Understand the definition of x^r, and the concepts fixed point, fixed point iteration, and contraction mapping. Understand the the idea of coupled systems of equations.
Understand elementary vector algebra, including scaling, addition, scalar multiplication and projection of vectors.
AMB&S ch. 20 (and also ch. 15-19)
18.1, 18.3abd but simplify by considering 1/(2+x^2) instead of 1/(1+x^2),
19.1, 19.2a, 19.3b, 19.4, 19.10, 19.11, 19.12, 19.13, 19.14, 19.16, (19.17,)
19.18 but simplify by considering g(x)=x^2/(10-x) with L=21/81 on [-1 1] instead of g(x)=x^4/(10-x)^2,
(19.19, 19.21,) 19.22ab
Project f(x)=0 , including modeling, solver implementation, application to model equations, analysis and conclusions, presentation.
Make sure you have functioning and fully understood bisection and fixed point solvers (part of project f(x)=0). Seek to extend your fixed point solver so as to be applicable also to systems of equations. Recall how vectors (lists) and matrices are created and manipulated in matlab.
19.5 (part of project), some of application problems 19.6, 19.7, 19.8, 19.9 (possible application parts of project).