This course is replaced by MAT3440 – Dynamical systems.

Undervisningsplan

DatoUndervises avStedTemaKommentarer / ressurser
19.01.2010Xavier Raynaud  Auditorium 4 Vilhelm Bjerknes hus  Modelling via differential equations, Separable equations  Blanchard, Devaney and Hall, Section 1.1 and 1.2 
21.01.2010--  --  Separable equations, Slope fields  --, Section 1.2-1.3 
26.01.2010--  --  Euler's method  --, Section 1.4

--, Exercises 5,11,19,25,27,31 in section 1.2 (solution) 

28.01.2010--  --  Convergence proof of Euler's method. Improved Euler and Runge-Kutta methods  --, Section 1.4, Section 7.1-7.3 
02.02.2010--  --  Linear equations  --, Secton 1.8

--, Exercises 9,13 p.49, 17 p.51, 20 p.65 and this exercise. (solution) 

04.02.2010--  --  Existence and uniqueness of solutions  --, Section 1.5 
09.02.2010--  --  First order systems - direction fields  --, Section 2.1,2.2

--, Exercises 19 p.135, 26 p.137, 47 p.141, 55 p.143 (solution) 

11.02.2010--  --  Linear systems, linearity principle  --, Section 3.1 
16.02.2010--  --  Linear systems with real eigenvalues  --, Section 3.2,3.3

These exercises and BDH, ex1,8,20 p.164-167, ex 21,27 p.186-187. (solution) 

18.02.2010--  --  Linear systems with real/complex eigenvalues  --, Section 3.3,3.4 
23.02.2010--  --  Linear systems with complex eigenvalues   --, Section 3.4

--, ex. 16,28,29,33 section 3.1; ex. 14 section 3.2; ex. 12,20 section3.3. (solution) 

25.02.2010--  --  Linear systems with repeated eigenvalues. Generalized eigenvectors.  Edwards and Penney, Section 5.6. Lecture notes 
09.03.2010--  --  Generalized eigenvectors  EP, Section 5.6

BHL, ex. 1,10,11,23 section 3.4, ex. 12 section 3.5. (solution) 

11.03.2010--  --  Generalized eigenvectors, Matrix solutions  EP, Section 5.7. examples 
16.03.2010--  --  Matrix exponential  EP, Section 5.7

EP, ex. 26,33,35 p. 406-407. In ex.35, the railway cars problem is from Fig 5.6.2 (and not 5.6.1 as indicated in the text). In ex. 33, there is a mistake in v_2; compute the correct chain. (solution) 

18.03.2010--  --  Matrix exponential - Linear system with forcing term  EP, Section 5.7,5.8 
06.04.2010--  --  Calculus of variation  Sydsæter, Seierstad, Strøm (SSS), Matematisk Analyse: seksjon 11.1-11.2

Seierstad, Sydsæter (SS), Optimal control with economic applications: section 1.1.

EP, ex. 1,33, p.420, 18 p.428 BHL ex 3 p.466 (solution) 

08.04.2010--  --  Calculus of variation  SSS, sections 11.3-11.4 (SS, chap.1 sections 2,4,6) 
13.04.2010--  --  Calculus of variation  SSS, ex 1,3,6,8 p.341 (english version, solutions) 
15.04.2010--  --  Calculus of variation   SSS, Section 11.5 (SS chap.1, section 5) 
20.04.2010--  --  Dynamic programming  lecture notes on dynamic programming

exercises (solutions) 

22.04.2010--  --  Dynamic programming   
27.04.2010--  --  Dynamic programming  Shortest path problem.

exercises (solutions) 

29.04.2010--  --  Optimal control theory  SSS, section 12.1-2 (SS chap.2 sections 1-3) 
04.05.2010--  --  Optimal control theory  SSS, Section 12.4-5

exercises. (solutions) 

06.05.2010--  --  Optimal control theory  SSS, section 12.6,12.8 
11.05.2010--  --  Optimal control theory  SSS, Section 12.6,12.8

exercises (solutions) 

18.05.2010--  --  Optimal control theory (exercises)  exercises from last week. 
20.05.2010--  --  Optimal control theory (exercises) + repetition  exercises on optimal control theory (SSS, ex.4 p. 383, ex.1 p.390).

Repetition ex. 20c p.289 and 11c p.305 in BDH.

Exercise 3 in exam 2008 (INF-MAT1310)

(solutions) 

25.05.2010--  --  Repetition  exam from 2007 (MAT-INF1310) (solutions) 
27.05.2010--  --  Repetition  exam from 2008 (MAT2310) (only exercise 1) (solutions)

exam from 2007 (MAT2310) (solutions) 

Published Dec. 15, 2009 5:18 PM - Last modified May 31, 2010 4:05 PM