Plan for MA 104 høsten 1998

Forelesningsplan

Denne planen er bare ment å være veiledende, og legger opp til en jevn progresjon på ca. 15 sider per dobbeltforelesning. Til å begynne med vil nok forelesningene kunne ligge noe foran dette skjemaet.

Pensum

Fraleigh & Beauregard: Linear Algebra. Addison-Wesley. Kapittel 1 - 9, unntatt avsnittene 1.8, 2.5, 6.4, 6.5, 8.4 og 9.4.

1.1 Vectors in Euclidean Spaces, 1.2 The Norm and the Dot Product, 1.3 Matrices and Their Algebra, 1.4 Solving Systems of Linear Equations, 1.5 Inverses of Square Matrices, 1.6 Homogeneous Systems, Subspaces, and Bases, 1.7 Application to Population Distribution.

2.1 Independence and Dimension, 2.2 The Rank of a Matrix, 2.3 Linear Transformations of Euclidean Spaces, 2.4 Linear Transformations of the Plane.

3.1 Vector Spaces, 3.2 Basic Concepts of Vector Spaces, 3.3 Coordinatization of Vectors, 3.4 Linear Transformations, 3.5 Inner-Product Spaces.

4.1 Areas, Volumes and Cross Products, 4.2 The Determinant of a Square Matrix, 4.3 Computation of Determinants and Cramer's Rule, 4.4 Linear Transformations and Determinants.

5.1 Eigenvalues and Eigenvectors, 5.2 Diagonalization, 5.3 Two Applications.

6.1 Projections, 6.2 The Gram-Schmidt Process, 6.3 Orthogonal Matrices.

7.1 Coordinatization and Change of Basis, 7.2 Matrix Representations and Similarity.

8.1 Diagonalization of Quadratic Forms, 8.2 Applications to Geometry, 8.3 Applications to Extrema.

9.1 Algebra of Complex Numbers, 9.2 Matrices and Vector Spaces with Complex Scalars, 9.3 Eigenvalues and Diagonalization.

rognes@math.uio.no / oppdatert 4. september 1998