Calculus, Early Transcendentals / With Two Cd-roms - 5th edition

Stewart, James :

James Stewart received his M.S. from Stanford University and his Ph.D. from the University of Toronto. He did research at the University of London and was influenced by the famous mathematician George Polya at Stanford. Stewart is currently a Professor of Mathematics at McMaster University. His research field is harmonic analysis. James Stewart is the author of a best-selling calculus textbook series published by Brooks/Cole, including CALCULUS, 5th Edition, CALCULUS: EARLY TRANSCENDENTALS, 5th Edition, and CALCULUS: CONCEPTS AND CONTEXTS, 2nd Edition, as well as a series of precalculus texts.

1. FUNCTIONS AND MODELS.

Four Ways to Represent a Function. Mathematical Models: A Catalog of Essential F unctions. New Functions from Old Functions. Graphing Calculators and Computers. Exponential Functions. Inverse Functions and Logarithms. Review. Principles of P roblem Solving.

2. LIMITS AND DERIVATIVES.

The Tangent and Velocity Problems. The Limit of a Function. Calculating Limits U sing the Limit Laws. The Precise Definition of a Limit. Continuity. Limits at In finity; Horizontal Asymptotes. Tangents, Velocities, and Other Rates of Change. Derivatives. Writing Project: Early Methods for Finding Tangents. The Derivative as a Function. Review. Problems Plus.

3. DIFFERENTIATION RULES.

Derivatives of Polynomials and Exponential Functions. The Product and Quotient R ules. Rates of Change in the Natural and Social Sciences. Derivatives of Trigono metric Functions. The Chain Rule. Implicit Differentiation. Higher Derivatives, Applied Project: Where Should a Pilot Start Descent? , Applied Project: Building a Better Roller Coaster. Derivatives of Logarithmic Functions. Hyperbolic Funct ions. Related Rates. Linear Approximations and Differentials, Laboratory Project : Taylor Polynomials. Review. Problems Plus.

4. APPLICATIONS OF DIFFERENTIATION.

Maximum and Minimum Values, Applied Project: The Calculus of Rainbows. The Mean Value Theorem. How Derivatives Affect the Shape of a Graph. Indeterminate Forms and L'Hospital's Rule, Writing Project: The Origins of L'Hospital's Rule. Summar y of Curve Sketching. Graphing with Calculus and Calculators. Optimization Probl ems, Applied Project: The Shape of a Can. Applications to Business and Economics . Newton's Method. Antiderivatives. Review. Problems Plus.

5. INTEGRALS.

Areas and Distances. The Definite Integral, Discovery Project: Area Functions. T he Fundamental Theorem of Calculus. Indefinite Integrals and the Net Change Theo rem, Writing Project: Newton, Leibniz and the Invention of Calculus. The Substit ution Rule. The Logarithm Defined as an Integral. Review. Problems Plus.

6. APPLICATIONS OF INTEGRATION.

Areas between Curves. Volume. Volumes by Cylindrical Shells. Work. Average Value of a Function, Applied Project: Where to Sit at the Movie. Review. Problems Plu s.

7. TECHNIQUES OF INTEGRATION.

Integration by Parts. Trigonometric Integrals. Trigonometric Substitution. Integ ration of Rational Functions by Partial Fractions. Strategy for Integration. Int egration Using Tables and Computer Algebra Systems, Discovery Project: Patterns in Integrals. Approximate Integration. Improper Integrals. Review. Problems Plus .

8. FURTHER APPLICATIONS OF INTEGRATION.

Arc Length. Discovery Project: Arc Length Contest .Area of a Surface of Revoluti on, Discovery Project: Rotating on a Slant. Applications to Physics and Engineer ing. Applications to Economics and Biology. Probability. Review. Problems Plus.

9. DIFFERENTIAL EQUATIONS.

Modeling with Differential Equations. Direction Fields and Euler's Method. Separ able Equations, Applied Project: How Fast Does a Tank Drain?, Applied Project: W hich is Faster, Going Up or Coming Down? Exponential Growth and Decay, Applied P roject: Calculus and Baseball. The Logistic Equation. Linear Equations. Predator -Prey Systems. Review. Problems Plus.

10. PARAMETRIC EQUATIONS AND POLAR COORDINATES.

Curves Defined by Parametric Equations, Laboratory Project: Families of Hypocycl oids. Calculus with Parametric Curves, Laboratory Project: Bezier Curves. Polar Coordinates. Areas and Lengths in Polar Coordinates. Conic Sections. Conic Secti ons in Polar Coordinates. Review. Problems Plus.

11. INFINITE SEQUENCES AND SERIES.

Sequences, Laboratory Project: Logistic Sequences. Series. The Integral Test and Estimates of Sums. The Comparison Tests. Alternating Series. Absolute Convergen ce and the Ratio and Root Tests. Strategy for Testing Series. Power Series. Repr esentation of Functions as Power Series. Taylor and Maclaurin Series. Laboratory Project: An Ellusive Limit. The Binomial Series, Writing Project: How Newton Di scovered the Binomial Series. Applications of Taylor Polynomials, Applied Projec t: Radiation from the Stars. Review. Problems Plus.

12. VECTORS AND THE GEOMETRY OF SPACE.

Three-Dimensional Coordinate Systems. Vectors. The Dot Product. The Cross Produc t, Discovery Project: The Geometry of a Tetrahedron. Equations of Lines and Plan es. Cylinders and Quadric Surfaces. Cylindrical and Spherical Coordinates, Labor atory Project: Families of Surfaces. Review. Problems Plus.

13. VECTOR FUNCTIONS.

Vector Functions and Space Curves. Derivatives and Integrals of Vector Functions . Arc Length and Curvature. Motion in Space: Velocity and Acceleration, Applied Project: Kepler's Laws. Review. Problems Plus.

14. PARTIAL DERIVATIVES.

Functions of Several Variables. Limits and Continuity. Partial Derivatives. Tang ent Planes and Linear Approximations. The Chain Rule. Directional Derivatives an d the Gradient Vector. Maximum and Minimum Values, Applied Project: Designing a Dumpster, Discovery Project: Quadratic Approximations and Critical Points. Lagra nge Multipliers, Applied Project: Rocket Science, Applied Project: Hydro-Turbine Optimization. Review. Problems Plus.

15. MULTIPLE INTEGRALS.

Double Integrals over Rectangles. Iterated Integrals. Double Integrals over Gene ral Regions. Double Integrals in Polar Coordinates. Applications of Double Integ rals. Surface Area. Triple Integrals, Discovery Project: Volumes of Hyperspheres . Triple Integrals in Cylindrical and Spherical Coordinates, Applied Project: Ro ller Derby, Discovery Project: The Intersection of Three Cylinders. Change of Va riables in Multiple Integrals. Review. Problems Plus.

16. VECTOR CALCULUS.

Vector Fields. Line Integrals. The Fundamental Theorem for Line Integrals. Green 's Theorem. Curl and Divergence. Parametric Surfaces and Their Areas. Surface In tegrals. Stokes' Theorem, Writing Project: Three Men and Two Theorems. The Diver gence Theorem. Summary. Review. Problems Plus.

17. SECOND-ORDER DIFFERENTIAL EQUATIONS.

Second-Order Linear Equations. Nonhomogeneous Linear Equations. Applications of Second-Order Differential Equations. Series Solutions. Review. Problems Plus.

Appendixes.
Answers to Odd-Numbered Exercises.
Index.