MATH 311 - Topics in Applied Math. I

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. (courtsey of Professor Narcowich)

Weekly Schedule

Part I

  • Week 1 Equations and matrices
    Sections 2.1A, 2.2, 2.3

  • Week 2 Matrices and determinants
    Sections 2.3, 2.4, 2.5

  • Week 3 Linear transformations on Rn, vector spaces
    Sections 2.5, 3.1, 3.2

  • Week 4 Linear transformations, image and null space.
    Sections 3.3, 3.4

  • Week 5 Coordinates and dimension. (Bases, linear independence, linear dependence, change of coordinates)
    Section 3.5. Review for Test 1.

  • Week 6 Test 1, Coordinates and dimension. (Bases, linear independence, linear dependence, change of coordinates)
    Section 3.6

  • Week 7 Inner products, orthogonal bases, rotation.
    Section 3.7

    Part II

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

  • Week 9 Bessel functions, Fourier series
    Sections 14.7, 14.8

  • Week 10 Fourier series, separation of variables. Review for Test 2
    Sections 14.9A, 14.10A

  • Week 11 Test 2. Heat equation
    Sections 14.10A, 14.10B

    Part III

  • Week 12 Vector analysis, gradient, line integrals
    Sections 5.2, 5.4 , 8.1

  • Week 13 Div, curl, Green's Theorem
    Sections 8.4, 9.1

  • Week 14 surface Integrals, Gauss's Theorem, Stokes's Theorem
    9.3, 9.4, 9.5

  • Week 15 , Catch-up, Review for Final.