KMN 2.1-2.2 or H 1.2-1.3

Norms & condition numbers GVL3 2.2, 2.3, 2.7 or H 2.3-2.4

Gaussian elimination GVL3 3.1,3.2,3.4 or H 2.2

Cholesky and LDL^T factorization GVL3 4.1,4.2 or H 2.5.1

Symmetric eigenvalue problem & Power method GVL3 8.1, 8.2 or H 4.3.1-4.3.8

Least squares, normal eqs & QR factorization GVL3 5.1,5.2,5.3 or H 3.1-3.5

Newton’s method (nonlinear equations) DS 2.2,2.4,5.1,5.2 or H 5.1-5.3

Newton’s method (optimization) DS 5.5 or H 6.2.3,6.3.3

Basic theory H 9.1 or KMN 8.1

Forward & backward Euler, stability and order KMN 8.4,8.5,8.8 or H 9.2,9.3,9.4

Comments: Where several texts are listed, you need to read only one, but you also must understand the principles underlying the material (which are usually facts from linear algebra or calculus). GVL3, DS and KMN are all more in-depth than H.

[DS] J. E. Dennis and R. B. Schnabel, Numerical Methods for Unconstrained Optimization and Nonlinear Equations, Prentice Hall, 1983.

[GVL3] G. Golub and C. Van Loan, Matrix Computations, 3^rd Ed., Johns Hopkins Univ. Press, 1996. (Note that earlier editions also cover the syllabus material but some sections are numbered differently.)

[H] M. Heath, Scientific Computing: An Introductory Survey, McGraw Hill, 1997

[KMN] D. Kahaner, C. Moler and S. Nash, Numerical Methods and Software, Prentice Hall, 1989.