Thomas Calculus Multivariable 15th Edition By George Brinton Thomas, Joel R. Hass
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Thomas Calculus Multivariable 15th Edition By George Brinton Thomas, Joel R. Hass

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777
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24.42 MB
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Digital PDF
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eBook[PDF]
About this ebook
The Thomas' Calculus: Multivariable (15th Edition) textbook by George B. Thomas, Joel R. Hass, Christopher E. Heil, and Maurice D. Weir focuses strictly on advanced multivariable calculus concepts, spanning Chapters 11 through 17 of the complete calculus text. It also introduces cutting-edge digital resources and modern applications tailored for data science and engineering. [1, 2, 3, 4, 5]
Core Multivariable Topics Covered
  • Parametric Equations and Polar Coordinates (Chapter 10/11 standalone): Parametric curves, calculus with parametric equations, polar coordinates, and conic sections. [1]
  • Vectors and the Geometry of Space: Three-dimensional coordinate systems, vectors, dot products, cross products, lines, and planes in space. [1, 2]
  • Vector-Valued Functions: Space curves, motion in space (velocity and acceleration), arc length, unit tangent vectors, and curvature. [1]
  • Partial Derivatives: Functions of several variables, limits and continuity in higher dimensions, partial derivatives, the chain rule, directional derivatives, gradient vectors, tangent planes, and extreme values (including Lagrange multipliers). [1, 2, 3, 4]
  • Multiple Integrals: Double and triple integrals, integrals in polar, cylindrical, and spherical coordinates, substitution in multiple integrals (Jacobians), and applications to mass and moments. [1, 2, 3]
  • Integrals and Vector Fields: Line integrals, vector fields, work, circulation, flux, Green's Theorem, surface integrals, Stokes' Theorem, and the Divergence Theorem. [1, 2, 3, 4]
  • Differential Equations: First-order and second-order differential equations, including applications to oscillatory and mechanical systems. [1]
New 15th Edition Enhancements
  • Machine Learning Foundations: A brand-new appendix explicitly introduces Determinants and Gradient Descent, providing vital mathematical background for students pursuing artificial intelligence, data science, and neural networks.
  • Advanced Online Content: Expanded Pearson eText digital chapters now cover Complex Functions, Fourier Series, and Wavelets.
  • Notation Update: Structural update shifting standard terminology from \(\sin ^{-1}\) to \(\arcsin \) notation for absolute geometric clarity. [1, 2, 3]

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Topics

artificial intelligence data science and neural networks. Determinants and Gradient Descent Differential Equations: First-order and second-order differential equations Integrals and Vector Fields integrals in polar cylindrical and spherical coordinates limits and continuity in higher dimensions Multiple Integrals: Double and triple integrals Parametric Equations and Polar Coordinates Partial Derivatives: Functions of several variables shifting standard terminology from \(\sin ^{-1}\) to \(\arcsin \) notation for absolute geometric clarity Vector-Valued Functions: Space curves Vectors and the Geometry of Space
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