Syllabus for Math 415

Topics covered: Matrices, determinants, systems of linear equations, vector spaces and bases, eigenvalues, eigenvectors, diagonalization, inner product spaces, orthogonal functions, Fourier series, and applications.

Prerequisite: MATH 241 or 242

Required Text: Steven Leon, Linear Algebra with Applications, 7th Edition, Pearson Prentice Hall, 2006.

Math 415: Weekly Schedule

  • August 23 Systems of linear equations, row-echelon form.
    Sections 1.1--1.3

  • August 28, 30 Elementary matrices, begin determinants.
    Sections 1.4, 1.5, 2.1

  • September 4, 6 Cramers rule, begin vector spaces.
    Sections 2.2--2.3, 3.1

  • September 11, 13 Subspaces and Linear Independence.
    Sections 3.2, 3.3

  • September 18, 20 Test 1 (9/18) Basis and dimension.
    Sections 3.4

  • September 25, 27 Change of basis, row space and column space.
    Sections 3.5, 3.6

  • October 2, 4 Linear transformations, Matrix representation, similar matrices.
    Section 4.1--4.3

  • October 9, 11 Eigenvalues, Eigenvectors, Diagonalization.
    Sections 6.1--6.3 Drop deadline (10/12)

  • October 16, 18 Test 2 (10/16) Scalar product, orthogonal subspaces.
    Section 5.1, 5.2

  • October 23, 25 Least squares approximation, Inner products.
    Section 5.3, 5.4

  • October 30, Nov 1 Orthonormal sets, Gram-Schmidt process.
    Sections 5.5, 5.6

  • November 6, 8 Fourier series, Hermitian matrices
    Class notes, Section 6.4

  • November 13, 15 Test 3 (11/13)
    Hand back test

  • November 27, 29 SVD, Quadratic forms.
    Sections 6.5, 6.6

  • December 4, 6 Quick review of 6.5,6.6, Positive definite matrices, wrap-up.
    Section 6.7

  • FINAL EXAM December 10 130pm (9am section) and December 13 8am (1030am section)
    YOU MAY SWITCH FROM 12/13 exam to 12/10, but not the other direction.
    Final is comprehensive, and will take place in AH 245.

    Updated 12/03/07 (hks).