Lectures 38/39, Friday/Monday, 12/5/08 and 12/8/08: Theoretical complements

Topics

n-dimensional Euclidean spaces, Rⁿ
Euclidean norm, || x ||
Functions from Rⁿ to R^m
Differentiability of a function from Rⁿ to R^m
Derivative matrix, and connection with earlier derivative concepts (derivatives of vector-valued functions, gradients, Jacobians)
Taylor's formula for functions Rⁿ to R^m,
First-order Taylor polynomial, and connection with linear approximation of functions f(x,y)
Matrix form of chain rule

Read

Since this material is not adequately covered in the book, I have prepared a handout, Theoretical Complements. This handout contains all the concepts and definitions you need to know. While the material is not suitable for computational problems, you should know the definitions and concepts, and you should be prepared for an exam question that probes this knowledge (possibly in true/false or multiple choice format).

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Last modified Fri 05 Dec 2008 07:36:18 AM CST