This preview shows page 1. Sign up to view the full content.
Unformatted text preview: 424 CHAPTER 4. MAPPINGS AND TRANSFORMATIONS 4.2 Differentiable Mappings We have seen several versions of the notion of a derivative in previous sections: for a realvalued function f of one real variable, the derivative is a number, which gives the slope of the line tangent to the graph y = f ( x ) at the given point; for a vectorvalued function of one real variable, the derivative is a vector, giving the velocity of the motion described by the function, or equivalently giving the coefficients of the time variable in the natural parametrization of the tangent line; for a realvalued function of a vector variable, the derivative is the linear part of an affine function making firstorder contact with the function at the given point. We can combine these last two interpretations to formulate the derivative of a vectorvalued function of a vector variable. Extending our terminology from realvalued functions (as in 3.2 ) to (vectorvalued) mappings, we define an affine mapping to be a mapping of the form...
View
Full
Document
This note was uploaded on 10/20/2011 for the course MAC 2311 taught by Professor All during the Spring '08 term at University of Florida.
 Spring '08
 ALL
 Calculus, Derivative, Transformations, Slope

Click to edit the document details