Theory

Goal:
To understand the concept "linearization" and the related definition of the derivative. Further, to understand the different "rules of differentiation", for example for the power functions x^r, sums and products, and for composite and inverse functions. Finally, to understand Newtons method, both for a scalar equation and systems of equations.

AMB&S chap 23, 24.

Excercises:
23.1, 23.2, 23.6, 23.7
24.1, 24.2, 24.4 hint: use the fact that 2^(x+h)-2^x=2^x(2^h-1) (why?), 24.5.

Matlab

Goal:
Understanding that computer arithmetic is not exact, and how this relates for example to computations of derivatives.
To learn how to use matlab to handle arbitrary linear systems of equations including under and over-determined such systems.

Exercises:
23.3, 23.4, 24.3.

Activity plan:

L=Lecture, S=Studio, G=Group work
L1: Linearization and the derivative, differentiation rules. Numerical differentiation.
S1: More on linear systems of equations, including underdetermined systems. Some related exercises
G1: Computing derivatives. Derivatives of products, composite functions etc. Partial derivatives. Some exercises on differentiation.
L2: Applications of derivatives. Newtons method. L'Hopsital rules.
S2: Overdetermined linear systems of equations. The least squares method. Some exercises on Least Squares. Newtons method. Experiment with the Newton solver under RM+. Make your own implementation of Newtons method!
L3: Concluding analysis.
S3: Newtons method for systems.
G2: Newtons method and L'Hopitals rules.

Examination:

Requested: Solutions to old exams 99 00

/Kenneth