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