Understanding elementary matrix algebra, and the determinant and inverse of a matrix. Understanding a linear system of equations both as a set of lines/(hyper)planes in x-space and in the space of column vectors. Understanding that f(x)=Ax is a linear function/mapping in x, (like the projection Px onto a given matrix, the rotation Rx, etc).
Understand the extension of the number system to complex numbers, and the algebra of these.
Understanding the definition of a graph having a tangent, the concept of "linearization" of a function close to a given point, and the related definition of the derivative of a function.
AMB&S chap. 20 (last part), 21 (some parts, for example sections 21.22 and 21.26) and 23 (the Derivative, first part)
23.1, 23.2, 23.6, 23.7
Project f(x)=0 : Oral presentation on Friday. Written report on Monday morning!
To learn relevant matlab notation and syntax related to elementary matrix calculation, and to get to better understand the matrix algebra through matlab.
L=Lecture, S=Studio, G=Group work
L1: Reconsideration of the introductory analysis.
S1: Linear systems of equations. Gaussian elimination. Row pivoting. The determinant. Inverse matrix. Geometric interpretation. Linear algebra using Matlab. Work on project f(x)=0.
G1: Complete project and continue working on suggested problems from the book
L2: Linearization, tangent and the derivative. AMB&S chap. 23.
S2: Suggested work on linearization.
G2: Oral presentation of project f(x)=0.