University Calculus: Early Transcendentals, Multivariable, 3rd edition
Published by Pearson (December 24th 2014) - Copyright © 2016
3rd edition
ISBN-13: 9780321999603
What's included
Overview
University Calculus, Early Transcendentals, Multivariable, Third Edition helps students generalize and apply the key ideas of calculus through clear and precise explanations, thoughtfully chosen examples, meticulously crafted figures, and superior exercise sets. This text offers the right mix of basic, conceptual, and challenging exercises, along with meaningful applications. This revision features more examples, more mid-level exercises, more figures, improved conceptual flow, and the best in technology for learning and teaching.
KEY TOPICS: Infinite Sequences and Series; Parametric Equations and Polar Coordinates; Vectors and the Geometry of Space; Vector-Valued Functions and Motion in Space; Partial Derivatives; Multiple Integrals; Integration in Vector Fields; First-Order Differential Equations (Online); Second-Order Differential Equations (Online)
MARKET: For all readers interested in calculus.
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Table of contents
9. Infinite Sequences and Series
9.1 Sequences
9.2 Infinite Series
9.3 The Integral Test
9.4 Comparison Tests
9.5 Absolute Convergence; The Ratio and Root Tests
9.6 Alternating Series and Conditional Convergence
9.7 Power Series
9.8 Taylor and Maclaurin Series
9.9 Convergence of Taylor Series
9.10 The Binomial Series and Applications of Taylor Series
10. Parametric Equations and Polar Coordinates
10.1 Parametrizations of Plane Curves
10.2 Calculus with Parametric Curves
10.3 Polar Coordinates
10.4 Graphing in Polar Coordinates
10.5 Areas and Lengths in Polar Coordinates
10.6 Conics in Polar Coordinates
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
11.5 Lines and Planes in Space
11.6 Cylinders and Quadric Surfaces
12. Vector-Valued Functions and Motion in Space
12.1 Curves in Space and Their Tangents
12.2 Integrals of Vector Functions; Projectile Motion
12.3 Arc Length in Space
12.4 Curvature and Normal Vectors of a Curve
12.5 Tangential and Normal Components of Acceleration
12.6 Velocity and Acceleration in Polar Coordinates
13. Partial Derivatives
13.1 Functions of Several Variables
13.2 Limits and Continuity in Higher Dimensions
13.3 Partial Derivatives
13.4 The Chain Rule
13.5 Directional Derivatives and Gradient Vectors
13.6 Tangent Planes and Differentials
13.7 Extreme Values and Saddle Points
13.8 Lagrange Multipliers
14. Multiple Integrals
14.1 Double and Iterated Integrals over Rectangles
14.2 Double Integrals over General Regions
14.3 Area by Double Integration
14.4 Double Integrals in Polar Form
14.5 Triple Integrals in Rectangular Coordinates
14.6 Moments and Centers of Mass
14.7 Triple Integrals in Cylindrical and Spherical Coordinates
14.8 Substitutions in Multiple Integrals
15. Integration in Vector Fields
15.1 Line Integrals
15.2 Vector Fields and Line Integrals: Work, Circulation, and Flux
15.3 Path Independence, Conservative Fields, and Potential Functions
15.4 Green's Theorem in the Plane
15.5 Surfaces and Area
15.6 Surface Integrals
15.7 Stokes' Theorem
15.8 The Divergence Theorem and a Unified Theory
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