Spring 2008
MATH 311-504: Topics in Applied Mathematics
First day hand-out
Suggested weekly schedule (has already been altered)
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