Trotter, Calculus of Vector Functions, 3rd. edition, Prentice Hall, 1972.R E Williamson, R H Crowell, and H F Trotter. Cal- culus of Vector Functions. Prentice Hall, New Jersey, 1972.Williamson, R.-E., Crowell, R.H., Trotter, H.F. (1968) Calculus of Vector Functions. Prentice-...
CHAPTER 9Calculus of Vector- andMatrix-Valued FunctionsIn Section 1 of this chapter we develop the calculus of vector- and matrix-valuedfunctions. There are two ways of going about it: by representing vectors andmatrices in terms of their components and entries with respect to some basis andusi...
1 单变量函数的微分 Differentiation of Univariate Functions 1.1 Difference Quotient 1.2 导数 Derivative 1.3 泰勒级数 Taylor Series 1.4 求导规则 Differential Rules 2 偏微分与梯度 Partial Differentiation & Gradients 2.1 偏微分 2.2 偏微分的链式法则 3 向量函数的梯度 Gradients of Vector-Based Functions 3.1 ...
calculus of vectors[′kal·kyə·ləs əv ′vek·tərz] (mathematics) That branch of calculus concerned with differentiation and integration of vector-valued functions. McGraw-Hill Dictionary of Scientific & Technical Terms, 6E, Copyright © 2003 by The McGraw-Hill Companies, Inc. ...
Functional calculus, away toapplyvarioustypes offunctions tooperators Schubert calculus, abranch ofalgebraicgeometry Tensorcalculus(alsocalledtensoranalysis), ageneralization ofvectorcalculusthatencompassestensorfields Vector calculus(alsocalledvectoranalysis),comprisingspecializednotationsformultivariableanalysis ofvectors...
{d\mathbf{r}}}{\mathop{dt}} & \text{Parametric vector evaluation} \\ = & \int_a^b [Mg'(t) + Nh'(t) + Pk'(t)]\mathop{dt} & \text{Parametric scalar evaluation} \\ = & \int_C M\mathop{dx} + N\mathop{dy} + P\mathop{dz} & \text{Scalar differential form} \end{...
Vector fields as derivatives Integration of forms Multilinear algebra Continuous differentiability Tangent space and normal space via gradients Dual space and dual basis Critical point analysis for multivariate functions, etc. Applications of Calculus ...
The Derivatives of Vector Functions Let x and y be vectors of orders n and m respectively: 1. Derivative of Vector with Respect to Vector The derivative of the vector y with respect to vector x is the n × m matrix 2. Derivative of a Scalar with Respect to Vector ...
13. VECTOR FUNCTIONS. 14. PARTIAL DERIVATIVES. 15. MULTIPLE INTEGRALS. 16. VECTOR CALCULUS. APPENDIXES. INDEX. 作者简介 James Stewart McMaster University The late James Stewart received his M.S. from Stanford University and his Ph.D. from the University of Toronto. He did research at the Univ...
A major reason to study vector functions over a surface is to measure flux. Flux is an important concept in electricity and magnetism. An intuitive way to visualize flux is the passage of a fluid through a membrane. The divergence and curl are two of the most important operators in vector ...