Thomas' Calculus
Multivariable
Paperback Engels 2014 13e druk 9780321884053Samenvatting
This text is designed for the multivariable component a three-semester or four-quarter calculus course (math, engineering, and science majors).
Thomas’ Calculus, Multivariable, Thirteenth Edition, introduces readers to the intrinsic beauty of calculus and the power of its applications. For more than half a century, this text has been revered for its clear and precise explanations, thoughtfully chosen examples, superior figures, and time-tested exercise sets. With this new edition, the exercises were refined, updated, and expanded—always with the goal of developing technical competence while furthering readers’ appreciation of the subject. Co-authors Hass and Weir have made it their passion to improve the text in keeping with the shifts in both the preparation and ambitions of today's learners.
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, Integrals and Vector Fields, Second-Order Differential Equations
MARKET: For all readers interested in calculus.
Specificaties
Lezersrecensies
Inhoudsopgave
10.1 Sequences
10.2 Infinite Series
10.3 The Integral Test
10.4 Comparison Tests
10.5 Absolute Convergence; The Ratio and Root Tests
10.6 Alternating Series and Conditional Convergence
10.7 Power Series
10.8 Taylor and Maclaurin Series
10.9 Convergence of Taylor Series
10.10 The Binomial Series and Applications of Taylor Series
11. Parametric Equations and Polar Coordinates
11.1 Parametrizations of Plane Curves
11.2 Calculus with Parametric Curves
11.3 Polar Coordinates
11.4 Graphing Polar Coordinate Equations
11.5 Areas and Lengths in Polar Coordinates
11.6 Conic Sections
11.7 Conics in Polar Coordinates
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
12.5 Lines and Planes in Space
12.6 Cylinders and Quadric Surfaces
13. Vector-Valued Functions and Motion in Space
13.1 Curves in Space and Their Tangents
13.2 Integrals of Vector Functions; Projectile Motion
13.3 Arc Length in Space
13.4 Curvature and Normal Vectors of a Curve
13.5 Tangential and Normal Components of Acceleration
13.6 Velocity and Acceleration in Polar Coordinates
14. Partial Derivatives
14.1 Functions of Several Variables
14.2 Limits and Continuity in Higher Dimensions
14.3 Partial Derivatives
14.4 The Chain Rule
14.5 Directional Derivatives and Gradient Vectors
14.6 Tangent Planes and Differentials
14.7 Extreme Values and Saddle Points
14.8 Lagrange Multipliers
14.9 Taylor's Formula for Two Variables
14.10 Partial Derivatives with Constrained Variables
15. Multiple Integrals
15.1 Double and Iterated Integrals over Rectangles
15.2 Double Integrals over General Regions
15.3 Area by Double Integration
15.4 Double Integrals in Polar Form
15.5 Triple Integrals in Rectangular Coordinates
15.6 Moments and Centers of Mass
15.7 Triple Integrals in Cylindrical and Spherical Coordinates
15.8 Substitutions in Multiple Integrals
16. Integrals and Vector Fields
16.1 Line Integrals
16.2 Vector Fields and Line Integrals: Work, Circulation, and Flux
16.3 Path Independence, Conservative Fields, and Potential Functions
16.4 Green's Theorem in the Plane
16.5 Surfaces and Area
16.6 Surface Integrals
16.7 Stokes' Theorem
16.8 The Divergence Theorem and a Unified Theory
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