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**Unformatted text preview: **1 TABLE OF CONTENTS Chapter 1 Euclidean space A. The basic vector space B. Distance C. Right angle D. Angles E. A little trigonometry F. Balls and spheres G. Isoperimetric inequalities Chapter 2 Differentiation A. Functions of one real variable B. Lengths of curves C. Directional derivatives D. Pathology E. Differentiability of real-valued functions F. Sufficient condition for differentiability G. A first look at critical points H. Geometric significance of the gradient I. A little matrix algebra J. Derivatives for functions R n → R m K. The chain rule L. Confession M. Homogeneous functions and Euler’s formula Chapter 3 Higher order derivatives A. Partial derivatives B. Taylor’s theorem C. The second derivative test for R 2 D. The nature of critical points E. The Hessian matrix F. Determinants G. Invertible matrices and Cramer’s rule H. Recapitulation I. A little matrix calculus 2 Chapter 4 Symmetric matrices and the second derivative test A. Eigenvalues and eigenvectors B. Eigenvalues of symmetric matricesB....

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