Thomas’ Calculus: Multivariable – George B. Thoma’s – 12th Edition


This text is designed for the multivariable component a three-semester or four-quarter calculus course (math, engineering, and science majors).

Calculus hasn’t changed, but your students have. Today’s students have been raised on immediacy and the desire for relevance, and they come to calculus with varied mathematical backgrounds. Thomas’ Calculus, Twelfth Edition, helps your students successfully generalize and apply the key ideas of calculus through clear and precise explanations, clean design, thoughtfully chosen examples, and superior exercise sets. Thomas offers the right mix of basic, conceptual, and challenging exercises, along with meaningful applications. This significant revision features more examples, more mid-level exercises, more figures, and improved conceptual flow.

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  • 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 in Polar Coordinates
    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. Integration in 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

    17. Second-Order Differential Equations (online)
    17.1 Second-Order Linear Equations
    17.2 Nonhomogeneous Linear Equations
    17.3 Applications
    17.4 Euler Equations
    17.5 Power-Series Solutions
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