Fall 2009
  • MATH 311-505: Topics in Applied Mathematics
  • Time and venue:   TR 11:10 a.m.-12:25 p.m., MILN 216

    First day hand-out

    Office hours:
  • Wednesday, 10 a.m.-12 p.m.
  • Thursday, 10 a.m.-11 a.m.
  • by appointment

  • Office hours for the week of December 7:
  • Tuesday, 10 a.m.-11 a.m.
  • Wednesday, 10 a.m.-1 p.m.
  • Thursday, 10 a.m.-1 p.m.
  • Final exam:  Friday, December 11, 3:00-5:00 p.m., MILN 216

    Sample problems for the final exam (Solutions)

    Sample problems for Test 1 (Solutions)

    Sample problems for Test 2 (Solutions)


    Homework assignments ##1-12


    Course outline:

    Part I: Elementary linear algebra

  • Systems of linear equations
  • Matrices
  • Determinants

    Leon's book: Chapters 1-2
    Lecture 1: Systems of linear equations.
  • Leon 1.1

  • Lecture 2: Gaussian elimination. Row echelon form. Gauss-Jordan reduction.
  • Leon 1.1-1.2

  • Lecture 3: Some applications of systems of linear equations. Matrix algebra.
  • Leon 1.2-1.3

  • Lecture 4: Matrix multiplication. Diagonal matrices. Inverse matrix.
  • Leon 1.3-1.4

  • Lecture 5: Inverse matrix (continued). Determinants.
  • Leon 1.4, 2.1

  • Lecture 6: Evaluation of determinants.
  • Leon 2.1-2.2


  • Part II: Abstract linear algebra

  • Vector spaces
  • Linear independence
  • Basis and dimension
  • Change of basis
  • Linear transformations

    Leon's book: Chapters 3-4
    Lecture 7: Vector spaces. Subspaces.
  • Leon 3.1-3.2

  • Lecture 8: Span. Spanning set.
  • Leon 3.2

  • Lecture 9: Linear independence. Basis of a vector space.
  • Leon 3.3-3.4

  • Lecture 10: Basis and dimension.
  • Leon 3.4

  • Lecture 11: Rank and nullity of a matrix. Basis and coordinates. Change of basis.
  • Leon 3.5-3.6

  • Lecture 12: Change of coordinates (continued). Review for Test 1.
  • Leon 3.5 (change of coordinates), 1.1-1.4, 2.1-2.2, 3.1-3.4, 3.6 (review for Test 1)

  • Lecture 13: Linear transformations. General linear equations. Matrix transformations.
  • Leon 4.1-4.2

  • Lecture 14a: Matrix of a linear transformation.
  • Leon 4.2-4.3


  • Part III: Advanced linear algebra

  • Eigenvalues and eigenvectors
  • Diagonalization
  • Orthogonality
  • Inner products and norms
  • The Gram-Schmidt orthogonalization process

    Leon's book: Chapters 5-6 (selected sections)
    Lecture 14b: Eigenvalues and eigenvectors.
  • Leon 6.1

  • Lecture 15: Eigenvalues and eigenvectors (continued).
  • Leon 6.1, 6.3

  • Lecture 16: Diagonalization. Euclidean structure in Rn.
  • Leon 6.2-6.3, 5.1

  • Lecture 17: Orthogonal complement. Orthogonal projection.
  • Leon 5.1-5.2

  • Lecture 18: Least squares problems. Norms and inner products.
  • Leon 5.3-5.4

  • Lecture 19: Orthogonal sets. The Gram-Schmidt orthogonalization process.
  • Leon 5.5-5.6

  • Lecture 20: The Gram-Schmidt process (continued). Review for Test 2.
  • Leon 3.5, 4.1-4.3, 5.1-5.6, 6.1, 6.3


  • Part IV: Applied linear algebra

  • Boundary value problems
  • Heat equation
  • Fourier series
  • Bessel functions

    Spiegel's book: Chapters 1, 2, 6
    Lecture 21: Boundary value problems. Separation of variables.
  • Spiegel, Ch. 1

  • Lecture 22: Fourier's solution of the heat equation. Fourier series.
  • Spiegel, Ch. 1-2

  • Lecture 23: Fourier series (continued).
  • Spiegel, Ch. 2

  • Lecture 24: Heat equation (continued). Bessel functions.
  • Spiegel, Ch. 2, 6

  • Lecture 25: Bessel functions (continued).
  • Spiegel, Ch. 6

  • Lecture 26: Review for the final exam.
  • Leon 1.1-1.4, 2.1-2.2, 3.1-3.6, 4.1-4.3, 5.1-5.6, 6.1, 6.3
  • Spiegel, Ch. 1, 2, 6