MATH 311 - Topics in Applied Math. I

TEXTBOOK: see current textbook list

CATALOG DESCRIPTION: See catalog description here

Topics covered: Matrices, determinants, systems of linear equations, eigenvalues, eigenvectors, diagonalization of symmetric matrices, inner product spaces, orthogonal functions, Bessel functions, and applications.

Prerequisite: MATH 221, 251 or 253; MATH 308 or concurrent enrollment therein.

Text: Richard E. Williamson and Hale F. Trotter, Multivariable Mathematics, 4th ed., Prentice-Hall, Englewood Cliffs, NJ, 2004.   Click on the link to get a list of errors and misprints in the text.

Weekly Schedule

  • Week 1 Vectors
    Sections 1.1-1.4, 1.6.

  • Week 2 Equations and matrices
    Sections 2.1A, 2.2, 2.3

  • Week 3 Matrices and determinants
    Sections 2.3, 2.4, 2.5

  • Week 4 Linear transformations on Rn. Review for Test 1 .
    Sections 2.5, 3.1

  • Week 5 Test 1, vector spaces, linear transformations.
    Sections 3.2, 3.3

  • Week 6 Linear transformations, image and null space.
    Sections 3.3, 3.4.

  • Week 7 Coordinates and dimension. (Bases, linear independence, linear dependence, change of coordinates)
    Section 3.5A-3.5C, 3.6C.

  • Week 8 Eigenvalues and eigenvectors, diagonalization
    Sections 3.6A, 3.6B.

  • Week 9 Inner products, orthogonal bases. Review for Test 2.
    Sections 3.7A, 3.7B. (Assign problems #12-17 on symmetric matrices.)

  • Week 10 Test 2, rotations
    Section 3.7C

  • Week 11 Series solutions to ODEs (review), Legendre polynomials, Bessel's equation and Bessel functions
    Sections 14.6, 14.7 (problem #7,#8)

  • Week 12 Bessel functions, Fourier series
    Sections 14.7, 14.8

  • Week 13 Fourier series, separation of variables - heat equation
    Sections 14.9A, 14.10A (Thanksgiving comes on this week in the fall.)

  • Week 14 Heat equation, catch up
    Sections 14.10A, 14.10B

  • Week 15 Review for Final.

    Updated 8/24/05 (fjn).

    Last modified by rww on Thu Aug 25 13:49:49 2005