Syllabus for 18.06 Linear Algebra Summer Course 2009
This is a rough syllabus. Please contact the instructor if you have any questions.
Lecture 1 M June 8 Introduction, Chapter 1 Vectors
Lecture 2 W June 10 2.1 – 2.4 Linear Equations, Elimination, Matrix Operations
Lecture 3 F June 12 2.4, 2.5 Computing with Matrices, Inverse
Lecture 4 M June 15 2.6 – 2.7 Factorization, Permutation, Transpose
Lecture 5 W June 17 3.1 3.2 Vector Space, Subspaces, Nullspace, dimension
Lecture 6 F June 19 3.2 – 3.3 Rank & Row Reduced Form
Lecture 7 M June 22 3.4 – 3.5 Solving Ax=b
Lecture 8 W June 24 3.6 Four Fundamental Subspaces
Lecture 9 F June 26 4.1 – 4.2 Orthogonality, Projections
Lecture 10 M June 29 4.3 Least Square Approximation
Lecture 11 W July 1 4.4 Orthogonal Basis, GramSchmidt
F July 3 - No class
Lecture 12 M July 6 5.1-5.2 Determinants: Formulas and Properties
Lecture 13 W July 8 5.3 Cramer's Rule
Exam 1 F July 10 Chapters 1-5
Lecture 14 M July 13 6.1 Introduction to eigenvalues
Lecture 15 W July 15 6.2 Diagonalizing a matrix
Lecture 16 F July 17 6.3 Application to differential Equations
Lecture 17 M July 20 6.4 Symmetric Matrices
Lecture 18 W July 22 6.5 Positive definite Matrices
Lecture 19 F July 24 6.6 Similar Matrices
Lecture 20 M July 26 6.6 Jordan Normal Form
Lecture 21 W July 29 6.7 Singular Value Decomposition
Lecture 22 F July 31 Review Review for Midterm 2
Exam 2 M August 3 Chapters 1-6
Lecture 23 W August 5 7.1-7.2 Linear Transformations
Lecture 24 F August 7 7.3 Change of Basis
Lecture 25 M August 10 7.4 More on Linear Transformations
Lecture 26 W August 12 8.4, 10.2, 10.3 Fourier Transform and Fast Fourier Transform
Lecture 27 F August 14 Final Review Review for the Final Exam
Final Exam M August 17 Final Exam. Good Luck!