Multivariable Calculus, International Edition （International）

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Multivariable Calculus, International Edition （International）

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  • 製本 Paperback:紙装版/ペーパーバック版／ページ数 568 p.
  • 言語 ENG
  • 商品コード 9780495831501
  • DDC分類 515.94

Full Description

Known for accuracy, precision, and rigor, Soo Tan now brings those same qualities to the Calculus course. With his clear, concise writing style, and use of relevant, real world examples, Tan introduces abstract mathematical concepts with his intuitive approach that captures student interest without compromising mathematical rigor. In keeping with this emphasis on conceptual understanding, each exercise set begins with concept questions and each end-of-chapter review section includes fill-in-the-blank questions which help students master the definitions and theorems in each chapter. Additionally, many questions asking for the interpretation of graphical, numerical, and algebraic results are included among both the examples and the exercise sets.

Contents

10. CONIC SECTIONS, PARAMETRIC EQUATIONS, AND POLAR COORDINATES.
Conic Sections. Plane Curves and Parametric Equations. The Calculus of Parametric Equations. Polar Coordinates. Areas and Arc Lengths in Polar Coordinates. Conic Sections in Polar Coordinates. Chapter Review. Challenge Problems.
11. VECTORS AND THE GEOMETRY OF SPACE.
Vectors in the Plane. Coordinate Systems and Vectors in Three-Space. The Dot Product. The Cross Product. Lines and Planes in Space. Surfaces in Space. Cylindrical and Spherical Coordinates. Chapter Review. Challenge Problems.
12. VECTOR-VALUED FUNCTIONS
Vector-Valued Functions and Space Curves. Differentiation and Integration of Vector- Valued Functions. Arc Length and Curvature. Velocity and Acceleration. Tangential and Normal Components of Acceleration. Chapter Review. Challenge Problems.
13. FUNCTIONS OF SEVERAL VARIABLES.
Functions of Two or More Variables. Limits and Continuity. Partial Derivatives. Differentials. The Chain Rule. Directional Derivatives and Gradient Vectors. Tangent Planes and Normal Lines. Extrema of Functions of Two Variables. Lagrange Multipliers. Chapter Review. Challenge Problems.
14. MULITPLE INTEGRALS.
Double Integrals. Iterated Integrals. Double Integrals in Polar Coordinates. Applications of Double Integrals. Surface Area. Triple Integrals. Triple Integrals in Cylindrical and Spherical Coordinates. Change of Variables in Multiple Integrals. Chapter Review. Challenge Problems.
15. VECTOR ANALYSIS.
Vector Fields. Divergence and Curl. Line Integrals. Independence of Path and Conservative Vector Fields. Green's Theorem. Parametric Surfaces. Surface Integrals. The Divergence Theorem. Stoke's Theorem. Chapter Review. Challenge Problems.
APPENDICES.
A. The Real Number Line, Inequalities, and Absolute Value. B. Proofs of Selected Theorems.