Calculus : early transcendentals / created by James Stewart

Includes index

Preface
To the student
Diagnostic tests
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. Graphing calculators and computers
1.5. Exponential functions
1.6. 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
3.6. Derivatives of logarithmic functions
3.7. Rates of change in the natural and social sciences
3.8. Exponential growth and decay
3.9. Related rates
3.10. Linear approximations and differentials
Laboratory project : Taylor polynomials
3.11. 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. Graphing with calculus and calculators
4.7. Optimization problems
Applied project : the shape of a can
4.8. Newton's method
4.9. 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
6.2. Volumes
6.3. Volumes by cylindrical shells
6.4. Work
6.5. Average value of a function
Applied projects : 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
8.3. Applications to physics and engineering
Discovery project : complementary coffee cups
8.4. Applications to economics and biology
8.5. Probability
Review
Problems plus
9. Differential equations
9.1. Modeling with differential equations
9.2. Direction fields and Euler's method
9.3. Separable equations
Applied project : how fast does a tank drain?
Applied project : which is faster, going up or coming down?
9.4. Models for population growth
Applied project : calculus and baseball
9.5. Linear equations
9.6. Predator-prey systems
Review
Problems plus
10. Parametric equations and polar coordinates
10.1. Curves defined by parametric equations
Laboratory project : running circles around circles
10.2. Calculus with parametric curves
Laboratory project : Bézier curves
10.3. Polar coordinates
10.4. Areas and lengths in polar coordinates
10.5. Conic sections
10.6. Conic sections in polar coordinates
Review
Problems plus
11. Infinite sequences and series
11.1. Sequences
Laboratory project : logistic sequences
11.2. Series
11.3. The integral test and estimates of sums
11.4. The comparison tests
11.5. Alternating series
11.6. Absolute convergence and the ratio and root tests
11.7. Strategy for testing series
11.8. Power series
11.9. Representations of functions as power series
11.10. Taylor and Maclaurin series
Laboratory project : an elusive limit
Writing project : how Newton discovered the binomial series
11.11. Applications of Taylor polynomials
Applied project : radiation from the stars
Review
Problems plus. 12. Vectors and the geometry of space
12.1. Three-dimensional coordinate systems
12.2. Vectors
12.3. The dot product
12.4. The cross product
Discovery project : the geometry of a tetrahedrom
12.5. Equations of lines and planes
Laboratory project : putting 3D in perspective
12.6. Cylinders and quadric surfaces
Review
Problems plus
13. Vector functions
13.1. Vector functions and space curves
13.2. Derivatives and integrals of vector functions
13.3. Arc length and curvature
13.4. Motion in space : velocity and acceleration
Applied project : Kepler's laws
Review
Problems plus
14. Partial derivatives
14.1. Functions of several variables
14.2. Limits and continuity
14.3. Partial derivatives
14.4. Tangent planes and linear approximations
14.5. The chain rule
14.6. Directional derivatives and the gradient vector
14.7. Maximum and minimum values
Applied project : designing a dumpster
Discovery project : quadratic approximation and critical points
14.8. Lagrange multipliers
Applied project : rocket science
Applied project : hydro-turbine optimization
Review
Problems plus. 15. Multiple integrals
15.1. Double integrals over rectangles
15.2. Iterated integrals
15.3. Double integrals over general regions
15.4. Double integrals in polar coordinates
15.5. Applications of double integrals
15.6. Triple integrals
Discovery project : volumes of hyperspheres
15.7. Triple integrals in cylindrical coordinates
Discovery project : the intersection of three cylinders
15.8. Triple integrals in spherical coordinates
Applied project : roller derby
15.9. Change of variables in multiple integrals
Review
Problems plus
16. Vector calculus
16.1. Vector fields
16.2. Line integrals
16.3. The fundamental theorem for line integrals
16.4. Green's theorem
16.5. Curl and divergence
16.6. Parametric surfaces and their areas
16.7. Surface integrals
16.8. Stokes' theorem
Writing project : three men and two theorems
16.9. The divergence theorem
16.10. Summary
Review
Problems plus
17. Second-order differential equations
17.1. Second-order linear equations
17.2. Nonhomogeneous linear equations
17.3. Applications of second-order differential equations
17.4. Series solutions
Review
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

Appropriate for the traditional 2 or 3-term college calculus course, this textbook presents the fundamentals of calculus. Topics include, but are not limited to: a review of polynomials, trigonometric, exponential, and logarithmic functions, followed by discussions of limits, derivatives, applications of differential calculus to real-world problem areas, an overview of integration, basic techniques for integration, a variety of applications of integration, and an introduction to (systems of) differential equations