- Matrix rank, and its use to know when a linear system has solution
- Interpolation theory: Students should find the interpolation polynomial and plot the points and the polynomial to understand the concept and visualize the interpolation errors in several points.
- To solve differential equations using several approaches for comparison
For sure, the need higher-order thinking skills and writing and oral abilities

I am a professor in a University in Ecuador, the size of my classes is of 25-35 students for basic courses, and 8-15 for medium and high-level courses. Many of my courses have lab activities, and several of them develop a long project during the semester. To do these labs, students need to solve equations, plot functions, solve differential equations or linear programming problems; thus, students should learn to handle these the objects and solvers in an appropriate platform.

Students use their own calculator for simple calculations and several online free platform and Calculators on the internet, as Octave and Geogebra, also R and Python libraries.

Usually students know the basic of Matlab notation because they use Octave; but it should be helpful if they could understand the math behind some concepts and theorems, for example, the Existence and Uniqueness of solution of a linear System Theorem, or the family of antiderivative of a function, or the feasible region of a linear programming problem.

By oral examination, written exams, or in presentations.

Marsden, Jerrold E. and Weinstein, Alan J. (1985) Calculus I. Springer-Verlag , New York. ISBN 0387909745.
https://authors.library.caltech.edu/25030/
Hefferson Jim, Linear Algebra. https://joshua.smcvt.edu/linearalgebra/
Differential equations and linear algebra. https://math.mit.edu/~gs/dela/