Essential Calculus

By

Rating

Product Description

Product Details

1. FUNCTIONS AND LIMITS. Functions and Their Representations. A Catalog of Essential Functions. The Limit of a Function. Calculating Limits. Continuity. Limits Involving Infinity. 2. DERIVATIVES. Derivatives and Rates of Change. The Derivative as a Function. Basic Differentiation Formulas. The Product and Quotient Rules. The Chain Rule. Implicit Differentiation. Related Rates. Linear Approximations and Differentials. 3. INVERSE FUNCTIONS: EXPONENTIAL, LOGARITHMIC, AND INVERSE TRIGONOMETRIC FUNCTIONS. Exponential Functions. Inverse Functions and Logarithms. Derivatives of Logarithmic and Exponential Functions. Exponential Growth and Decay. Inverse Trigonometric Functions. Hyperbolic Functions. Indeterminate Forms and l"Hospital"s Rule. 4. APPLICATIONS OF DIFFERENTIATION. Maximum and Minimum Values. The Mean Value Theorem. Derivatives and the Shapes of Graphs. Curve Sketching. Optimization Problems. Newton"s Method. Antiderivatives. 5. INTEGRALS. Areas and Distances. The Definite Integral. Evaluating Definite Integrals. The Fundamental Theorem of Calculus. The Substitution Rule. 6. TECHNIQUES OF INTEGRATION. Integration by Parts. Trigonometric Integrals and Substitutions. Partial Fractions. Integration with Tables and Computer Algebra Systems. Approximate Integration. Improper Integrals. 7. APPLICATIONS OF INTEGRATION. Areas between Curves. Volumes. Volumes by Cylindrical Shells. Arc Length. Area of a Surface of Revolution. Applications to Physics and Engineering. Differential Equations. 8. SERIES. Sequences. Series. The Integral and Comparison Tests. Other Convergence Tests. Power Series. Representing Functions as Power Series. Taylor and Maclaurin Series. Applications of Taylor Polynomials. 9. PARAMETRIC EQUATIONS AND POLAR COORDINATES. Parametric Curves. Calculus with Parametric Curves. Polar Coordinates. Areas and Lengths in Polar Coordinates. Conic Sections in Polar Coordinates. 10. VECTORS AND THE GEOMETRY OF SPACE. Three-Dimensional Coordinate Systems. Vectors. The Dot Product. The Cross Product. Equations of Lines and Planes. Cylinders and Quadric Surfaces. Vector Functions and Space Curves. Arc Length and Curvature. Motion in Space: Velocity and Acceleration. 11. PARTIAL DERIVATIVES. Functions of Several Variables. Limits and Continuity. Partial Derivatives. Tangent Planes and Linear Approximations. The Chain Rule. Directional Derivatives and the Gradient Vector. Maximum and Minimum Values. Lagrange Multipliers. 12. MULTIPLE INTEGRALS. Double Integrals over Rectangles. Double Integrals over General Regions. Double Integrals in Polar Coordinates. Applications of Double Integrals. Triple Integrals. Triple Integrals in Cylindrical Coordinates. Triple Integrals in Spherical Coordinates. Change of Variables in Multiple Integrals. 13. VECTOR CALCULUS. Vector Fields. Line Integrals. The Fundamental Theorem for Line Integrals. Green"s Theorem. Curl and Divergence. Parametric Surfaces and Their Areas. Surface Integrals. Stokes" Theorem. The Divergence Theorem. Appendix A. Trigonometry. Appendix B. Proofs. Appendix C. Sigma Notation. Appendix D. The Logarithm Defined as an Integral

The late 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 University. Stewart was most recently Professor of Mathematics at McMaster University, and his research field was harmonic analysis. Stewart was the author of a best-selling calculus textbook series published by Cengage Learning, including CALCULUS, CALCULUS: EARLY TRANSCENDENTALS, and CALCULUS: CONCEPTS AND CONTEXTS, as well as a series of precalculus texts.

Ask a Question About this Product More... |

Look for similar items by category

People also searched for

How Fishpond Works

Fishpond works with suppliers all over the world to bring you a huge selection of products, really great prices, and delivery included on over 25 million products that we sell.
We do our best every day to make Fishpond an awesome place for customers to shop and get what they want — all at the best prices online.

Webmasters, Bloggers & Website Owners

You can earn a 8%
commission by selling Essential Calculus: Early Transcendentals, International Metric Edition
on your website. It's easy to get started - we will give you example code.
After you're set-up, your website can earn you money while you work, play or even sleep!
You should start right now!

Authors / Publishers

Item ships from and is sold by Fishpond.com, Inc.

↑

Back to top