I. Preliminaries: Mathematical Modeling, Errors, Hardware, and Software -- 1. Errors and Arithmetic -- 2. Sensitivity Analysis: When a Little Means a Lot -- 3. Computer Memory and Arithmetic: A Look Under the Hood -- 4. Design of Computer Programs: Writing Your Legacy -- II. Dense Matrix Compututions -- 5. Matrix Factorization -- 6. Case Study: Image Deblurring: I Can See' Clearly Now / James G. Nagy and Dianne P. O'Leary -- 7. Case Study: Updating and Downdating Matrix Fuctorizations: A Change in Plans -- 8. Case Study: The Direction-of-Arrival Problem -- III. Optimization and Data Fitting -- 9. Numerical Methods for Unconstrained Optimization -- 10. Numerical Methods for Constrained Optimization -- 11. Case Study: Classified Information: The Data Clustering Problem / Nargess Memarsadeghi and Dianne P. O'Leary -- 12. Case Study: Achieving a Common Viewpoint: Yaw, Pitch, and Roll / David A. Schug and Dianne P. O'Leary -- 13. Case Study: Fitting Exponentials: An Interest in Rates -- 14. Case Study: Blind Deconvolution: Errors, Errors Everywhere -- 15. Case Study: Blind Deconvolution: A Matter of Norm -- IV. Monte Carlo Computations -- 16. Monte Carlo Principles -- 17. Case Study: Monte Carlo Minimization and Counting: One, Two, Too Many / Isabel Reichl, Francis Sullivan and Dianne P. O'Leary -- 18. Case Study: Multidimensional Integration: Partition and Conquer -- 19. Case Study: Models of Infection: Person to Person -- V. Ordinary Differential Equations -- 20. Solution of Ordinary Differential Equations -- 21. Case Study: More Models of Infection: It's Epidemic -- 22. Case Study: Robot Control: Swinging Like a Pendulum / Yalin E. Sagduyu and Dianne P. O'Leary -- 23. Case Study: Finite Differences and Finite Elements Getting to Know You -- VI. Nonlinear Equations and Continuation Methods -- 24. Nonlinear Systems -- 25. Case Study: Variable-Geometry Trusses -- 26. Case Study: Beetles, Cannibalism, and Chaos

VII. Sparse Matrix Computations, with Application to Partial Differential Equations -- 27. Solving Sparse Linear Systems Taking the Direct Approach -- 28. Iterative Methods for Linear Systems -- 29. Case Study: Elastoplastic Torsion: Twist and Stress -- 30. Case Study: Fast Solvers and Sylvester Equations Both Sides Now -- 31. Case Study: Eigenvalues: Valuable Principles -- 32. Multigrid Methods: Managing Massive Meshes.