Fall 2008
MATH 304-503: Linear Algebra
Time and venue: MWF 11:30 a.m.-12:20 p.m., MILN 216
First day hand-out
Suggested weekly schedule
Help sessions for MATH 220/323/304: Monday - Thursday, 6:00PM - 8:00PM, ENPH 213
Time change on the following dates: 9/22, 10/13, 11/3, 12/1, 5:30PM - 7:30PM, ENPH 213
Final exam: Wednesday, December 10, 10:30 a.m.-12:30 p.m., Milner 216
Part IV (2 weeks): Applied linear algebra
Matrix exponentials
Symmetric and orthogonal matrices
Rotations in space
Orthogonal polynomials
Lecture 35: Matrix exponentials.
Leon 6.2-6.3
Lecture 36: Complex eigenvalues and eigenvectors. Symmetric and orthogonal matrices.
Leon 5.5, 6.3-6.4
Lecture 37: Rotations in space.
Leon 5.5, 6.3
Lecture 38: Orthogonal polynomials.
Leon 5.7
Lecture 39: 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 24: Scalar product.
Leon 5.1
Lecture 25: Orthogonal subspaces.
Leon 5.2
Lecture 26: Orthogonal projection. Least squares problems.
Leon 5.2-5.3
Lecture 27: Norms and inner products.
Leon 5.4
Lecture 28: Inner product spaces.
Leon 5.4
Lecture 29: Orthogonal sets. The Gram-Schmidt process.
Leon 5.5-5.6
Lecture 30: The Gram-Schmidt process (continued).
Leon 5.6
Lecture 31: Eigenvalues and eigenvectors. Characteristic equation.
Leon 6.1
Lecture 32: Eigenvalues and eigenvectors of a linear operator.
Leon 6.1, 6.3
Lecture 33: Bases of eigenvectors. Diagonalization.
Leon 6.1, 6.3
Lecture 34: 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 11: Vector spaces.
Leon 3.1
Lecture 12: Subspaces of vector spaces. Span.
Leon 3.1-3.2
Lecture 13: Span (continued). Linear independence.
Leon 3.2-3.3
Lecture 14: Linear independence (continued).
Leon 3.3
Lecture 15: Basis of a vector space.
Leon 3.3-3.4
Lecture 16: Basis and dimension.
Leon 3.4
Lecture 17: Basis and coordinates.
Leon 3.5
Lecture 18: Rank and nullity of a matrix.
Leon 3.6
Lecture 19: Linear transformations. Kernel and range.
Leon 4.1
Lecture 20: Review for Test 1.
Leon 1.1-1.4, 2.1-2.2, 3.1-3.6
Lecture 21: General linear equations. Matrix transformations.
Leon 4.1-4.2
Lecture 22: Matrix of a linear transformation.
Leon 4.2-4.3
Lecture 23: Similarity of matrices.
Leon 4.3
Part I (3.5 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.
Leon 1.1-1.2
Lecture 3: Applications of systems of linear equations.
Leon 1.2
Lecture 4: Row echelon form. Gauss-Jordan reduction.
Leon 1.1-1.2
Lecture 5: Matrix algebra.
Leon 1.3
Lecture 6: Diagonal matrices. Inverse matrix.
Leon 1.3
Lecture 7: Inverse matrix (continued).
Leon 1.3-1.4
Lecture 8: Inverse matrix (continued). Elementary matrices. Transpose of a matrix.
Leon 1.3-1.4
Lecture 9: Determinants.
Leon 2.1-2.2
Lecture 10: Evaluation of determinants.
Leon 2.1-2.2