Applied analytical methods

Course 191560371, academic year 2010/2011, block 2B. The course is part of the curriculum for Applied Mathematics, specialization MPCM (Mathematical Physics and Computational Mechanics) of the Faculty of Electrical Engineering, Mathematics and Computer Science at the University of Twente. Students from Applied Mathematics, Physics, and the Engineering disciplines are invited. Also students from all other areas, where optimization problems might arise, are most welcome.

Attention, please !
  • The written exam will take place on Wednesday, June 29, 13:45 - 16:45 in room VR 7 (building Vrijhof).
  • Students are not allowed to take lecture notes, books, pocket calculators, laptop computers, smartphones, or similar into the exam. Only a single sheet of A4 paper is allowed, one side of which has to be completely blank. Figure out yourself what you might wish to put on the non-blank side ... :-).
  • Success to all participants in the exam, and have a nice summer holiday!

Variational techniques play a fundamental role in a variety of fields. While optimization problems are abundant also in disciplines like economy and life sciences, the course concentrates on applications from the natural and technical sciences. The topics are highly relevant for different branches of mathematics, e.g. for people interested in numerics. The basics of variational calculus are introduced, with emphasis on the characterization of optimal or critical states, and on the role of boundary conditions. We adopt a practical viewpoint: Rather than spending too much effort on technical details of an abstract mathematical formalism, we obtain an overview of the methods, leaving the details to be sorted out where they arise in specific problems.

Contents: Introduction to variational calculus, unconstrained variational problems, theory of first and second variation, dynamic variational principles, discrete and continuous Lagrangian and Hamiltonian systems, constrained variational problems, variational characterizations of linear eigenvalue problems; examples from classical mechanics / theoretical physics.

The course is based on the lecture notes Applied Analytical Methods, part I - Basic Variational Structures and Methods by Brenny van Groesen (available only online at this moment). The weekly procedure consists of lectures and exercise classes from week 16, April 20, till week 24, June 15, on Wednesdays and / or Thursdays, hours 8+9 in rooms HB-2B and HB-2A (building Hal B, entrance Waaier). The course closes with a written examination in week 26.

The prospective schedule is as follows:
Week Date Time Room
16 We, 20.04. 15:45 - 17:30 HB-2B Lecture, chapters 1, 2 Problems I (ps)  Problems I (pdf)
Th, 21.04. 15:45 - 17:30 HB-2A Lecture, chapter 2
17 We, 27.04. 15:45 - 17:30 HB-2B Lecture, chapters 2, 3
18 We, 04.05. 09:00 Deadline for homework delivery!
15:45 - 17:30 HB-2B Exercises, problems I Problems II (ps)  Problems II (pdf)
19 We, 11.05. 15:45 - 17:30 HB-2B Lecture, chapter 3
Th, 12.05 15:45 - 17:30 HB-2A Lecture, chapter 4 Problems III (ps)  Problems III (pdf)
20 We, 18.05 09:00 Deadline for homework delivery!
15:45 - 17:30 HB-2B Exercises, problems II
21 We, 25.05 15:45 - 17:30 HB-2B Lecture, chapter 4
Th, 26.05 15:45 - 17:30 HB-2A Lecture, chapter 6
22 We, 01.06 09:00 Deadline for homework delivery!
15:45 - 17:30 HB-2B Exercises, problems III Problems IV (ps)  Problems IV (pdf)
23 We, 08.06. 15:45 - 17:30 HB-2B Lecture, chapter 6
24 We, 15.06. 09:00 Deadline for homework delivery!
15:45 - 17:30 HB-2B Exercises, problems IV
26 We, 29.06. 13:45-16:45 VR 7 Exam

Depending on the progress of the course, the contents may be subject to change.

Homework exercises will be scheduled for approximately every two weeks. While a discussion on the topics of the homework is encouraged, the problems are to be solved and to be written down individually. The solutions are to be handed in at the date / time indicated by the dots (postbox AAM in the AACS secretariat CI H-315, alternatively in CR 2.435, office M. Hammer) in the table above, at the latest. We'll use the exercise classes for a detailed discussion of the problems, where every student is supposed to be able to explain her or his (then corrected) solutions. Each participant should regularly present an answer to (part of) a problem.

Grading for this course will be based with a weight of 1/2 on the results of the homework exercises, according to a point scheme for the delivered solutions and according to the participation in the exercise classes. The outcome of the exam will determine the second half of the grade.