CAAM 335 · Matrix AnalysisSpring 2008 · Rice University
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| 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 |