Syllabus for 18.06 Linear Algebra Summer Course 2008
This is an approximate syllabus. Please contact the instructor if you have any questions.
Lecture 1 M June 9 Introduction, Chapter 1 Vectors
Lecture 2 W June 11 2.1 - 2.4 Linear equations, Elimination, Matrix operations
Lecture 3 F June 13 2.4, 2.5 Computing with matrices, inverse
Lecture 4 M June 16 2.6, 2.7 Factorization, Permutation, Transpose
Lecture 5 W June 18 3.1, 3.2 Vector Space, Subspaces, Nullspace, Dimension, HW 1 due
Lecture 6 F June 20 3.2, 3.3 Rank, Row reduced form
Lecture 7 M June 23 3.4, 3.5 Solving Ax=b, Independence
Lecture 8 W June 25 3.6 Basis, Dimension, Four fundamental subspaces, HW 2 due
Lecture 9 F June 27 4.1, 4.2 Orthogonality, Projections
Lecture 10 M June 30 4.3 Least square approximation
Lecture 11 W July 2 4.4 Orthogonal Basis, Gram-Schmidt
F July 4 Independence Day, no class
M July 7 Exam 1, Chapters 1 - 4, HW 3 due
Lecture 12 W July 9 5.1, 5.2 Determinants: formulas and properties
Lecture 13 F July 11 5.3 Cramer's rule
Lecture 14 M July 14 6.1 Introduction to eigenvalues
Lecture 15 W July 16 6.2 Diagonalizing a matrix
Lecture 16 F July 18 6.3 Application to differential equations, HW 4 due
Lecture 17 M July 21 6.4 Symmetric matrices
Lecture 18 W July 23 6.5 Positive definite matrices
Lecture 19 F July 25 6.6 Similar matrices, Jordan normal form
Lecture 20 M July 28 6.7 Singular value decomposition, HW 5 due
Lecture 21 W July 30 7.1, 7.2 Linear transformations
Lecture 22 F August 1 Review for Midterm 2
M August 4 Exam 2, Chapters 1 - 6, HW 6 due
Lecture 23 W August 6 7.3, 7.4 Change of basis, Pseudoinverse
Lecture 24 F August 8 9. Numerical linear algebra
Lecture 25 M August 11 8.4 Linear programming
Lecture 26 W August 13 10.2, 10.3 Fourier transform, Fast Fourier transform
Lecture 27 F August 15 Review for the Final exam, HW 7 due
M August 18 9-12 2-131 Final exam