In the following "K&D" means "Numerical Analysis" by Kincaid and Cheeney and "B&F" means "Numerical Analysis" by Burden and Faires, fifth edition.

1. Computer arithmetic, K&C Chapter 2, B&F Section 1.2
2. Solution of single equation, K&C Chapter 3, omitting Laguerre iteration, section 3.6 and error analysis for the secant method, B&F Chapter 2.
3. Solution of linear systems, K&C, Sections 4.1,4.3,4.4,4.6 (with only Jacoi and Gauss-Siedel iterations). B&F Sections 6.1,6.2,6.3, Chapter 7.
4. Numerical Linear Algebra, K&C, Section 5.1,5.2 (QR factorization only), B&F sections 9.1,9.2.
5. Interpolation, K&C, Sections 6.1,6.2,6.4,6.12, B&F Sections 3.1,3.2,3.4,3.5,8.5,8.6.
6. Numerical differentiation and integration, K&C, Sections 7.1-7.4, B&F, sections 4.1-4.7.
7. Ordinary differential equations, K&C, Sections 8.1-8.6, B&F, Sections 5.1-5.6,5.9,5.10.
8. Partial differential equations, B&F, Chapter 12.