# Scientific Computing with Case Studies

## by Dianne P. O'Leary

SIAM Press , 2009 This website contains additional notes, exercises, case studies, etc.
No solutions to exercises or challenges are provided.

• Unit I. Preliminaries: Mathematical Modeling, Errors, Hardware, and Software
• Supplementary exercises
• Sample lecture notes: Slides and Handout

• Unit II. Dense Matrix Computations
• Supplementary exercises
• Sample lecture notes: Slides and Handout

• Unit III. Optimization and Data Fitting
• Supplementary exercises
• An example of a good linesearch: cvsrch.m and cstep.m
• Sample lecture notes: Slides and Handout

• Unit IV. Monte Carlo Computations
• Supplementary exercises
• Demonstration: demorand.m . Check the distribution of pseudorandom numbers.
• Sample lecture notes: Slides and Handout

• Unit V. Solution of Differential Equations
• Supplementary exercises
• Sample lecture notes: Slides Part 1, Slides Part 2, and Handout Part 1, Handout Part 2

• Unit VI. Nonlinear Systems and Continuation Methods
• Supplementary exercises
• Homotopy example applying the method to a simple problem.
• Sample lecture notes: Slides and Handout

• Unit VII. Sparse Matrix Computations, with Applications to Partial Differential Equations
• Supplementary exercises
• A summary of some convergence results for stationary iterative methods
• Demonstration: spar5.m . spar50.m is this program with "m=50" and nested dissection removed.
• Sample lecture notes: Slides Part 1, Slides Part 2, and Handout Part 1, Handout Part 2

• Supplementary Case Studies. Instructors might find some inspiration in these when writing assignments, and students can use them for additional practice, but they come without warranty.

• SVD for Image and Video Filtering by Ashwin Swaminathan
Matrix computations (2004).
• Modeling of a Seat Suspension System by Gregory J. Hiemenz.
Ordinary differential equations. (2006) (There is a sign error in the first term of equation (14).)
• Gaining Insight in Markov Chains by Using Monte Carlo Simulations by David Rouff.
Monte Carlo methods. (2006)
• Protein Folding Using Homotopy Methods by James Robert White.
Solution of nonlinear equations and optimization. (2006)
• What's the Score? Matrices, Documents, and Queries, by Dianne P. O'Leary.
Matrix computations for latent semantic analysis. (2008)
• Taking Stock of Our Situation: Pricing and Randomness by Dianne P. O'Leary.
Markov chains and stochastic differential equations in financial modeling. (2008)
• "Good" Can Mean So Many Things by Dianne P. O'Leary.
Assessing and modifying matrix software. (2010)
• A Random Walk to Capacitance by Dianne P. O'Leary.
Monte Carlo simulations, algorithm benchmarking, error assessment. (2010)
• Light a Single Candle by Dianne P. O'Leary.
Separable least squares datafitting for supernovae light curves. (2010)
• The Phantom of the Operations by Dianne P. O'Leary.
Spline interpolation and smoothing, least squares datafitting, quadrature (including Monte Carlo), understanding modelling error. (2010)