Fall 2010
MATH 304-506: Linear Algebra
Time and venue: MWF 10:20-11:10 a.m., MILN 216
Office hours (MILN 004):
Monday, 11:30 a.m.-1:00 p.m.
Wednesday, 11:30 a.m.-1:00 p.m.
by appointment
Help sessions (BLOC 148):
Mondays - Thursdays (until December 9), 5:30-8:00 p.m.
Additional office hours (MILN 004):
Wednesday, December 8, 11:30 a.m.-1:00 p.m.
Friday, December 10, 2:00-4:00 p.m.
Monday, December 13, 12:00-2:00 p.m.
Final exam: Tuesday, December 14, 8:00-10:00 a.m., MILN 216
Rules for the exam: no books, no lecture notes, no calculators. Bring paper and a stapler.
Course outline:
Part I: Elementary linear algebra
Systems of linear equations
Gaussian elimination, Gauss-Jordan reduction
Matrices, matrix algebra
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: Row echelon form. Gauss-Jordan reduction.
Leon 1.1-1.2
Lecture 4: Applications of systems of linear equations.
Leon 1.2
Lecture 5: Matrix algebra.
Leon 1.3
Lecture 6: Diagonal matrices. Inverse matrix.
Leon 1.3-1.4
Lecture 7: Inverse matrix (continued).
Leon 1.4
Lecture 8: Elementary matrices. Transpose of a matrix. Determinants.
Leon 1.3-1.4, 2.1
Lecture 9: Properties of determinants.
Leon 2.1-2.2
Lecture 10: Evaluation of determinants. Cramer's rule.
Leon 2.2-2.3
Part II: Abstract linear algebra
Vector spaces
Linear independence
Basis and dimension
Coordinates, change of basis
Linear transformations
Leon's book: Chapters 3-4
Lecture 11: Vector spaces.
Leon 3.1
Lecture 12: Subspaces of vector spaces.
Leon 3.1-3.2
Lecture 13: Span. Spanning set.
Leon 3.2
Lecture 14: Linear independence.
Leon 3.3
Lecture 15: Wronskian. Basis of a vector space.
Leon 3.3-3.4
Lecture 16: Basis and dimension.
Leon 3.4
Lecture 17: Rank and nullity of a matrix.
Leon 3.2, 3.6
Lecture 18: Basis and coordinates. Change of coordinates.
Leon 3.5
Lecture 19: Review for Test 1.
Leon 1.1-1.4, 2.1-2.2, 3.1-3.4, 3.6
Lecture 20: Linear transformations. Range and kernel.
Leon 4.1
Lecture 21: General linear equations. Matrix transformations. Matrix of a linear transformation.
Leon 4.1-4.2
Lecture 22: Matrix of a linear transformation (continued). Similar matrices.
Leon 4.2-4.3
Part III: Advanced linear algebra
Orthogonality
Inner products and norms
The Gram-Schmidt orthogonalization process
Eigenvalues and eigenvectors
Diagonalization
Leon's book: Sections 5.1-5.6, 6.1, 6.3
Lecture 23: Euclidean structure in Rn. Orthogonality.
Leon 5.1-5.2
Lecture 24: Orthogonal complement. Orthogonal projection.
Leon 5.2
Lecture 25: Orthogonal projection (continued). Least squares problems.
Leon 5.2-5.3
Lecture 26: Norms and inner products.
Leon 5.4
Lecture 27: Inner product spaces. Orthogonal sets.
Leon 5.4-5.5
Lecture 28: Orthogonal bases. The Gram-Schmidt orthogonalization process.
Leon 5.5-5.6
Lecture 29: The Gram-Schmidt process (continued).
Leon 5.6
Lecture 30: Eigenvalues and eigenvectors. Characteristic equation.
Leon 6.1
Lecture 31: Eigenvalues and eigenvectors (continued).
Leon 6.1
Lecture 32: Bases of eigenvectors. Diagonalization.
Leon 6.1, 6.3
Lecture 33: Diagonalization (continued).
Leon 6.2-6.3
Lecture 34: Review for Test 2.
Leon 3.5, 4.1-4.3, 5.1-5.6, 6.1, 6.3
Part IV: Topics in applied linear algebra
Matrix exponentials
Rotations in space
Orthogonal polynomials
Markov chains
Leon's book: Sections 5.5, 5.7, 6.1-6.4
Lecture 35: Matrix exponentials.
Leon 6.2-6.3
Lecture 36: Complexification. Symmetric and orthogonal matrices.
Leon 5.5, 6.2, 6.4
Lecture 37: Rotations in space.
Leon 5.5, 6.2, 6.4
Lecture 38: Orthogonal polynomials.
Leon 5.7
Lecture 39: Markov chains.
Leon 6.3
Lecture 40: Review for the final exam.
Leon 1.1-1.4, 2.1-2.2, 3.1-3.6, 4.1-4.3, 5.1-5.7, 6.1-6.3