UNIVERSITY OF TENNESSEE, KNOXVILLE
MATH 251- FALL 2005- SYLLABUS (A. Freire's section)
41 lectures, including 3 in-class exams

Text: Elementary Linear Algebra, by Howard Anton- J.Wiley, 8th ed. (2000)

Ch. 1: SYSTEMS OF LINEAR EQUATIONS AND MATRICES

1.1, 1.2: Gaussian elimination
1.3, 1.4, 1.5: Matrix algebra; inverses
1.6 solution of systems and invertibility
(1.7- independent reading)

Ch. 3, 4: EUCLIDEAN VECTOR SPACES

3.3, 4.1: dot product and projections
3.5: lines, planes in 3-space
4.2: geometry of linear transfomations
4.3: matrix of a lin.transf; eigenvectors

Ch.5: VECTOR SPACES

5.1, 5.2: vector spaces and subspaces
5.3:, 5.4: linear independence, basis, dimension
5.5, 5.6: row and column spaces, nullspace, rank and nullity

Ch.6,7: INNER PRODUCT SPACES; DIAGONALIZATION

6.2: orthogonal complements
6.3: orthonormal bases and Gram-Schmidt
6.5: orthogonal transformations and rotation matrices
(7.1: review of material in 4.3: independent reading)
7.2, 7.3: diagonalization
9.5, 9.6, 9.7: quadratic forms, conic sections, quadric surfaces

Ch.7, 9: APPLICATIONS (as many as time permits)

9.1: systems of differential equations
* stochastic matrices and Markov chains (economics, population models)
6.4, 9.3: least squares, least squares fitting/ linear regression (statistics)
* graphs and networks
* linear programming (optimization)

*= not in text; notes will be provided