Spring 2007
  • Math 311-503: Topics in Applied Mathematics
    •

    First day hand-out

    Suggested weekly schedule (has already been altered)


    Homework assignments ##1-10



    Final exam (Solutions)

    Sample problems for the final exam (Solutions)


    Sample problems for Test 2 (Solutions)

    Test 2 (Solutions)


    Sample problems for Test 1 (Solutions)

    Test 1 (Solutions)



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

  • Norms and inner products
  • Orthogonal polynomials
  • Matrix exponentials

    Williamson/Trotter: Sections 3.7, 13.2

    Lecture 3-1: Complex eigenvalues and eigenvectors.
  • Williamson/Trotter 3.6

    • Lecture 3-2: Norms. Inner products. Orthogonal bases.
  • Williamson/Trotter 3.7

    • Lecture 3-3: The Gram-Schmidt process.
  • Williamson/Trotter 3.7

    • Lecture 3-4: The Gram-Schmidt process (continued). Symmetric matrices. Orthogonal matrices.
  • Williamson/Trotter 3.7

    • Lecture 3-5: Orthogonal matrices (continued). Orthogonal polynomials.
  • Williamson/Trotter 3.7

    • Lecture 3-6: Orthogonal polynomials (continued). Matrix exponentials.
  • Williamson/Trotter 3.7, 13.2

    • Lecture 3-7: Matrix exponentials (continued). The Cayley-Hamilton theorem.
  • Williamson/Trotter 13.2

    • Lecture 3-8: Review for the final exam.
  • Williamson/Trotter 1-3, 13.2



    • Part II (5 weeks): Advanced linear algebra

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


    • Williamson/Trotter: Chapter 3

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

    • Lecture 2-2: Matrix transformations. Subspaces.
  • Williamson/Trotter 3.1-3.2

    • Lecture 2-3: Linear span. Image and null-space.
  • Williamson/Trotter 3.2-3.4

    • Lecture 2-4: Image and null-space (continued). General linear equations.
  • Williamson/Trotter 3.1-3.4

    • Lecture 2-5: Isomorphism. Bases and coordinates.
  • Williamson/Trotter 3.4-3.5

    • Lecture 2-6: Bases and coordinates (continued). Dimension.
  • Williamson/Trotter 3.5

    • Lecture 2-7: Matrix of a linear map. Eigenvalues and eigenvectors. Characteristic equation.
  • Williamson/Trotter 3.6

    • Lecture 2-8: Eigenvalues and eigenvectors (continued). Bases of eigenvectors.
  • Williamson/Trotter 3.6

    • Lecture 2-9: Change of coordinates. Jordan normal form.
  • Williamson/Trotter 3.6

    • Lecture 2-10: Complex numbers. Review for Test 2.
  • Williamson/Trotter 3.1-3.6



    • Part I (4 weeks): Elementary linear algebra

  • Vectors
  • Systems of linear equations
  • Matrices
  • Determinants


    • Williamson/Trotter: Chapters 1-2

    Lecture 1: Vectors. Dot product. Lines and planes.
  • Williamson/Trotter 1.1-1.4

    • Lecture 2: Lines and planes. Systems of linear equations.
  • Williamson/Trotter 1.3, 1.5, 2.1

    • Lecture 3: Systems of linear equations. Matrices.
  • Williamson/Trotter 2.1-2.2

    • Lecture 4: Linearly independent vectors. Matrix algebra.
  • Williamson/Trotter 2.2-2.3

    • Lecture 5: Matrix algebra (continued). Inverse matrices.
  • Williamson/Trotter 2.3-2.4

    • Lecture 6: Inverse matrices (continued). Determinants.
  • Williamson/Trotter 2.4-2.5

    • Lecture 7: Determinants (continued). Cross product.
  • Williamson/Trotter 1.6, 2.5