Analys & Linjär algebra K+Kf+Bt, del a, ht 2002,

home, week 1, week 2, week 3, week 4, week 5, week 6, week 7

Theory

Goal:
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.

Reading:
AMB&S chap. 20 (last part), 21 (some parts, for example sections 21.22 and 21.26) and 23 (the Derivative, first part)

Excercises:
23.1, 23.2, 23.6, 23.7

Project:
Project f(x)=0 : Oral presentation on Friday. Written report on Monday morning!

Matlab

Goal:
To learn relevant matlab notation and syntax related to elementary matrix calculation, and to get to better understand the matrix algebra through matlab.

Reading:

Exercises:

Activity plan:

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.

/Kenneth