1.2.12. Week 12 - 11/4

Agenda for this week:

This week covers important topics related to the applications of eigenvalues and eigenvectors. The section on Change of Basis and Difference Equations shows how a number of interesting problems are solved. For example, Google’s page ranking algorithm uses the change of basis technique with a Markov matrix. The section on Systems of Linear ODEs is especially important to engineers interested in control systems.

Reading:

• 8.5. Diagonalization and Powers of A
• 8.6. Change of Basis and Difference Equations
• 8.7. Systems of Linear ODEs

Video Lectures:

• Sections 8.5.1-2 - Diagonalization and Powers of A (22:13)
• Section 8.6 - Change of Basis (14:20)
• Section 8.6.1 - Difference Equations (11:24)
• Section 8.6.3 - Application: Markov Chains (11:02)
• Section 8.7 - Systems of Linear ODEs (12:29)

Annotated notes:

• Systems of Linear ODEs - notes/SysODE.pdf
• Diagonalization and Powers of - notes/Diag_Powers.pdf
• Diagonalization - notes/Diagonalization.pdf

Assignments:

• Markov Matrix of Land Use
• Video: Markov Matrix Homework assignment NOTE: There was a small error in the Markov matrix used in the video, it has been corrected in the LandUse.mat file. The procedure used is what is important.
• Systems of Linear ODEs Homework
• Video: Systems of Linear ODEs Homework assignment
• Attendance Quizzes: AQ08_4, AQ08_5, Week 12 Attendance Quiz Hints