Calculus of Vector Functions Hale F. Trotter, Richard E. Williamson, Richard H. Crowell
Publisher: Prentice Hall

Vector-Valued Functions and Motion in Space: Vector Functions. Apr 22, 2011 - Multivariate Calculus: Vectors and the Geometry of Space; Vector Functions; Partial Derivatives; Multiple Integrals; Vector Calculus; Second-Order Differential Equations. Aug 15, 2013 - Concepts of Calculus A variety of mathematical operations with functions are needed in order to do the calculus of this course. We can also think of abla f as a function which takes in vectors and spits out vectors, by plugging in the input vector into each partial f / partial x_i . Arc Length and the Unit Tangent Vector T. Curvature and the Unit Normal Vector N. Vector Calculus multivariable calculus, designed for students who have completed courses in single-variable calculus. Since the derivative of the vector form provides dy/dt and dx/dt, dy/dx can be obtained simply by manipulating notation. Dec 7, 2007 - An operational calculus converts derivatives and integrals to operators that act on functions, and by doing so ordinary and partial linear differential equations can be reduced to purely algebraic equations that are much easier to solve. Nov 30, 2013 - We will assume something about the reader's knowledge, but it's a short list: know how to operate with vectors and the dot product, know how to take a partial derivative, and know that in single-variable calculus the local maxima and a function f(x) and understand x to be a vector in mathbb{R}^n . Any such function is called a 1-form (a.k.a. The traditional topics are covered: basic vector algebra; lines, planes and surfaces; vector-valued functions; functions of 2 or 3 variables; partial derivatives; optimization; multiple integrals; line and surface integrals. Aug 7, 2013 - These cover worksheets, functions, plotting, programming, units, statistics, calculus, vectors and matrices, linear and non-linear equations and differential equations. This is a text on elementary multivariable calculus, designed for students who have completed courses in single-variable calculus. Jun 22, 2012 - The resultant is a vector joining the head of the first vector to the tail of the last vector; If 2 vectors, a and b, are parallel in the same direction, |a + b| = |a| + |b| and in the same direction; If a and b have opposite directions and | a | > | b |, then | a .. This unit begins with students developing a better understanding of these essential concepts. Oct 21, 2011 - The notation here is meant to emphasize the idea that (alpha) is a function: in particular, it's a linear function that eats a vector and produces a scalar. Torsion and the Unit Binormal Vector B. When dealing with cartesian functions, the notation is dy/dx. Sep 24, 2008 - It has been a typical exercise for beginners to write an evaluator for some variation of λ calculus.