Nyhetsflöde

period 4, 12/13

Course objectives The aim of this course is to provide the basic theory required for solving complex control problems. The course presents theory and methodology for modelling and analysis of signals and systems, and methods for design of feedback controllers. Special emphasis is placed on:

* Control of systems with multiple inputs and outputs
* Fundamental limitations for control performance
* Sensitivity and robustness in feedback systems
* Synthesis of controllers through optimization
* Predictive control with constraints
Personnel Mikael Johansson: Lectures

Håkan Terelius, Computer exercises and labs

Olle Trollberg, Computer exercises and labs

Hanna Holmqvist, administrator

Course litterature and software The course follows the book:

Torkel Glad and Lennart Ljung; Control Theory - Multivariable and Nonlinear Methods, Taylor and Francis Ltd, ISBN 0748408789 (Swedish version: T. Glad and L. Ljung; Reglerteori, flervariabla och olinjära metoder, Studentliteratur, 2:a upplagan, ISBN 91-44-03003-7)

Additional course material (mostly in English)

* Exercises and solutions
* Computer exercises and laboratory project
are also sold at STEX, at the entrance level of Osquldas väg 10.

The following material contains high-quality supplementary reading:

* Skogestad, S. och Postlethwaite, I.: Multivariable Feedback Control, Analysis and Design, John Wiley & Sons, 1996
* Åström, K.J. och Wittenmark, B.: Computer Controlled Systems, Theory and Design, 3rd ed, Prentice Hall, 1997
* Goodwin, G.C., Graebe, S.F. och Salgado M.E.: Control System Design, Prentice Hall 2001
* Maciejowski, J.M.: Predictive Control with Constraints, Prentice-Hall, 2002.
Matlab is available in most of the computer rooms in KTH. Under Linux, you need to write module add matlab to be able to start Matlab. A student version of Matlab is available for use at home via KTH Program Distribution.

Disposition The course consists of 14 lectures and 8 exercise sessions. In addition, four compulsory computer exercises and a compulsory laboratory project form part of the course. Grading is based on a 5-hour written final exam.

Schedule Note: The schedule is preliminary. Although the dates are fixed, some lecture content might be changed or shifted around.

Lectures LecDayDateTimePlaceContentReferences Lec 1 Wed March 20 10 - 12 V3 Introduction; Signal norms and system gains, small gain theorem Textbook: Ch 1 Lec 2 Thur March 21 10 - 12 V3 The closed-loop system Textbook: Ch 6 Lec 3 Mon March 25 10 - 12 V3 Robustness Lec 4 Thur March 28 10 - 12 V3 Limitations and conflicts Textbook: Ch 7 Lec 5 Wed April 10 10 - 12 V3 Multivariable systems Textbook: Ch 7, 8 Lec 6 Mon April 15 13 - 15 V3 Decentralized control and decoupling Textbook: Ch 10 Lec 7 Wed April 17 10 - 12 V3 Multivariable loop shaping Textbook: Ch 2-3 Lec 8 Mon April 22 15 - 17 V3 Linear-quadratic control Textbook: Ch 9 Lec 9 Fri April 26

13 - 15 V3 Design example and relation to H2 Lec 10 Thur May 2 13 - 15 V3 Glover-McFarlane and controller order reduction Lec 11 Fri May 3 13 - 15 V3 Dealing with hard constraints Textbook: Ch 10 Lec 12 Wed May 8 13 - 15 V3 Model predictive control Textbook: Ch 16 Lec 13 Thur May 16 13 - 15 V3 Model predictive control Textbook: Ch 16 Lec 14 Fri May 17 13 - 15 V3 Summary and review Exercises There is one ordinary exercise group. In addition, since the hours for the exercises conflict with other courses for some students, we offer one Q&A session per week where students can come and get help with the exercises. For the Q&A sessions you are expected to go through the exercise notes before coming to the Q&A session to get help with the parts you find difficult. Notes from the exercises will be available through the course homepage before the Q&A session.

The numbers indicated for the exercise sessions in the column "References" refer to problems in the 2011 edition of the exercise compendium.

Exercises

Group ATimePlaceReferencesAt home Ex 1 Fri March 22, 10-12 Q34 1.4, 1.5, 1.6, 6.2 1.3 Ex 2 Mon April 8, 10-12 V3 7.1, 7.2, 6.5, 7.19 7.14,7.18 Ex 3 Thur April 11, 08-10 V3 2.3, 2.5, 3.2, 3.12 3.15 Ex 4 Tues April 16, 10-12 V01 8.2, 8.5, 8.17 8.1 Ex 5 Fri April 19, 10-12 V01 10.2, 10.4, 10.8 10.12 Ex 6 Wed April 24, 08-10 V01 9.3, 97, 9.1 9.9a, 9.3 Ex 7 Tues April 30, 10-12 V01 7.3, 10.3, 10.9 Ex 8 Tues May 14, 10-12 V01 4.1, 16.2, 16.4 Question and Answer Sessions for Exercises (mainly for those who can not make the ordinary exercises).

Group BTimePlaceReferences Q&A 1 Fri March 22, 13-15 V33 Ex 1, Ex 2, Lab 1 Q&A 2 Thur April 11, 10-12 V3 Ex 3, Ex 4, Lab 2 Q&A 3 Fri April 19, 13-15 V01 Ex 5, Ex 6, Lab 3 Q&A 4 Tues April 30, 13-15 V01 Ex 7 Q&A 5 Tues May 14, 13-15 V01 Ex 8, Lab 4 Computer exercises The computer exercises are to be solved using Matlab in groups of two students. A written report for computer exercise 1 and 3 are to be handed in by 130408 and 130502, respectively. Computer exercises 2 and 4 are reported by filling in a short form (which can be downloaded below) which should be handed in no later than 130424 and 130510, respectively. All reports and forms should be handed in to STEX.

A printed version of the computer exercises is sold at STEX. PDF versions of the computer exercises, and associated Matlab-files are found above.

Students can go to the exercise group that they prefer (no assignment of groups).

Computer exercises - Group A  

No.ContentExerciseReport Deadline 1 Wed March 27 10-12 XQ23 Loop shaping Lab 1 130408 2 FriWed April 17 13-15 XQ23 MIMO, RGA, decentralized control Lab 2 130424 3 Tue April 23 08-10 XQ23 H_inf control, robustness Lab 3 130502 4 Mon May 6 13-15 XQ23 Decoupling, Robust Loop Shaping Lab 4 130510 Computer exercises - Group B  

No.ContentExerciseReport Deadline 1 Wed March 27 13-15 XQ23 Loop shaping Lab 1 130408 2 Fri April 17 15-17 XQ23 MIMO, RGA, decentralized control Lab 2 130424 3 Tue April 23 13-15 XQ23 H_inf control, robustness Lab 3 130502 4 Mon May 6 15-17 XQ23 Decoupling, Robust Loop Shaping Lab 4 130510 Project The laboratory project considers a multivariable process whose properties can be modified to display a wide range of dynamical properties. The project is performed in groups of 4 students in the Control lab, A:225, Osquldas väg 10, level 2.

Registration for the laboratory will be available through the course home page. Those students who have not managed to form a group of four students prior to registration should register for a time and a process that some other group (with less than four students) have registered for. Note that you will need to book the same lab process (e.g., A,B,C,...) on both occasions. Written reports should be handed in to STEX no later than 130517. The report should present the results in a systematic and concise manner.

Exam The exam is scheduled for Saturday, May 25, 09.00-14.00. You will need to register for the exam using the exam registration system in KTH student web pages, "My Pages". You are allowed to bring the following material to the exam: the course book for EL2520 (advanced course) and EL1000/1110/1120 (basic course), copies of slides from this year’s lectures, mathematical tables and pocket calculator. Note that exercise materials (ovningsuppgifter, ex-tentor och losningar) are NOT allowed.

Old Exams
* 110523 Exam (pdf 73 kB) 110523 Solutions (pdf 63 kB)
* 090311 Exam (pdf 92 kB) 090311 Solutions (pdf 62 kB)
* 080314 Exam (pdf 83 kB) 080314 Solutions  (pdf 57 kB)
* 070604 Exam (pdf 72 kB) 070604 Solutions  (pdf 50 kB)
* 070309 Exam (pdf 130 kB) 070309 Solutions  (pdf 46 kB)
* 060605 Exam  (pdf 64 kB) 060605 Solutions  (pdf 54 kB)
* 060311 Exam (pdf 78 kB) 060311 Solutions (pdf 64 kB)
* 050830 Exam (pdf 60 kB) 050830 Solutions  (pdf 48 kB)

period 4, 12/13

Course objectives The aim of this course is to provide the basic theory required for solving complex control problems. The course presents theory and methodology for modelling and analysis of signals and systems, and methods for design of feedback controllers. Special emphasis is placed on:

* Control of systems with multiple inputs and outputs
* Fundamental limitations for control performance
* Sensitivity and robustness in feedback systems
* Synthesis of controllers through optimization
* Predictive control with constraints
Personnel Mikael Johansson: Lectures

Håkan Terelius, Computer exercises and labs

Olle Trollberg, Computer exercises and labs

Hanna Holmqvist, administrator

Course litterature and software The course follows the book:

Torkel Glad and Lennart Ljung; Control Theory - Multivariable and Nonlinear Methods, Taylor and Francis Ltd, ISBN 0748408789 (Swedish version: T. Glad and L. Ljung; Reglerteori, flervariabla och olinjära metoder, Studentliteratur, 2:a upplagan, ISBN 91-44-03003-7)

Additional course material (mostly in English)

* Exercises and solutions
* Computer exercises and laboratory project
are also sold at STEX, at the entrance level of Osquldas väg 10.

The following material contains high-quality supplementary reading:

* Skogestad, S. och Postlethwaite, I.: Multivariable Feedback Control, Analysis and Design, John Wiley & Sons, 1996
* Åström, K.J. och Wittenmark, B.: Computer Controlled Systems, Theory and Design, 3rd ed, Prentice Hall, 1997
* Goodwin, G.C., Graebe, S.F. och Salgado M.E.: Control System Design, Prentice Hall 2001
* Maciejowski, J.M.: Predictive Control with Constraints, Prentice-Hall, 2002.
Matlab is available in most of the computer rooms in KTH. Under Linux, you need to write module add matlab to be able to start Matlab. A student version of Matlab is available for use at home via KTH Program Distribution.

Disposition The course consists of 14 lectures and 8 exercise sessions. In addition, four compulsory computer exercises and a compulsory laboratory project form part of the course. Grading is based on a 5-hour written final exam.

Schedule Note: The schedule is preliminary. Although the dates are fixed, some lecture content might be changed or shifted around.

Lectures LecDayDateTimePlaceContentReferences Lec 1 Wed March 20 10 - 12 V3 Introduction; Signal norms and system gains, small gain theorem Textbook: Ch 1 Lec 2 Thur March 21 10 - 12 V3 The closed-loop system Textbook: Ch 6 Lec 3 Mon March 25 10 - 12 V3 Robustness Lec 4 Thur March 28 10 - 12 V3 Limitations and conflicts Textbook: Ch 7 Lec 5 Wed April 10 10 - 12 V3 Multivariable systems Textbook: Ch 7, 8 Lec 6 Mon April 15 13 - 15 V3 Decentralized control and decoupling Textbook: Ch 10 Lec 7 Wed April 17 10 - 12 V3 Multivariable loop shaping Textbook: Ch 2-3 Lec 8 Mon April 22 15 - 17 V3 Linear-quadratic control Textbook: Ch 9 Lec 9 Fri April 26

13 - 15 V3 Design example and relation to H2 Lec 10 Thur May 2 13 - 15 V3 Glover-McFarlane and controller order reduction Lec 11 Fri May 3 13 - 15 V3 Dealing with hard constraints Textbook: Ch 10 Lec 12 Wed May 8 13 - 15 V3 Model predictive control Textbook: Ch 16 Lec 13 Thur May 16 13 - 15 V3 Model predictive control Textbook: Ch 16 Lec 14 Fri May 17 13 - 15 V3 Summary and review Exercises There is one ordinary exercise group. In addition, since the hours for the exercises conflict with other courses for some students, we offer one Q&A session per week where students can come and get help with the exercises. For the Q&A sessions you are expected to go through the exercise notes before coming to the Q&A session to get help with the parts you find difficult. Notes from the exercises will be available through the course homepage before the Q&A session.

The numbers indicated for the exercise sessions in the column "References" refer to problems in the 2011 edition of the exercise compendium.

Exercises

Group ATimePlaceReferencesAt home Ex 1 Fri March 22, 10-12 Q34 1.4, 1.5, 1.6, 6.2 1.3 Ex 2 Mon April 8, 10-12 V3 7.1, 7.2, 6.5, 7.19 7.14,7.18 Ex 3 Thur April 11, 08-10 V3 2.3, 2.5, 3.2, 3.12 3.15 Ex 4 Tues April 16, 10-12 V0L51 8.2, 8.5, 8.17 8.1 Ex 5 Fri April 19, 10-12 V01L52 10.2, 10.4, 10.8 10.12 Ex 6 Wed April 24, 08-10 V01Q36 9.3, 97, 9.1 9.9a, 9.3 Ex 7 Tues April 30, 10-12 V0122 7.3, 10.3, 10.9 Ex 8 Tues May 14, 10-12 V0132 4.1, 16.2, 16.4 Question and Answer sessions where students can get help with problems or the topics covered in the course.

Group BTimePlaceReferences Q&A 1 Fri March 22, 13-15 V33 Ex 1, Ex 2, Lab 1 Q&A 2 Thur April 11, 10-12 V3 Ex 3, Ex 4, Lab 2 Q&A 3 Fri April 19, 13-15 V0Q21 Ex 5, Ex 6, Lab 3 Q&A 4 Tues April 30, 13-15 V01Q36 Ex 7 Q&A 5 Tues May 14, 13-15 V0132 Ex 8, Lab 4 Computer exercises The computer exercises are to be solved using Matlab in groups of two students. A written report for computer exercise 1 and 3 are to be handed in by 130408 and 130502, respectively. Computer exercises 2 and 4 are reported by filling in a short form (which can be downloaded below) which should be handed in no later than 130424 and 130510, respectively. All reports and forms should be handed in to STEX.

A printed version of the computer exercises is sold at STEX. PDF versions of the computer exercises, and associated Matlab-files are found above.

Students can go to the exercise group that they prefer (no assignment of groups).

Computer exercises - Group A  

No.ContentExerciseReport Deadline 1 Wed March 27 10-12 XQ23 Loop shaping Lab 1 130408 2 Wed April 17 13-15 XQ23 MIMO, RGA, decentralized control Lab 2 130424 3 Tue April 23 08-10 XQ23 H_inf control, robustness Lab 3 130502 4 Mon May 6 13-15 XQ23 Decoupling, Robust Loop Shaping Lab 4 130510 Computer exercises - Group B  

No.ContentExerciseReport Deadline 1 Wed March 27 13-15 XQ23 Loop shaping Lab 1 130408 2 Fri April 17 15-17 XQ23 MIMO, RGA, decentralized control Lab 2 130424 3 Tue April 23 13-15 XQ23 H_inf control, robustness Lab 3 130502 4 Mon May 6 15-17 XQ23 Decoupling, Robust Loop Shaping Lab 4 130510 Project The laboratory project considers a multivariable process whose properties can be modified to display a wide range of dynamical properties. The project is performed in groups of 4 students in the Control lab, A:225, Osquldas väg 10, level 2.

Registration for the laboratory will be available through the course home page. Those students who have not managed to form a group of four students prior to registration should register for a time and a process that some other group (with less than four students) have registered for. Note that you will need to book the same lab process (e.g., A,B,C,...) on both occasions. Written reports should be handed in to STEX no later than 130517. The report should present the results in a systematic and concise manner.

Exam The exam is scheduled for Saturday, May 25, 09.00-14.00. You will need to register for the exam using the exam registration system in KTH student web pages, "My Pages". You are allowed to bring the following material to the exam: the course book for EL2520 (advanced course) and EL1000/1110/1120 (basic course), copies of slides from this year’s lectures, mathematical tables and pocket calculator. Note that exercise materials (ovningsuppgifter, ex-tentor och losningar) are NOT allowed.

Old Exams
* 110523 Exam (pdf 73 kB) 110523 Solutions (pdf 63 kB)
* 090311 Exam (pdf 92 kB) 090311 Solutions (pdf 62 kB)
* 080314 Exam (pdf 83 kB) 080314 Solutions  (pdf 57 kB)
* 070604 Exam (pdf 72 kB) 070604 Solutions  (pdf 50 kB)
* 070309 Exam (pdf 130 kB) 070309 Solutions  (pdf 46 kB)
* 060605 Exam  (pdf 64 kB) 060605 Solutions  (pdf 54 kB)
* 060311 Exam (pdf 78 kB) 060311 Solutions (pdf 64 kB)
* 050830 Exam (pdf 60 kB) 050830 Solutions  (pdf 48 kB)

period 4, 12/13

Course objectives The aim of this course is to provide the basic theory required for solving complex control problems. The course presents theory and methodology for modelling and analysis of signals and systems, and methods for design of feedback controllers. Special emphasis is placed on:

* Control of systems with multiple inputs and outputs
* Fundamental limitations for control performance
* Sensitivity and robustness in feedback systems
* Synthesis of controllers through optimization
* Predictive control with constraints
Personnel Mikael Johansson: Lectures

Håkan Terelius, Computer exercises and labs

Olle Trollberg, Computer exercises and labs

Hanna Holmqvist, administrator

Course litterature and software The course follows the book:

Torkel Glad and Lennart Ljung; Control Theory - Multivariable and Nonlinear Methods, Taylor and Francis Ltd, ISBN 0748408789 (Swedish version: T. Glad and L. Ljung; Reglerteori, flervariabla och olinjära metoder, Studentliteratur, 2:a upplagan, ISBN 91-44-03003-7)

Additional course material (mostly in English)

* Exercises and solutions
* Computer exercises and laboratory project
are also sold at STEX, at the entrance level of Osquldas väg 10.

The following material contains high-quality supplementary reading:

* Skogestad, S. och Postlethwaite, I.: Multivariable Feedback Control, Analysis and Design, John Wiley & Sons, 1996
* Åström, K.J. och Wittenmark, B.: Computer Controlled Systems, Theory and Design, 3rd ed, Prentice Hall, 1997
* Goodwin, G.C., Graebe, S.F. och Salgado M.E.: Control System Design, Prentice Hall 2001
* Maciejowski, J.M.: Predictive Control with Constraints, Prentice-Hall, 2002.
Matlab is available in most of the computer rooms in KTH. Under Linux, you need to write module add matlab to be able to start Matlab. A student version of Matlab is available for use at home via KTH Program Distribution.

Disposition The course consists of 14 lectures and 8 exercise sessions. In addition, four compulsory computer exercises and a compulsory laboratory project form part of the course. Grading is based on a 5-hour written final exam.

Schedule Note: The schedule is preliminary. Although the dates are fixed, some lecture content might be changed or shifted around.

Lectures LecDayDateTimePlaceContentReferences Lec 1 Wed March 20 10 - 12 V3 Introduction; Signal norms and system gains, small gain theorem Textbook: Ch 1 Lec 2 Thur March 21 10 - 12 V3 The closed-loop system Textbook: Ch 6 Lec 3 Mon March 25 10 - 12 V3 Robustness Lec 4 Thur March 28 10 - 12 V3 Limitations and conflicts Textbook: Ch 7 Lec 5 Wed April 10 10 - 12 V3 Multivariable systems Textbook: Ch 7, 8 Lec 6 Mon April 15 13 - 15 V3 Decentralized control and decoupling Textbook: Ch 8 Lec 7 Wed April 17 10 - 12 V3 Multivariable loop shaping Textbook: Ch 10.1-10.2, 10.4 Lec 8 Mon April 22 15 - 17 V3 Linear-quadratic control Textbook: Ch 5.1-5.4, 9.1-9.3, 9.A Lec 9 Fri April 26

13 - 15 V3 Design example and relation to H2 Textbook: Ch 10.3 Lec 10 Thur May 2 13 - 15 V3 Glover-McFarlane and controller order reduction Textbook: Ch 10.5, 3.6 Lec 11 Fri May 3 13 - 15 V3 Dealing with hard constraints Lecture slides Lec 12 Wed May 8 13 - 15 V3 Model predictive control Textbook Ch 2.2, 3.7, 4 + Lecture slides Lec 13 Thur May 16 13 - 15 V3 Model predictive control Textbook: Ch 16 Lec 14 Fri May 17 13 - 15 V3 Summary and review Exercises There is one ordinary exercise group. In addition, since the hours for the exercises conflict with other courses for some students, we offer one Q&A session per week where students can come and get help with the exercises. For the Q&A sessions you are expected to go through the exercise notes before coming to the Q&A session to get help with the parts you find difficult. Notes from the exercises will be available through the course homepage before the Q&A session.

The numbers indicated for the exercise sessions in the column "References" refer to problems in the 2011 edition of the exercise compendium.

Exercises

Group ATimePlaceReferencesAt home Ex 1 Fri March 22, 10-12 Q34 1.4, 1.5, 1.6, 6.2 1.3 Ex 2 Mon April 8, 10-12 V3 7.1, 7.2, 6.5, 7.19 7.14,7.18 Ex 3 Thur April 11, 08-10 V3 2.3, 2.5, 3.2, 3.12 3.15 Ex 4 Tues April 16, 10-12 L51 8.2, 8.5, 8.17 8.1 Ex 5 Fri April 19, 10-12 L52 10.2, 10.4, 10.8 10.12 Ex 6 Wed April 24, 08-10 Q36 9.3, 9.7, 9.1 9.9a, 9.3 Ex 7 Tues April 30, 10-12 V22 7.3, 10.3, 10.9 Ex 8 Tues May 14, 10-12 V32 4.1, 16.2, 16.4 Question and Answer sessions where students can get help with problems or the topics covered in the course.

Group BTimePlaceReferences Q&A 1 Fri March 22, 13-15 V33 Ex 1, Ex 2, Lab 1 Q&A 2 Thur April 11, 10-12 V3 Ex 3, Ex 4, Lab 2 Q&A 3 Fri April 19, 13-15 Q21 Ex 5, Ex 6, Lab 3 Q&A 4 Tues April 30, 13-15 Q36 Ex 7 Q&A 5 Tues May 14, 13-15 V32 Ex 8, Lab 4 Computer exercises The computer exercises are to be solved using Matlab in groups of two students. A written report for computer exercise 1 and 3 are to be handed in by 130408 and 130502, respectively. Computer exercises 2 and 4 are reported by filling in a short form (which can be downloaded below) which should be handed in no later than 130424 and 130510, respectively. All reports and forms should be handed in to STEX.

A printed version of the computer exercises is sold at STEX. PDF versions of the computer exercises, and associated Matlab-files are found above.

Students can go to the exercise group that they prefer (no assignment of groups).

Computer exercises - Group A  

No.ContentExerciseReport Deadline 1 Wed March 27 10-12 XQ23 Loop shaping Lab 1 130408 2 Wed April 17 13-15 XQ23 MIMO, RGA, decentralized control Lab 2 130424 3 Tue April 23 08-10 XQ23 H_inf control, robustness Lab 3 130502 4 Mon May 6 13-15 XQ23 Decoupling, Robust Loop Shaping Lab 4 130510 Computer exercises - Group B  

No.ContentExerciseReport Deadline 1 Wed March 27 13-15 XQ23 Loop shaping Lab 1 130408 2 Fri April 17 15-17 XQ23 MIMO, RGA, decentralized control Lab 2 130424 3 Tue April 23 13-15 XQ23 H_inf control, robustness Lab 3 130502 4 Mon May 6 15-17 XQ23 Decoupling, Robust Loop Shaping Lab 4 130510 Project The laboratory project considers a multivariable process whose properties can be modified to display a wide range of dynamical properties. The project is performed in groups of 4 students in the Control lab, A:225, Osquldas väg 10, level 2.

Registration for the laboratory will be available through the course home page. Those students who have not managed to form a group of four students prior to registration should register for a time and a process that some other group (with less than four students) have registered for. Note that you will need to book the same lab process (e.g., A,B,C,...) on both occasions. Written reports should be handed in to STEX no later than 130517. The report should present the results in a systematic and concise manner.

Exam The exam is scheduled for Saturday, May 25, 09.00-14.00. You will need to register for the exam using the exam registration system in KTH student web pages, "My Pages". You are allowed to bring the following material to the exam: the course book for EL2520 (advanced course) and EL1000/1110/1120 (basic course), copies of slides from this year’s lectures, mathematical tables and pocket calculator. Note that exercise materials (ovningsuppgifter, ex-tentor och losningar) are NOT allowed.

Old Exams
* 1208 Exam (pdf)
* 1205 Exam (pdf)
* 110523 Exam (pdf 73 kB) 110523 Solutions (pdf 63 kB)
* 090311 Exam (pdf 92 kB) 090311 Solutions (pdf 62 kB)
* 080314 Exam (pdf 83 kB) 080314 Solutions  (pdf 57 kB)
* 070604 Exam (pdf 72 kB) 070604 Solutions  (pdf 50 kB)
* 070309 Exam (pdf 130 kB) 070309 Solutions  (pdf 46 kB)
* 060605 Exam  (pdf 64 kB) 060605 Solutions  (pdf 54 kB)
* 060311 Exam (pdf 78 kB) 060311 Solutions (pdf 64 kB)
* 050830 Exam (pdf 60 kB) 050830 Solutions  (pdf 48 kB)

Lecture slides:¶


* Lecture 1:  [PDF, one slide per page] [PDF, four slides per page]
* Lecture 2:  [PDF, one slide per page] [PDF, four slides per page]

Lecture slides:

* Lecture 1:  [PDF, one slide per page] [PDF, four slides per page]
* Lecture 2:  [PDF, one slide per page] [PDF, four slides per page]
* Lecture 3:  [PDF, one slide per page] [PDF, four slides per page]

Lecture slides:

* Lecture 1:  [PDF, one slide per page] [PDF, four slides per page]
* Lecture 2:  [PDF, one slide per page] [PDF, four slides per page]
* Lecture 3:  [PDF, one slide per page] [PDF, four slides per page]

Lecture slides
* Lecture 1:  [PDF, one slide per page] [PDF, four slides per page]
* Lecture 2:  [PDF, one slide per page] [PDF, four slides per page]
* Lecture 3:  [PDF, one slide per page] [PDF, four slides per page]
* Lecture 4:  [PDF, one slide per page] [PDF, four slides per page] 
* Lecture 5:  [PDF, one slide per page] [PDF, four slides per page]
* Lecture 6:  [PDF, one slide per page]
* Lecture 7:  [PDF, one slide per page] [PDF, four slides per page]

Current exercise notes
* 2013-03-22 Exercise 1 (1.3 1.4 1.5 1.6 6.2)
* 2013-04-08 Exercise 2 (7.1 7.2 6.5 7.19)
* 2013-04-11 Exercise 3 (2.3 3.12 2.5 3.2)

Old exercise notes
* 2012-03-22 Exercises 7.10, 7.9 (pdf 123 kB)
* 2012-03-29 Exercises 6.2, 7.1, 1.4, 1.5, 1.6  (pdf 1,0 MB)
* 2012-04-11 Exercises 3.12, 3.32, 7.3 (pdf 964 kB)
* 2012-04-20 Exercises 2.3, 2.5, 8.2 (pdf 466 kB)
* 2012-04-24 Exercises 6.5, 7.2, 7.17, 7.18, 7.19 (pdf 778 kB)
* 2012-05-02 Exercises 9.3, 9.7, 9.9 (updated) (pdf 661 kB)
* 2012-05-11 Exercises 10.3, 10.4 (pdf 471 kB)
* 2012-05-15 Exercises 3.2, 4.1, 16.2, 16.4 (pdf 804 kB)