This will be the last ordinary lecture / problem session. We will discuss:
1. The type of critical points of almost linear autonomous systems versus its linearization.
2. Exam 2011 Problem 3 (and Problem 1 if there is enough time). Misprint in 3a: Show that p is a decreasing function (not increasing).
See the Schedule for the exam set in Norwegian.
The solution sets are now available in the Math. building, 7th floor.
All solution sets are now available at the 7th floor of the Mathematics building.
Those who did not get their solutions approved, will have a new chance with deadline May 7, 2:30 p.m.
We will discuss the Maximum Principle and Mangasarian's Theorem under various endpoint conditions. These are some of the most important results in Control Theory.
In addition to theory from Sectiom 5.7 and 5.8 in EP we will do Exercise 5.7.3 and 5.7.21.
No lecture on Tuesday March 25.
No problem session on Thursday March 27.
The obligatory problems are now available at
Your solutions must be handed in at the seventh floor of the Mathematics building by 2:30 PM, April 10.
On Tuesday February 11 we will talk about Convexity/Concavity for functions of several variables. In addition we will start on the Euler equation in the Calculus of Variations. See the Lecture Notes
or the books of Sydsæter et al.
For those who would like to move a bit deeper into Optimal Control Theory, we recommend the book
Daniel Liberzon, Calculus of Variations and Optimal Control Theory,
which is available in the bookstore and in the library. This book also contains a proof of a version of the Maximum Principle in Control Theory.
In addition to the given exercises, we will look at Section 1.6 in E&P about reducible equations. See the Schedule.