Calculus Volume 3

Livro digital

Título:
Calculus Volume 3

Autor:
OpenStax

Categoria:
Tecnologia > Geral

Doador:
Raffaello D. N.

Sinopse:
The jump from single-variable to multivariable calculus is one of the highest dropout points in STEM programs — not because the ideas are inaccessible, but because the geometric intuition required is rarely built deliberately. Calculus Volume 3 by OpenStax takes that transition seriously, opening with a revisit of parametric equations and polar coordinates before progressively extending every familiar concept into three dimensions. The table of contents is a map from vectors in space to the theorems that unify electromagnetism and fluid mechanics. The book works through vector-valued functions and their derivatives, then dives into differentiation of multivariable functions: partial derivatives, directional derivatives, the gradient, tangent planes, and Lagrange multipliers for constrained optimization. Multiple integration follows — double and triple integrals, change of variables, and applications in mass, center of mass, and probability. Vector calculus closes the main arc: vector fields, line integrals, flux, divergence, and curl, culminating in Green's Theorem, Stokes' Theorem, and the Divergence Theorem. A final chapter covers second-order differential equations. The densest volume in the OpenStax Calculus trilogy, and the most directly connected to applications in physics and engineering. Published by Rice University under Creative Commons, it completes the series with the same academic rigor as the previous volumes — and at no cost.