Spring 2011
  • MATH 304-505: Linear Algebra
    •

    Time and venue:   TR 11:10 a.m.–12:25 p.m., MILN 216

    First day hand-out

    Office hours (MILN 004):
  • Wednesday, 9:00–11:00 a.m.
  • Thursday, 10:00–11:00 a.m.
  • by appointment

    • Help sessions (BLOC 117):
  • Monday – Thursday, 5:30–8:00 p.m.
    •
    Office hours before the final (MILN 004):
  • Thursday, May 5, 10:00 a.m.-1:00 p.m.
  • Friday, May 6, 1:00-3:00 p.m.
    •

    Final exam:  Friday, May 6, 3:00–5:00 p.m., MILN 216

    Rules for the exam:  no books, no lecture notes, no calculators.  Bring paper and a stapler.

    Sample problems for the final exam (Solutions)

    Sample problems for Test 1 (Solutions)

    Sample problems for Test 2 (Solutions)


    Homework assignments ##1-11

    Course outline:

    Part I: Elementary linear algebra

  • Systems of linear equations
  • Gaussian elimination, Gauss-Jordan reduction
  • Matrices, matrix algebra
  • Determinants

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

    • Lecture 2: Gaussian elimination (continued). 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 1.3-1.5

    • Lecture 5: Inverse matrix (continued).
  • Leon 1.4-1.5

    • Lecture 6: Transpose of a matrix. Determinants.
  • Leon 1.4, 2.1-2.2

    • Lecture 7: Evaluation of determinants. The Vandermonde determinant. Cramer's rule.
  • Leon 2.2-2.3


    • Part II: Abstract linear algebra

  • Vector spaces
  • Linear independence
  • Basis and dimension
  • Coordinates, change of basis
  • Linear transformations

    Leon's book: Chapters 3-4
    Lecture 8: Vector spaces. Subspaces.
  • Leon 3.1-3.2

    • Lecture 9: Subspaces of vector spaces (continued). Span. Spanning set.
  • Leon 3.1-3.2

    • Lecture 10: Linear independence. Wronskian.
  • Leon 3.3

    • Lecture 11: Basis and dimension.
  • Leon 3.4

    • Lecture 12: Rank and nullity of a matrix.
  • Leon 3.2, 3.6

    • Lecture 13: Review for Test 1.
  • Leon 1.1-1.5, 2.1-2.2, 3.1-3.4, 3.6

    • Lecture 14: Basis and coordinates. Change of basis. Linear transformations.
  • Leon 3.5, 4.1

    • Lecture 15: Linear transformations (continued). Range and kernel. Matrix transformations.
  • Leon 4.1-4.2

    • Lecture 16: Matrix transformations (continued). Matrix of a linear transformation.
  • Leon 4.2-4.3


    • Part III: Advanced linear algebra

  • Orthogonality, least squares problems
  • Inner products and norms
  • The Gram-Schmidt orthogonalization process
  • Eigenvalues and eigenvectors
  • Diagonalization

    Leon's book: Sections 5.1-5.6, 6.1, 6.3
    Lecture 17: Euclidean structure in Rn. Orthogonality. Orthogonal complement.
  • Leon 5.1-5.2

    • Lecture 18: Orthogonal complement (continued). Orthogonal projection. Least squares problems.
  • Leon 5.1-5.3

    • Lecture 19: Least squares problems (continued). Norms and inner products.
  • Leon 5.3-5.4

    • Lecture 20: Inner product spaces. Orthogonal sets.
  • Leon 5.4-5.5

    • Lecture 21: The Gram-Schmidt orthogonalization process. Eigenvalues and eigenvectors of a matrix.
  • Leon 5.5-5.6, 6.1

    • Lecture 22: Eigenvalues and eigenvectors (continued). Characteristic equation.
  • Leon 6.1, 6.3

    • Lecture 23: Diagonalization. Review for Test 2.
  • Leon 3.5, 4.1-4.3, 5.1-5.6, 6.1, 6.3


    • Part IV: Topics in applied linear algebra

  • Matrix exponentials
  • Rotations in space
  • Orthogonal polynomials

    Leon's book: Sections 5.5, 5.7, 6.2-6.4
    Lecture 24: Matrix exponentials.
  • Leon 6.2-6.3

    • Lecture 25: Complex eigenvalues and eigenvectors. Orthogonal matrices. Rotations in space.
  • Leon 5.5, 6.2-6.4

    • Lecture 26: Orthogonal polynomials. Review for the final exam.
  • Leon 1.1-1.5, 2.1-2.2, 3.1-3.6, 4.1-4.3, 5.1-5.7, 6.1-6.3