Where Should a Pilot Begin Descent?

Implicit Differentiation.

Laboratory Task: Families of Implicit Curves.

Rates of Change in the Natural and Social Sciences.

Related Rates.

Linear Approximations and Differentials.

Laboratory Task: Taylor Polynomials.

Review.

Problems Addendum.

3. APPLICATION OF DIFFERENTIATION.

Maximum and Minimum Values.

Applied Problem: The Calculus of Rainbows.

The Mean Value Theorem.

How Derivatives Influence the Shape of a Graph.

Limits at Infinity; Horizontal Asymptotes.

Summary of Curve Sketching.

Graphing with Calculus and Calculators.

Optimization Problems.

Applied Problem: The Shape of a Can.

Applied Problem: Planes and Birds: Minimizing Energy.

Newton’s Method.

Antiderivatives.

Review.

Problems Addendum.

4. INTEGRALS.

Areas and Distances.

The Definite Integral.

Discovery Task: Area Functions.

The Fundamental Theorem of Calculus.

Indefinite Integrals and the Net Change Theorem.

Writing Assignment: Newton, Leibniz, and the Invention of Calculus.

The Substitution Rule.

Review.

Problems Addendum.

5. APPLICATIONS OF INTEGRATION.

Areas Between Curves.

Applied Problem: The Gini Index.

Volumes.

Volumes by Cylindrical Shells.

Work.

Average Value of a Function.

Applied Problem: Calculus and Baseball.

Review.

Problems Addendum.

6. INVERSE FUNCTIONS: EXPONENTIAL, LOGARITHMIC, AND INVERSE TRIGONOMETRIC FUNCTIONS.

Inverted Functions.

Instructors may cover either Sections 6.2-6.4 or Sections 6.2*-6.4*

Exponential Functions and Their Derivatives.

Logarithmic Functions.

Derivatives of Logarithmic Functions.

The Natural Logarithmic Function

The Natural Exponential Function.

Standard Logarithmic and Exponential Functions.

Exponential Growth and Decay.

Applied Problem: Controlling Red Blood Cell Loss During Surgery.

Inverse Trigonometric Functions.

Applied Problem: Where to Sit at the Movies.

Hyperbolic Functions.

Indeterminate Forms and l’Hospital’s Rule.

Writing Assignment: The Origins of l’ Hospital’s Rule

Review.

Problems Addendum.

7. INTEGRATION TECHNIQUES.

Integration by Parts.

Trigonometric Integrals.

Trigonometric Substitution.

Integration of Rational Functions by Partial Fractions.

Method for Integration.

Integration Using Tables and Computer Algebra Systems.

Discovery Task: Patterns in Integrals.

Approximate Integration.

Improper Integrals.

Review.

Problems Addendum.

8. FURTHER APPLICATIONS OF INTEGRATION.

Arc Length.

Discovery Task: Arc Length Contest.

Area of a Surface of Revolution.

Discovery Task: Rotating on a Slant.

Applications to Physics and Engineering.

Discovery Task: Complementary Coffee Cups.

Applications to Economics and Biology.

Probability.

Review.

Problems Addendum.

9. DIFFERENTIAL EQUATIONS.

Modeling with Differential Equations.

Path Fields and Euler’s Method.

Separable Equations.

Applied Problem: How Fast Does a Tank Drain?

Applied Problem: Which is Faster, Going Up or Coming Down?

Models for Population Growth.

Linear Equations.

Predator-Prey Systems.

Review.

Problems Addendum.

10. PARAMETRIC EQUATIONS AND POLAR COORDINATES.

Curves Defined by Parametric Equations.

Laboratory Task: Running Circles Around Circles.

Calculus with Parametric Curves.

Laboratory Task: Bézier Curves.

Polar Coordinates.

Laboratory Task: Families of Polar Curves.

Areas and Lengths in Polar Coordinates.

Conic Sections.

Conic Sections in Polar Coordinates.

Review.

Problems Addendum.

11. INFINITE SEQUENCES AND SERIES.

Sequences.

Laboratory Task: Logistic Sequences.

Sequence.

The Integral Test and Estimates of Sums.

The Comparison Tests.

Alternating Series.

Absolute Convergence and the Ratio and Root Tests.

Method for Testing Series.

Power Series.

Representations of Functions as Power Series.

Taylor and Maclaurin Series.

Laboratory Task: An Elusive Limit.

Writing Assignment: How Newton Discovered the Binomial Series.

Applications of Taylor Polynomials.

Applied Problem: Radiation from the Stars.

Review.

Problems Addendum.

APPENDIXES.

A Numbers, Inequalities, and Absolute Values.

B Coordinate Geometry and Lines.

C Graphs of Second-Degree Equations.

D Trigonometry.

E Sigma Notation.

F Proofs of Theorems.

G Complex Numbers.

H Answers to Odd-Numbered Exercises.

INDEX.

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