Fall 2010
  • MATH 304-502: Linear Algebra
    •

    Time and venue:   MWF 9:10-10:00 a.m., MILN 216

    First day hand-out

    Office hours (MILN 004):
  • Monday, 11:30 a.m.-1:00 p.m.
  • Wednesday, 11:30 a.m.-1:00 p.m.
  • by appointment

    • Help sessions (BLOC 148):
  • Mondays - Thursdays (until December 9), 5:30-8:00 p.m.
    •
    Additional office hours (MILN 004):
  • Wednesday, December 8, 11:30 a.m.-1:00 p.m.
  • Friday, December 10, 2:00-4:00 p.m.
    •

    Final exam:  Monday, December 13, 8:00-10:00 a.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 2 (Solutions)

    Sample problems for Test 1 (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.
  • Leon 1.1

    • Lecture 2: Gaussian elimination.
  • Leon 1.1-1.2

    • Lecture 3: Row echelon form. Gauss-Jordan reduction.
  • Leon 1.1-1.2

    • Lecture 4: Applications of systems of linear equations.
  • Leon 1.2

    • Lecture 5: Matrix algebra.
  • Leon 1.3

    • Lecture 6: Diagonal matrices. Inverse matrix.
  • Leon 1.3-1.4

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

    • Lecture 8: Elementary matrices. Transpose of a matrix. Determinants.
  • Leon 1.3-1.4, 2.1

    • Lecture 9: Properties of determinants.
  • Leon 2.1-2.2

    • Lecture 10: Evaluation of determinants. 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 11: Vector spaces.
  • Leon 3.1

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

    • Lecture 13: Span. Spanning set.
  • Leon 3.2

    • Lecture 14: Linear independence.
  • Leon 3.3

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

    • Lecture 16: Basis and dimension.
  • Leon 3.4

    • Lecture 17: Rank and nullity of a matrix.
  • Leon 3.2, 3.6

    • Lecture 18: Basis and coordinates. Change of coordinates.
  • Leon 3.5

    • Lecture 19: Review for Test 1.
  • Leon 1.1-1.4, 2.1-2.2, 3.1-3.4, 3.6

    • Lecture 20: Linear transformations. Range and kernel.
  • Leon 4.1

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

    • Lecture 22: Matrix of a linear transformation (continued). Similar matrices.
  • Leon 4.2-4.3


    • Part III: Advanced linear algebra

  • Orthogonality
  • 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 23: Euclidean structure in Rn. Orthogonality.
  • Leon 5.1-5.2

    • Lecture 24: Orthogonal complement. Orthogonal projection.
  • Leon 5.2

    • Lecture 25: Orthogonal projection (continued). Least squares problems.
  • Leon 5.2-5.3

    • Lecture 26: Norms and inner products.
  • Leon 5.4

    • Lecture 27: Inner product spaces. Orthogonal sets.
  • Leon 5.4-5.5

    • Lecture 28: Orthogonal bases. The Gram-Schmidt orthogonalization process.
  • Leon 5.5-5.6

    • Lecture 29: The Gram-Schmidt process (continued).
  • Leon 5.6

    • Lecture 30: Eigenvalues and eigenvectors. Characteristic equation.
  • Leon 6.1

    • Lecture 31: Eigenvalues and eigenvectors (continued).
  • Leon 6.1

    • Lecture 32: Bases of eigenvectors. Diagonalization.
  • Leon 6.1, 6.3

    • Lecture 33: Diagonalization (continued).
  • Leon 6.2-6.3

    • Lecture 34: 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
  • Markov chains

    Leon's book: Sections 5.5, 5.7, 6.1-6.4
    Lecture 35: Matrix exponentials.
  • Leon 6.2-6.3

    • Lecture 36: Complexification. Symmetric and orthogonal matrices.
  • Leon 5.5, 6.2, 6.4

    • Lecture 37: Rotations in space.
  • Leon 5.5, 6.2, 6.4

    • Lecture 38: Orthogonal polynomials.
  • Leon 5.7

    • Lecture 39: Markov chains.
  • Leon 6.3

    • Lecture 40: Review for the final exam.
  • Leon 1.1-1.4, 2.1-2.2, 3.1-3.6, 4.1-4.3, 5.1-5.7, 6.1-6.3