Fall 2007
  • MATH 304-504: Linear Algebra
    •

    First day hand-out

    Suggested weekly schedule

    Help sessions for MATH 220/222/304:
    Mo, Tu, Th (5:30-8:00 p.m.) and We (7:00-9:30 p.m.) in ENPH 215


    Homework assignments ##1-12


    Final exam:   Tuesday, December 11, 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 (2.5 weeks): Applied linear algebra

  • Matrix exponentials
  • Symmetric and orthogonal matrices
  • Orthogonal polynomials
  • Markov chains

    Lecture 34: Matrix exponentials.
  • Leon 6.2-6.3

    • Lecture 35: Symmetric and orthogonal matrices.
  • Leon 5.5, 6.3-6.4

    • Lecture 36: Symmetric and orthogonal matrices (continued).
  • Leon 5.5, 6.3-6.4

    • Lecture 37: Rotations in space. Orthogonal polynomials.
  • Leon 5.5, 5.7, 6.3

    • Lecture 38: Orthogonal polynomials (continued).
  • Leon 5.7

    • Lecture 39: Markov chains.
  • Leon 6.3

    • Lecture 40: Review for the final exam.
  • Leon 1.1-1.4, 2.1-2.3, 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 23: Scalar product.
  • Leon 5.1

    • Lecture 24: Orthogonal subspaces.
  • Leon 5.2

    • Lecture 25: Least squares problems.
  • Leon 5.3

    • Lecture 26: Inner products and norms.
  • Leon 5.4

    • Lecture 27: Inner product spaces.
  • Leon 5.4

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

    • Lecture 29: The Gram-Schmidt process (continued).
  • Leon 5.5-5.6

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

    • Lecture 31: Bases of eigenvectors. Diagonalization.
  • Leon 6.1, 6.3

    • Lecture 32: Diagonalization (continued). Complex eigenvalues and eigenvectors.
  • Leon 6.1, 6.3

    • Lecture 33: 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 10b: Vector spaces.
  • Leon 3.1

    • Lecture 11: Vector spaces and their subspaces.
  • Leon 3.1-3.2

    • Lecture 12: Span.
  • Leon 3.2

    • Lecture 13: Linear independence.
  • Leon 3.3

    • Lecture 14: The Vandermonde determinant. Basis of a linear space.
  • Leon 3.3-3.4

    • Lecture 15: Basis and dimension.
  • Leon 3.4

    • Lecture 16: Basis and coordinates.
  • Leon 3.5

    • Lecture 17: Change of coordinates (continued). Rank and nullity of a matrix.
  • Leon 3.2, 3.5-3.6

    • Lecture 18: Column space of a matrix. Linear transformations. Kernel and range.
  • Leon 3.6, 4.1

    • Lecture 19: Kernel and range (continued). Matrix transformations.
  • Leon 4.1-4.2

    • Lecture 20: Review for Test 1.
  • Leon 1.1-1.4, 2.1-2.3, 3.1-3.6

    • Lecture 21: Matrix of a linear transformation.
  • Leon 4.2-4.3

    • Lecture 22: Similarity.
  • Leon 4.3

    • Part I (3 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. Row echelon form.
  • Leon 1.1-1.2

    • Lecture 3: Gauss-Jordan reduction. Applications of systems of linear equations.
  • Leon 1.2

    • Lecture 4: Another application of systems of linear equations. Matrix algebra.
  • Leon 1.2-1.3

    • Lecture 5: Matrix algebra (continued). Diagonal matrices. Inverse matrix.
  • Leon 1.3-1.4

    • Lecture 6: Inverse matrix (continued).
  • Leon 1.3-1.4

    • Lecture 7: Elementary matrices. Determinants.
  • Leon 1.4, 2.1-2.2

    • Lecture 8: Properties of determinants.
  • Leon 2.1-2.2

    • Lecture 9: Evaluation of determinants.
  • Leon 2.2

    • Lecture 10a: Cramer's rule.
  • Leon 2.3