Spring 2017

Time and venue:  MWF 11:30 a.m.–12:20 p.m., BLOC 163

First day hand-out

Office hours (BLOC 223b):
Help sessions (BLOC 161):
Additional office hours (BLOC 223b):

Quiz 1:  Friday, January 27  (topic: systems of linear equations)
Quiz 2:  Friday, February 3  (topics: matrix algrebra, inverse matrix)
Quiz 3:  Friday, February 10c  (topic: determinants)
Quiz 4:  Friday, February 17  (topics: vector spaces, subspaces, span)
Quiz 5:  Friday, February 24  (topic: linear independence)
Test 1:  Friday, March 3
Quiz 6:  Friday, March 10  (topics: basis and coordinates, change of basis)
Quiz 7:  Friday, March 24  (topics: linear transformations, matrix of a linear transformation)
Quiz 8:  Friday, March 31  (topics: eigenvalues and eigenvectors, diagonalization)
Quiz 9:  Friday, April 7  (topics: orthogonal complement, orthogonal projection, least squares solutions)
Test 2:  Wednesday, April 12
Quiz 10:  Friday, April 21  (topics: norms, inner products)
Quiz 11:  Friday, April 28  (topic: rigid motions)
Quiz 12:  Monday, May 1  (topic: matrix exponentials)
Final exam:  Tuesday, May 9, 10:30 a.m.–12:30 p.m.

Sample problems for the final exam (Solutions)

Sample problems for Test 1

Sample problems for Test 2

Suggested homework for quizzes

Course outline:

Part I: Elementary linear algebra


Leon's book: Chapters 1-2

Lecture 1: Systems of linear equations.
Lecture 2: Gaussian elimination.
Lecture 3: Row echelon form. Gauss-Jordan reduction.
Lecture 4: System with a parameter. Applications of systems of linear equations.
Lecture 5: Matrix algebra.
Lecture 6: Diagonal matrices. Inverse matrix.
Lecture 7: Inverse matrix (continued).
Lecture 8: Elementary matrices. Transpose of a matrix. Determinants.
Lecture 9: Properties of determinants.
Lecture 10: Evaluation of determinants. Cramer's rule.

Part II: Abstract linear algebra


Leon's book: Chapters 3-4

Lecture 11: Vector spaces.
Lecture 12: Vector spaces (continued). Subspaces of vector spaces.
Lecture 13: Subspaces of vector spaces (continued). Span. Spanning set.
Lecture 14: Span (continued). Linear independence.
Lecture 15: Linear independence (continued). Wronskian.
Lecture 16: Basis and dimension.
Lecture 17: Basis and dimension (continued).
Lecture 18: Rank and nullity of a matrix.
Lecture 19: Review for Test 1.
Lecture 20: Basis and coordinates. Change of basis.
Lecture 21: Change of basis (continued). Linear transformations.
Lecture 22: Range and kernel. General linear equations.
Lecture 23: Matrix transformations. Matrix of a linear transformation. Similar matrices.

Part III: Advanced linear algebra


Leon's book: Sections 5.1-5.6, 6.1, 6.3

Lecture 24: Eigenvalues and eigenvectors. Characteristic equation.
Lecture 25: Eigenvalues and eigenvectors of a linear operator.
Lecture 26: Eigenvalues and eigenvectors (continued). Basis of eigenvectors. Diagonalization.
Lecture 27: Diagonalization (continued). Euclidean structure in Rn.
Lecture 28: Orthogonal complement. Orthogonal projection.
Lecture 29: Orthogonal projection (continued). Least squares problems.
Lecture 30: Least squares problems (continued). Orthogonal bases. The Gram-Schmidt orthogonalization process.
Lecture 31: The Gram-Schmidt process (continued). Norm on a vector space.
Lecture 32: Review for Test 2.
Lecture 33: Inner product spaces.
Lecture 34a: Orthogonality in inner product spaces.

Part IV: Topics in applied linear algebra


Leon's book: Sections 5.5, 5.7, 6.1-6.4

Lecture 34b: Orthogonal polynomials.
Lecture 35: Complex eigenvalues and eigenvectors. Normal matrices.
Lecture 36: Orthogonal matrices. Rigid motions. Rotations in space.
Lecture 37: Matrix polynomials. Matrix exponentials.
Lecture 38: Markov chains.
Lecture 39: Review for the final exam.
Lecture 40: Review for the final exam (continued).