"The gradient of a scalar field is a vector field that points in the direction of the greatest rate of increase of the scalar, and its magnitude is that rate of increase."
Introduction to vector and tensor analysis : Wrede, Robert C
Do not settle for a blurry, illegal scan. Purchase the official Dover eBook (cheaper than a single pizza) or borrow a physical copy from your university library. If you absolutely need a free resource, check your library’s digital lending platform. The time you save with Wrede’s clear explanations will repay the cost many times over.
: Fundamental notions of n-space, Riemannian geometry, and the curvature tensor. Applications
If you are searching for the , you are likely looking for a rigorous yet accessible bridge between elementary calculus and advanced differential geometry. Why Wrede’s Text Remains a Classic
: Wrede uses classical vector notation while gradually introducing more rigorous tensor notation, including the Einstein summation convention .
Covers the algebra and calculus of vectors, including dot and cross products, gradient, divergence, and curl, as well as the integral theorems of Gauss, Stokes, and Green. Transformation Theory: