Designed for one-semester undergraduate level courses in multivariable calculus. This text combines traditional mainstream calculus with the most flexible approach to new ideas and calculator/computer technology. It contains problem sets and a fresh conceptual emphasis flavoured by new technological possibilities. The work includes around 3000 conceptual problems and interesting applications, a lead for writing assignments or class discussion, and extensive computer-generated visuals.
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For one-semester undergraduate-level courses in Multivariable Calculus.
This text combines traditional mainstream calculus with the most flexible approach to new ideas and calculator/computer technology. It contains superb problem sets and a fresh conceptual emphasis flavored by new technological possibilities.
Les mer
10. Polar Coordinates and Parametric Curves.
Analytic Geometry and the Conic Sections. Polar Coordinates. Area Computations in Polar Coordinates. Parametric Curves. Integral Computations with Parametric Curves. Conic Sections and Applications.
11. Infinite Series.
Introduction. Infinite Sequences. Infinite Series and Convergence. Taylor Series and Taylor Polynomials. The Integral Test. Comparison Tests for Positive-Term Series. Alternating Series and Absolute Convergence. Power Series. Power Series Computations. Series Solutions of Differential Equations.
12. Vectors, Curves, and Surfaces in Space.
Vectors in the Plane. Three-Dimensional Vectors. The Cross Product of Vectors. Lines and Planes in Space. Curves and Motions in Space. Curvature and Acceleration. Cylinders and Quadric Surfaces. Cylindrical and Spherical Coordinates.
13. Partial Differentiation.
Introduction. Functions of Several Variables. Limits and Continuity. Partial Derivatives. Multivariable Optimization Problems. Increments and Linear Approximation. The Multivariable Chain Rule. Directional Derivatives and the Gradient Vector. Lagrange Multipliers and Constrained Optimization. Critical Points of Functions of Two Variables.
14. Multiple Integrals.
Double Integrals. Double Integrals over More General Regions. Area and Volume by Double Integration. Double Integrals in Polar Coordinates. Applications of Double Integrals. Triple Integrals. Integration in Cylindrical and Spherical Coordinates. Surface Area. Change of Variables in Multiple Integrals.
15. Vector Calculus.
Vector Fields. Line Integrals. The Fundamental Theorem and Independence of Path. Green's Theorem. Surface Integrals. The Divergence Theorem. Stokes' Theorem.
Appendices.
Answers.
Index.
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Approximately 2500 conceptual problems and interesting applications—Covers all ranges of difficulty, including both theoretical and computationally oriented problems.
Encourages students to learn by doing. Ex.___
Section-ending Concepts: Questions & Discussion.
Serves students with a basis for either writing assignments or class discussion. Ex.___
Small optional section of matrix terminology and notation in the multivariable portion of the text.
A lively and accessible writing style.
Helps students feel comfortable with the topics covered, and their ability to master them. Ex.___
Extensive computer generated visuals throughout—Not usually found in other texts.
Highlights hundreds of Mathematica and MATLAB generated figures. Ex.___
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Free CD—Shows animations of nearly all the text examples. It also has the entire book in Maple notebooks.
420 new True/False Questions—Available on the CD. They focus on theory and push the student to read.
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Produktdetaljer
ISBN
9780130339676
Publisert
2002-05-23
Utgave
6. utgave
Utgiver
Vendor
Pearson
Vekt
100 gr
Høyde
100 mm
Bredde
100 mm
Dybde
100 mm
Aldersnivå
U, 05
Språk
Product language
Engelsk
Format
Product format
Heftet
Antall sider
560