This course covered linear algebra (LU, Cholesky, etc.), focusing on solving Ax=b and minimization problems. It then transitioned to nonlinear problems, including root finding and optimization, emphasizing iterative methods and conjugate gradients for large systems. Finally, it explored solving differential equations where the unknown is a function, highlighting the differences between time and space variables and the importance of well-posed problems. The final exam is cumulative and covers both linear and nonlinear methods, encouraging students to apply learned techniques to new problems. This segment highlights the shift from solving for numerical values to solving for functions as unknowns in the latter part of the course. It emphasizes the conceptual difference between root-finding (where the unknown is a point) and solving differential equations (where the unknown is a function), introducing the complexities and considerations involved in handling time and space variables within these new problem types. The discussion sets the stage for understanding the advanced methods needed to tackle these more challenging mathematical problems.