Spring 2008
  • MATH 311-504: Topics in Applied Mathematics
    •

    First day hand-out

    Suggested weekly schedule (has already been altered)



    Homework assignments ##1-11


    Sample problems for the final exam (Solutions)


    Test 2 (Solutions)

    Sample problems for Test 2 (Solutions)

    Test 1 (Solutions)

    Sample problems for Test 1 (Solutions)



    Part III (4 weeks): Advanced linear algebra and applications

  • Norms and inner products
  • Orthogonality
  • Symmetric and orthogonal matrices
  • Orthogonal polynomials
  • Introduction to Fourier series

    Williamson/Trotter: Sections 3.6-3.7, 14.8, 14.10

    Lecture 3-1: Complex numbers. Complex eigenvalues.
  • Williamson/Trotter 3.6B

    • Lecture 3-2: Complex eigenvalues and eigenvectors. Norm.
  • Williamson/Trotter 3.6B, 3.7A

    • Lecture 3-3: Norms and inner products.
  • Williamson/Trotter 3.7A

    • Lecture 3-4: Norms induced by inner products. Orthogonality.
  • Williamson/Trotter 3.7A-3.7B

    • Lecture 3-5: Orthogonal bases. The Gram-Schmidt orthogonalization process.
  • Williamson/Trotter 3.7A-3.7B

    • Lecture 3-6: The Gram-Schmidt process (continued).
  • Williamson/Trotter 3.7B

    • Lecture 3-7: Orthogonal polynomials.
  • Williamson/Trotter 3.7B

    • Lecture 3-8: Orthogonal polynomials (continued). Symmetric matrices.
  • Williamson/Trotter 3.7B-3.7C

    • Lecture 3-9: Symmetric and orthogonal matrices.
  • Williamson/Trotter 3.7C

    • Lecture 3-10: Rotations in space.
  • Williamson/Trotter 3.7C

    • Lecture 3-11: Fourier series.
  • Williamson/Trotter 14.8

    • Lecture 3-12: Fourier series (continued).
  • Williamson/Trotter 14.8

    • Lecture 3-13: Fourier's solution of the heat equation. Review for the final exam.
  • Williamson/Trotter 14.10

    • Lecture 3-14: Review for the final exam (continued).
  • Williamson/Trotter 1.1-1.6, 2.1-2.5, 3.1-3.7


    • Part II (5 weeks): Advanced linear algebra

  • Vectors spaces and linear maps
  • Bases and dimension
  • Eigenvalues and eigenvectors


    • Williamson/Trotter: Sections 3.1-3.6

    Lecture 2-1: Vector spaces. Linear maps.
  • Williamson/Trotter 3.2-3.3

    • Lecture 2-2: Linear maps (continued). Matrix transformations.
  • Williamson/Trotter 3.1, 3.3

    • Lecture 2-3: Subspaces of vector spaces. Span.
  • Williamson/Trotter 3.2

    • Lecture 2-4: Span (continued). Image and null-space.
  • Williamson/Trotter 3.2, 3.4

    • Lecture 2-5: Image and null-space (continued). General linear equations.
  • Williamson/Trotter 3.3-3.4

    • Lecture 2-6: Isomorphism. Linear independence (revisited).
  • Williamson/Trotter 3.3-3.5

    • Lecture 2-7: Basis and coordinates.
  • Williamson/Trotter 3.5

    • Lecture 2-8: Basis and dimension.
  • Williamson/Trotter 3.5

    • Lecture 2-9: Basis and dimension (continued). Matrix of a linear transformation.
  • Williamson/Trotter 3.5

    • Lecture 2-10: Matrix of a linear transformation (continued). Eigenvalues and eigenvectors.
  • Williamson/Trotter 3.5-3.6

    • Lecture 2-11: Eigenvalues and eigenvectors (continued). Bases of eigenvectors.
  • Williamson/Trotter 3.6

    • Lecture 2-12: Bases of eigenvectors (continued). Change of coordinates.
  • Williamson/Trotter 3.6

    • Lecture 2-13: Review for Test 2.
  • Williamson/Trotter 3.1-3.6


    • Part I (4.5 weeks): Elementary linear algebra

  • Vectors
  • Systems of linear equations
  • Matrices
  • Determinants


    • Williamson/Trotter: Chapters 1-2

    Lecture 1: Vectors. Dot product.
  • Williamson/Trotter 1.1-1.2, 1.4

    • Lecture 2: Orthogonal projection. Lines and planes.
  • Williamson/Trotter 1.3, 1.5

    • Lecture 3: Lines and planes (continued). Systems of linear equations.
  • Williamson/Trotter 1.3, 2.1A

    • Lecture 4: Applications of systems of linear equations.
  • Williamson/Trotter 2.1B

    • Lecture 5: Gaussian elimination. Row echelon form.
  • Williamson/Trotter 2.1A, 2.2A-2.2B

    • Lecture 6: Row echelon form (continued). Linear independence.
  • Williamson/Trotter 2.2

    • Lecture 7: Linear independence (continued). Matrix algebra.
  • Williamson/Trotter 2.2D, 2.3

    • Lecture 8: Matrix algebra (continued).
  • Williamson/Trotter 2.3

    • Lecture 9: Inverse matrix.
  • Williamson/Trotter 2.4

    • Lecture 10: Inverse matrix (continued). Determinant.
  • Williamson/Trotter 2.4-2.5

    • Lecture 11: Properties of determinants.
  • Williamson/Trotter 2.5

    • Lecture 12: Evaluation of determinants. Cross product.
  • Williamson/Trotter 1.6, 2.5

    • Lecture 13: Review for Test 1.
  • Williamson/Trotter 1.1-1.6, 2.1-2.5