Calculus : Early Transcendentls 8/e (stewart 성균관대)

.Preface
.To the Student.
.Diagnostic Tests
.Calculuators, Computers, and other Graphing Devices

.A Preview of Calculus
1. FUNCTIONS AND MODELS
1.1 Four Ways to Represent a Function
1.2 Mathematical Models: A Catalog of Essential Functions
1.3 New Functions from Old Functions
1.4 Exponential Functions
1.5 Inverse Functions and Logarithms
. Review
. Principles of Problem Solving

2. LIMITS AND DERIVATIVES
2.1 The Tangent and Velocity Problems
2.2 The Limit of a Function
2.3 Calculating Limits Using the Limit Laws
2.4 The Precise Definition of a Limit
2.5 Continuity
2.6 Limits at Infinity; Horizontal Asymptotes
2.7 Derivatives and Rates of Change
.Writing Project: Early Methods for Finding Tangents
2.8 The Derivative as a Function
.Review.
.Problems Plus.

3. DIFFERENTIATION RULES
3.1 Derivatives of Polynomials and Exponential Functions
. Applied Project: Building a Better Roller Coaster.
3.2 The Product and Quotient Rules
3.3 Derivatives of Trigonometric Functions
3.4 The Chain Rule
. Applied Project: Where Should a Pilot Start Descent?
3.5 Implicit Differentiation
. Laboratory Project: Families of Implicit Curves
3.6 Derivatives of Logarithmic Functions
3.7 Rates of Change in the Natural and Social Sciences
3.8 Related Rates
3.9 Linear Approximations and Differentials. Laboratory Project: Taylor Polynomials
3.10 Hyperbolic Functions
. Review
. Problems Plus.

4. APPLICATIONS OF DIFFERENTIATION
4.1 Maximum and Minimum Values
. Applied Project: The Calculus of Rainbows
4.2 The Mean Value Theorem
4.3 How Derivatives Affect the Shape of a Graph
4.4 Indeterminate Forms and l'Hospital's Rule
. Writing Project: The Origins of l'Hospital's Rule
4.5 Summary of Curve Sketching
4.6 Optimization Problems
. Applied Project: The Shape of a Can
. Applied Project: Planes and Birds: Minimizing Energy
4.7 Newton's Method
4.8 Antiderivatives
. Review
. Problems Plus

5. INTEGRALS
5.1 Areas and Distances
5.2 The Definite Integral. Discovery Project: Area Functions
5.3 The Fundamental Theorem of Calculus
5.4 Indefinite Integrals and the Net Change Theorem
. Writing Project: Newton, Leibniz, and the Invention of Calculus
5.5 The Substitution Rule. Review.
.Problems Plus

6. APPLICATIONS OF INTEGRATION
6.1 Areas Between Curves. Applied Project: The Gini Index.
6.2 Volume
6.3 Volumes by Cylindrical Shells
6.4 Work
6.5 Average Value of a Function
. Applied Project: Calculus and Baseball
. Applied Project: Where to Sit at the Movies
. Review
. Problems Plus.

7. TECHNIQUES OF INTEGRATION
7.1 Integration by Parts
7.2 Trigonometric Integrals
7.3 Trigonometric Substitution
7.4 Integration of Rational Functions by Partial Fractions
7.5 Strategy for Integration
7.6 Integration Using Tables and Computer Algebra Systems
. Discovery Project: Patterns in Integrals
7.7 Approximate Integration
7.8 Improper Integrals
. Review
. Problems Plus.

8. FURTHER APPLICATIONS OF INTEGRATION
8.1 Arc Length
. Discovery Project: Arc Length Contest
8.2 Area of a Surface of Revolution
. Discovery Project: Rotating on a Slant
. Theorem of Pappus
. Discovery Project: Complementary Coffee Cups
. Review
. Problems Plus.

9. PARAMETRIC EQUATIONS AND POLAR COORDINATES
9.1 Curves Defined by Parametric Equations
. Laboratory Project: Running Circles Around Circles
9.2 Calculus with Parametric Curves
. Laboratory Project: Bezier Curves
9.3 Polar Coordinates
. Laboratory Project: Families of Polar Curves
9.4 Areas and Lengths in Polar Coordinates
9.5 Conic Sections
9.6 Conic Sections in Polar Coordinates
. Review
. Problems Plus

10. INFINITE SEQUENCES AND SERIES
10.1 Sequences
. Laboratory Project: Logistic Sequences
10.2 Series
10.3 The Integral Test and Estimates of Sums
10.4 The Comparison Tests
10.5 Alternating Series
10.6 Absolute Convergence and the Ratio and Root Tests
10.7 Strategy for Testing Series
10.8 Power Series
10.9 Representations of Functions as Power Series
10.10 Taylor and Maclaurin Series
. Laboratory Project: An Elusive Limit
. Writing Project: How Newton Discovered the Binomial Series
10.11 Applications of Taylor Polynomials
. Applied Project: Radiation from the Stars
. Review.
.Problems Plus.

11. VECTORS AND THE GEOMETRY OF SPACE
11.1 Three-Dimensional Coordinate Systems
11.2 Vectors
11.3 The Dot Product
11.4 The Cross Product
. Discovery Project: The Geometry of a Tetrahedron
11.5 Equations of Lines and Planes
. Laboratory Project: Putting 3D in perspective
11.6 Cylinders and Quadric Surfaces
. Review
. Problems Plus

12. VECTOR FUNCTIONS
12.1 Vector Functions and Space Curves
12.2 Derivatives and Integrals of Vector Functions
12.3 Arc Length and Curvature
12.4 Motion in Space: Velocity and Acceleration
. Applied Project: Kepler's Laws
. Review
. Problems Plus

13. PARTIAL DERIVATIVES
13.1 Functions of Several Variables
13.2 Limits and Continuity
13.3 Partial Derivatives
13.4 Tangent Planes and Linear Approximation
. Applied Project: The Speedo LZR Race
13.5 The Chain Rule
13.6 Directional Derivatives and the Gradient Vector
13.7 Maximum and Minimum Values
. Applied Project: Designing a Dumpster
. Discovery Project: Quadratic Approximations and Critical Points
13.8 Lagrange Multipliers
. Applied Project: Rocket Science
. Applied Project: Hydro-Turbine Optimization
. Review
. Problems Plus.

14. MULTIPLE INTEGRALS
14.1 Double Integrals over Rectangles
14.2 Double Integrals over General Regions
14.3 Double Integrals in Polar Coordinates
14.4 Applications of Double Integrals
14.5 Surface Area
14.6 Triple Integrals
. Discovery Project: Volumes of Hyperspheres
14.7 Triple Integrals in Cylindrical Coordinates
. Discovery Project: The Intersection of Three Cylinders
14.8 Triple Integrals in Spherical Coordinates
. Applied Project: Roller Derby
14.9 Change of Variables in Multiple Integrals
. Review
. Problems Plus.

15. VECTOR CALCULUS
15.1 Vector Fields
15.2 Line Integrals
15.3 The Fundamental Theorem for Line Integrals
15.4 Green's Theorem
15.5 Curl and Divergence
15.6 Parametric Surfaces and Their Areas
15.7 Surface Integrals
15.8 Stokes' Theorem
. Writing Project: Three Men and Two Theorems
15.9 The Divergence Theorem
15.10 Summary
. Review
. Problems Plus.

.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 The Logarithm Defined as an Integral
.H Complex Numbers
.I Answers to Odd-Numbered Exercises

.INDEX