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Supplemental
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Parallel computing introduction
Lectures
Class 1 Introduction
Class 2 Errors, accuracy, and roundoff
- Questions
- Notes
- Slides
- Some good links
- Cook: Whats so hard about finding a hypotenuse?
- Cook: Math library functions that seem unnecessary
- Cook: Anatomy of a floating point number
- What every computer scientist should know about floating point arithmetic
- Base 3 is best
- Brian Hayes, “Third Base,” American Scientist 89(6):490-494(2001).
Class 3 Linear algebra review
Class 4 Linear systems-direct methods
Class 5-6 Linear systems-iterative methods
Class 7 Nonlinear equations I
Class 8 Nonlinear equations II
Class 9 Nonlinear equations III
Class 10 Numerical derivatives
Class 11 ODEs I
Class 12 ODEs II
Class 13 ODEs III
Class 14-15 Stability, consistency, stiffness
Class 16 BVPs: shooting methods
Class 17 BVPs: relaxation methods
Class 18 BVPs: BCs, nonlinear, nonuniform
Class 19 PDEs: introduction
Class 20 PDEs: parabolic
Class 21 PDEs: stability
Class 22 PDEs: multiDimensional
Class 23 PDEs: Elliptic PDEs, ADI method
Class 24 PDEs: Finite volume method
Class 25 PDEs: Finite volume method 2
Class 26 PDEs: Advection and diffusion
Class 27 PDEs: Advection and diffusion II exponential scheme
Class 28 Hyperbolic equations 1
Class 29 projects
Class 30 projects
Class 31 Hyperbolic equations, flux limiters, Euler equations
Class 32 Integration I
Class 33 Integration II
Class 34 Sample from PDF
Class 35 Gauss Quadrature
Class 36 Interpolation
Class 37 Curve fitting
Class 38 Spectral Methods
Class 39 Homotopy continuation
- Notes
- Papers
- Wayburn, Seader, 1987 Homotopy continuation methods for computer-aided process design.
- Kuno, Seader, 1988 Computing all real solutions to systems of nonlinear equations with a global fixed-point homotopy.
- Khaleghi, Jalali, 2007 Multiple solutions in stability analysis using homotopy continuation in complex space.
- Rahimian, Jalali, Seader, White, 2011 A new homotopy for seeking all real roots of a nonlinear equation.
- Jimenez-Islas, Martinez-Gonzalez, Navarrete-Bolanos, Botello-Alvarez Oliveros-Munos, 2013 Nonlinear Homotopic continuation methods: a chemical engineering perspective review.