The definition of the derivative. To understand the different "rules of differentiation", for example for the power functions x^r, sums and products, and for composite and inverse functions. Further, to understand Newtons method, both for a scalar equation and systems of equations.
AMBS chap 23, 24 and 25.
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.
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 linear systems of equations.
L=Lecture, S=Studio, G=Group work
Lecturer: Nils Svanstedt
L1: Chapter 23.
S1: Gaussian Elimination
G1: Computing derivatives. Derivatives of products, composite functions etc. Partial derivatives. Some exercises on differentiation.
L2: Chapter 24.
S2: Linearization, Newtons Method
L3: Chapter 25.
S3: Continue with A9. Linearization, Newtons Method
G2: Newtons method and L'Hopitals rules.
Matlab consultation: Thursday 17-19, room KD1, tutor: David Heintz.