Vector Calculus 5th Edition By Susan Jane Colley, Santiago Cañez
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Vector Calculus 5th Edition By Susan Jane Colley, Santiago Cañez

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Pages
654
File size
7.96 MB
Format
Digital PDF
Category
eBook[PDF]
About this ebook
The 5th Edition of Vector Calculus by Susan Jane Colley and Santiago Cañez covers a comprehensive range of topics in multivariable and vector calculus across 8 main chapters: [1, 2, 3, 4]
Chapter 1: Vectors
  • Vectors in two and three dimensions
  • Dot product, cross product, and geometry of lines and planes
  • Intro to n-dimensional Euclidean geometry
  • Alternative coordinate systems (polar, cylindrical, and spherical coordinates) [1, 2]
Chapter 2: Differentiation in Several Variables
  • Covers limits, continuity, partial derivatives, and differentiability
  • Explores the Chain Rule, gradients, and Taylor's theorem [1, 2, 3]
Chapters 3–8: Advanced Vector Calculus and Analysis
The remainder of the text covers vector-valued functions, optimization, and integration: [1]
  • Vector-Valued Functions (Ch. 3): Focuses on parameterized curves, motion, arc length, curvature, and vector fields.
  • Optimization (Ch. 4): Covers differentials, Taylor approximations, and Lagrange multipliers.
  • Integration (Ch. 5 & 6): Covers multiple integrals, change of variables, line integrals, and Green's theorem.
  • Vector Analysis (Ch. 7 & 8): Details surface integrals, Stokes's Theorem, the Divergence Theorem, and differential forms. [1, 2, 3, 4]

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Topics

Advanced Vector Calculus and Analysis and differential forms. and geometry of lines and planes and Green's theorem. and Lagrange multipliers. Chain Rule gradients and Taylor's theorem change of variables continuity partial derivatives and differentiability curvature and vector fields. differentials Taylor approximations Differentiation in Several Variables Dot product and cross product line integrals Multiple Integrals n-dimensional Euclidean geometry parameterized curves motion arc length polar cylindrical and spherical coordinates) Stokes's Theorem surface integrals the Divergence Theorem Vector-Valued Functions Vectors in two and three dimensions
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