Vector Analysis Versus Vector Calculus

In Example 15.7.1 we see that the total outward flux of a vector field across a closed surface can be found two different ways because of the Divergence Theorem. One computation took far less work to obtain. In that particular case, since 𝒮 was comprised of three separate surfaces, it was far simpler to compute one triple integral than three surface integrals (each of which required …
16.5 Surface Integrals of Vector Fields Chapter 17 Fundamental Theorems of Vector Analysis 17.1 Green's Theorem 17.2 Stokes' Theorem 17.3 Divergence Theorem Appendices - Quick Reference Guides A. Common Mathematical Operations - Traditional Notation versus Mathematica Notation
Vector algebra in two and three dimensions, multivariate differential and integral calculus, optimization, vector calculus including the theorems of Green, Gauss, and Stokes. Applications to economics, engineering, and all sciences, with emphasis on numerical and graphical solutions; use of graphing calculators or computers.
Differentiating Vector-1. Valued Functions . FUN. 9.5 Integrating Vector-1. Valued Functions. FUN. 9.6 Solving Motion Problems Using Parametric and Vector-Valued Functions. 1. FUN. 9.7 Defining Polar Coordinates and Differentiating in Polar Form. 2. CHA. 9.8 Find the Area of a Polar Region or the Area Bounded by a Single Polar Curve 3. CHA. 9.9 ...

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