 | In this session we learn matrix methods for solving constant coefficient linear systems of DE's. This method will supersede the method of elimination used in the last session. In order to use matrix methods we will need to learn about eigenvalues and eigenvectors of matrices. |
Session Activities
Read the course notes:
- Matrix Methods: Eigenvalues and Normal Modes: Introduction (PDF)
- Vectors and Matrices: Homogeneous Systems (PDF)
Complete the practice problem:
Watch the lecture video clip:
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Matrix Methods Introduction, First Example (00:30:14)
Matrix Methods Introduction, First Example
> Download from iTunes U (MP4 - 94MB)
> Download from Internet Archive (MP4 - 94MB)
Read the course notes:
Watch the lecture video clip:
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Matrix Systems: General Terminology (00:18:55)
Matrix Systems: General Terminology
> Download from iTunes U (MP4 - 94MB)
> Download from Internet Archive (MP4 - 94MB)
Read the course notes:
Learn from the Mathlet materials:
- Read about how to work with the Matrix/Vector Applet (PDF)
- Work with the Matrix/Vector Applet
Watch the lecture video clip:
- Complex Eigenvalues: Example (00:11:46)
Read the course notes:
Watch the lecture video clip:
-
Three Chamber Mixing Example: Repeated Roots (00:30:47)
Three Chamber Mixing Example: Repeated Roots
> Download from iTunes U (MP4 - 89MB)
> Download from Internet Archive (MP4 - 89MB)
Read the course notes:
Watch the problem solving videos:
- Linear Systems: Matrix Methods (00:08:00)
- Linear Systems: Complex Roots (00:11:49)
Check Yourself
Complete the problem sets:
- Problem Set Part I Problems (PDF)
- Problem Set Part I Solutions (PDF)
- Problem Set Part II Problems (PDF)
- Problem Set Part II Solutions (PDF)