# Syllabus - Mathematics 375 Topics in Linear Algebra and...

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Mathematics 375 Topics in Linear Algebra and Multivariable Calculus Fall 2005 Course Outline: I. Linear spaces (ch. 1): Review of vector algebra , Vector spaces and subspaces, dependent and linearly independent sets, bases and dimension, inner products and Euclidean spaces, or- thogonality and Gram-Schmidt process, projections and best approximation. II. Linear transformations and Matrices (ch. 2): Linear transformations, null space and range, algebraic operations on linear transformations, inverses, matrix representations, systems of linear equations. III. Diﬀerential calculus (ch. 8/9): Functions from R n to R m , scalar and vector ﬁelds, open balls and sets, limits and continuity, derivatives, directional and partial derivatives, higher order derivatives, chain rule. A ﬁrst order partial diﬀerential equation with constant coeﬃcients, implicit diﬀerentiation. IV. Determinants (ch. 3): Volume and orientation, a set of axioms for the determinant function, computa- tion, existence and uniqueness theorem, product formula, determinants and linear independence, cofactor expansions and Cramer’s rule. V. Eigenvalues and Eigenvectors (ch.4):

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## This note was uploaded on 07/28/2010 for the course MATH 375 taught by Professor Staff during the Fall '08 term at University of Wisconsin.

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Syllabus - Mathematics 375 Topics in Linear Algebra and...

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