CAAM 335 · Matrix Analysis

Spring 2008 · Rice University


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COURSE NOTES   //  LABORATORY


References

Lecture 22: Cauchy-Riemann Equations, complex differentiation
Lecture 21: Partial fraction expansions of rational functions
Lecture 20: Complex arithmetic; Euler's formula
- supplemental notes: lecture20.pdf on complex arithmetic and complex functions
- Read Chapter 7 of the course notes
Lecture 19: Backward Euler and forward Euler methods
- supplemental notes: lecture19.pdf on the forward Euler method
Lecture 18: Inverse Laplace Transform; resolvent; eigenvalues
- supplemental notes: lecture18.pdf on resolvents
Lecture 17: Using Laplace transforms to solve systems of differential equations
- supplemental notes: lecture17.pdf on Laplace transforms
Lecture 16: Introduction to dynamical systems and the Laplace transform
- supplemental notes: lecture16.pdf on Richardson's model of the arms race
- Read Chapter 6 of the course notes.
- arms_race.m: Richardson's model of the arms race
Lecture 15: Applications of least squares
- findfiber.m: recovery of spring constants from force, displacements via least squares
Lecture 14: Projectors and reflectors
- supplemental notes: lecture14.pdf on projectors
Lecture 13: Least Squares: normal equations, projectors
- supplemental notes: lecture13.pdf on deriving the normal equations via multivariable calculus
Lecture 12: Introduction to Least Squares
- Read Chapter 5 of the course notes
Lecture 11: Fundamental Theorem of Linear Algebra, part 2
- supplemental notes: lecture11.pdf
Lecture 10: Fundamental Theorem of Linear Algebra, part 1
- supplemental notes: lecture10.pdf
- Read Chapter 4 of the course notes
- plotline2.m, plotplane2.m, plotline3.m, plotplane3.m
Lecture 9: Range and null spaces
- supplemental notes: lecture9.pdf (a solution to the challenge posed in lecture8.pdf)
Lecture 8: Subspaces; range and null spaces
- supplemental notes: lecture8.pdf
- A diversion about dimensions: Flatland: A Romance of Many Dimensions
Lecture 7: Bi-axial truss, intro to range and null spaces
- fiber.m: 3-by-3 biaxial truss demo
- Read Chapter 3 of the course notes
Lecture 6: 2-d mechanical systems
- supplemental notes: lecture6.pdf
- Summer internships in Theoretical and Computational Neuroscience
- Instron bi-axial soft tissue test hardware (compare to model on page 26 of the notes)
Lecture 5: Matrix inverse, LU factorization
Lecture 4: 1-d mechanical systems; Gaussian elimination
- supplemental notes: lecture4.pdf
- Read Chapter 2 of the course notes
- Arthur Cayley, "A Memoir on the Theory of Matrices", 1858
Lecture 3: Networks with resistors and batteries; Intro to mechanical systems
- supplemental notes: lecture3.pdf (challenge: model the network on the second page)
- MATLAB demos: fib2.m, symfib.m
Lecture 2: Matrix models of resistor networks (neurons)
- supplemental notes: lecture2.pdf
- Read Chapter 1 of the course notes
- MATLAB demo: fib1.m
Lecture 1: Population modeling via matrix-vector multiplication
- supplemental notes: lecture1.pdf
- MATLAB demos: population.m, eigenvalue.m