Fall 2008
  • MATH 304-504: Linear Algebra
    •

    Time and venue:   MWF 10:20-11:10 a.m., MILN 216

    First day hand-out

    Suggested weekly schedule

    Help sessions for MATH 220/323/304:   Monday - Thursday, 6:00PM - 8:00PM, ENPH 213
    Time change on the following dates:   9/22, 10/13, 11/3, 12/1, 5:30PM - 7:30PM, ENPH 213


    Homework assignments ##1-12


    Final exam:   Tuesday, December 9, 8:00-10:00 a.m., Milner 216

    Sample problems for the final exam (Solutions)


    Sample problems for Test 2 (Solutions)

    Sample problems for Test 1 (Solutions)

    Part IV (2 weeks): Applied linear algebra

  • Matrix exponentials
  • Symmetric and orthogonal matrices
  • Rotations in space
  • Orthogonal polynomials

    Lecture 35: Matrix exponentials.
  • Leon 6.2-6.3

    • Lecture 36: Complex eigenvalues and eigenvectors. Symmetric and orthogonal matrices.
  • Leon 5.5, 6.3-6.4

    • Lecture 37: Rotations in space.
  • Leon 5.5, 6.3

    • Lecture 38: Orthogonal polynomials.
  • Leon 5.7

    • Lecture 39: Review for the final exam.
  • Leon 1.1-1.4, 2.1-2.3, 3.1-3.6, 4.1-4.3, 5.1-5.7, 6.1-6.4


    • Part III (4 weeks): Advanced linear algebra

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

    Leon's book: Chapters 5-6

    Lecture 24: Scalar product.
  • Leon 5.1

    • Lecture 25: Orthogonal subspaces.
  • Leon 5.2

    • Lecture 26: Orthogonal projection. Least squares problems.
  • Leon 5.2-5.3

    • Lecture 27: Norms and inner products.
  • Leon 5.4

    • Lecture 28: Inner product spaces.
  • Leon 5.4

    • Lecture 29: Orthogonal sets. The Gram-Schmidt process.
  • Leon 5.5-5.6

    • Lecture 30: The Gram-Schmidt process (continued).
  • Leon 5.6

    • Lecture 31: Eigenvalues and eigenvectors. Characteristic equation.
  • Leon 6.1

    • Lecture 32: Eigenvalues and eigenvectors of a linear operator.
  • Leon 6.1, 6.3

    • Lecture 33: Bases of eigenvectors. Diagonalization.
  • Leon 6.1, 6.3

    • Lecture 34: Review for Test 2.
  • Leon 4.1-4.3, 5.1-5.6, 6.1, 6.3


    • Part II (4.5 weeks): Abstract linear algebra

  • Vector spaces
  • Linear independence
  • Basis and dimension
  • Linear transformations
  • Range and kernel
  • Similarity

    Leon's book: Chapters 3-4

    Lecture 11: Vector spaces.
  • Leon 3.1

    • Lecture 12: Subspaces of vector spaces. Span.
  • Leon 3.1-3.2

    • Lecture 13: Span (continued). Linear independence.
  • Leon 3.2-3.3

    • Lecture 14: Linear independence (continued).
  • Leon 3.3

    • Lecture 15: Basis of a vector space.
  • Leon 3.3-3.4

    • Lecture 16: Basis and dimension.
  • Leon 3.4

    • Lecture 17: Basis and coordinates.
  • Leon 3.5

    • Lecture 18: Rank and nullity of a matrix.
  • Leon 3.6

    • Lecture 19: Linear transformations. Kernel and range.
  • Leon 4.1

    • Lecture 20: Review for Test 1.
  • Leon 1.1-1.4, 2.1-2.2, 3.1-3.6

    • Lecture 21: General linear equations. Matrix transformations.
  • Leon 4.1-4.2

    • Lecture 22: Matrix of a linear transformation.
  • Leon 4.2-4.3

    • Lecture 23: Similarity of matrices.
  • Leon 4.3


    • Part I (3.5 weeks): 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.
  • Leon 1.1-1.2

    • Lecture 3: Applications of systems of linear equations.
  • Leon 1.2

    • Lecture 4: Row echelon form. Gauss-Jordan reduction.
  • Leon 1.1-1.2

    • Lecture 5: Matrix algebra.
  • Leon 1.3

    • Lecture 6: Diagonal matrices. Inverse matrix.
  • Leon 1.3

    • Lecture 7: Inverse matrix (continued).
  • Leon 1.3-1.4

    • Lecture 8: Inverse matrix (continued). Elementary matrices. Transpose of a matrix.
  • Leon 1.3-1.4

    • Lecture 9: Determinants.
  • Leon 2.1-2.2

    • Lecture 10: Evaluation of determinants.
  • Leon 2.1-2.2