This
** preview**
has intentionally

**sections.**

*blurred***to view the full version.**

*Sign up**This preview shows
pages
1–2. Sign up
to
view the full content.*

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):

This
** preview**
has intentionally

This is the end of the preview. Sign up
to
access the rest of the document.

Ask a homework question
- tutors are online