• Matematisk modellering og numeriske metoder

    • In the Fall of 2013, I am responsible for the course Matematisk modellering og numeriske metoder at the Esbjerg campus of Aalborg University.

    People from various study programmes are required to take different parts of this course, and as some study programmes are held entirely in English, a few of the lectures will be in English, although the majority of the lectures will be in Danish.

    Tidligere års eksamenssæt kan findes her.

    The lectures will be held as follows. From 8 to (usually) 9, the students will work on exercises in their group rooms. From (usually) 9 to 11, there will be lectures in C113. From 11 to 12, the students will return to the group rooms to proceed on their exercises. I will visit them in the group rooms and answer questions. Departures from this schedule will be announced on this page (e.g. if the scheduled times are altered.). The lecture and exercise plans can be found below.

    Day Lecture Exercises related to Lecture Relevance for K5+M3 Relevance for B3 Relevance for EN3+ED3
    Thu 05 Sep   1     Lecture   Lecture  
    Fri 06 Sep   2     Lecture     Lecture
    Tue 17 Sep   3   1   Exercises and Lecture   Exercises and Lecture  
    Thu 19 Sep   4   3   Exercises and Lecture   Exercises and Lecture  
    Mon 23 Sep   5   4   Exercises and Lecture   Exercises and Lecture  
    Thu 26 Sep   6   5   Exercises and Lecture   Exercises and Lecture  
    Tue 01 Oct   7   2   Exercises and Lecture     Exercises and Lecture
    Thu 03 Oct   8   7   Exercises and Lecture   Lecture   Exercises and Lecture
    Tue 15 Oct   9   8   Exercises and Lecture   Exercises and Lecture   Exercises and Lecture
    Thu 17 Oct   10   9   Exercises and Lecture   Exercises and Lecture   Exercises
    Tue 22 Oct   11   6   Exercises and Lecture   Exercises and Lecture  
    Thu 24 Oct   12   10   Exercises and Lecture   Exercises and Lecture  
    Tue 29 Oct   13   11   Exercises and Lecture   Exercises and Lecture  
    Thu 31 Oct   14   12   Exercises and Lecture   Exercises and Lecture  
    Tue 05 Nov   15   15   Exercises and Lecture   Exercises and Lecture  
    Thu 07 Nov   16   16   Exercises and Lecture   Exercises and Lecture  
    Tue 12 Nov   17   17   Exercises and Lecture   Exercises and Lecture  
    Thu 14 Nov   18   18   Exercises and Lecture   Exercises and Lecture  
    Tue 19 Nov   19   19   Exercises and Lecture   Exercises and Lecture  
    Thu 21 Nov   20   20   Exercises and Lecture   Exercises and Lecture  
    Tue 26 Nov   21   21   Only Exercises   Only exercises  

    Lecture 1

    Lecture on Sections 1.1, 1.2, and 1.3.
    Exercises related to Lecture 1:
    1, 3 and 19 p. 8; 15 p. 11; 5 p. 18; 21 og 26 p. 19; 36 p. 20.
    Lecture notes can be found here.

    Lecture 2

    Lecture on Sections 6.1 and 6.2.
    Exercises related to Lecture 2:
    Exercises: 3 and 5 p. 210; 7 and 15 (hint: follow Example 6 found on the same page) p. 216.
    Lecture notes can be found here.
    Hints to exercises can be found here.

    Lecture 3

    Lecture on Sections 1.4, 1.5, and 1.7.
    Exercises related to Lecture 3:
    Exercises: 1, 2, and 3 p. 26; 5 and 9 p. 34; 39 p. 36.
    Lecture notes can be found here.

    Lecture 4

    Lecture on Sections 2.1, 2.2, 2.3, and 2.4.
    Exercises related to Lecture 4:
    Exercises: 12 and 15 p. 53; 1, 17, and 23 p. 59; 37 p. 60.
    Lecture notes can be found here.

    Lecture 5

    Lecture on Sections 2.5, 2.6, and 2.7.
    Exercises related to Lecture 5:
    Exercises: 3 and 7 p. 61; 5 and 7 p. 69; 1 and 5 p. 73; 3 and 11 p. 79; 1 and 5 p 84.
    Lecture notes can be found here.
    Hints to exercises can be found here.

    Lecture 6

    Lecture on Sections 2.8, 2.10, and 4.1.
    Exercises related to Lecture 6:
    Exercises: 7, 11, 19, and 25 p. 92; 5, 7, 11, and 14 p. 102; 11 p. 136.
    Lecture notes can be found here.
    Hints to exercises can be found here.

    Lecture 7

    Lecture on Sections 9.8 and 9.9.
    Exercises related to Lecture 7:
    Exercises: 5, 11, and 13 p. 406; 3 p. 408; 5, 7, 9, 11, and 14, 15, and 19 p. 409.
    Lecture notes can be found here.
    Hints to exercises can be found here.

    Lecture 8

    Lecture on Section 11.1.
    Exercises related to Lecture 8:
    Exercises: 1, 9, 11, 13, 17, 21, and 23 p. 482.
    Lecture notes can be found here.
    Hints to exercises can be found here.

    Lecture 9

    Lecture on Section 11.2.
    Exercises related to Lecture 9:
    Exercises: 1 p. 490; 11, 15, 19, 20, 25, 26, 27, and 30 p. 491.
    Lecture notes can be found here.
    Hints to exercises can be found here.

    Lecture 10

    Lecture on Sections 12.1, 12.2, and 12.3.
    Exercises related to Lecture 10:
    Exercises: 3, 7, and 14 p. 542; 1, 2, 3 and 5 p. 551; 7 and 9 p. 552.
    Lecture notes can be found here.
    Hints to exercises can be found here.

    Lecture 11

    Lecture on the rest of Section 12.3, Section 12.4, and possibly 12.5.
    Exercises related to Lecture 11:
    Exercises: 5 and 19 p. 556.
    Lecture notes can be found here.
    Hints to exercises can be found here.

    Lecture 12

    Lecture on Section 12.6.
    Exercises related to Lecture 12:
    Exercises: 1 and 4 p. 566; 5, 7, 11, 13, and 15 p. 567.
    Lecture notes can be found here.
    Hints to exercises can be found here.

    Lecture 13 and 14

    Lectures on finite element and finite volume methods.
    There will be no exercises for these lectures, instead you are encouraged
    to read the notes on the subject that can be found here.
    Lecture notes can be found here.

    Lecture 15

    Lecture on Sections 19.1 and 19.2.
    Exercises related to Lecture 15:
    Exercises: 4 and 6 p. 794; 5 and 9 (try also using Newton's method as well as the secant method) p. 804.
    Lecture notes can be found here.
    Hints to exercises can be found here.

    Lecture 16

    Lecture on Section 19.3.
    Exercises related to Lecture 16:
    Exercises: 3, 5, and 7 p. 816; 9 (try also using Newton' forward difference formula instead of the Lagrange interpolations method) p. 817.
    Lecture notes can be found here.
    Hints: all exercises should be pretty straight-forward if you follow the theory from the notes and detailed answers can be found in the Appendix of the book.

    Lecture 17

    Lecture on Section 19.5.
    Exercises related to Lecture 17:
    Exercises: 1, 2, 7, 8, (7 and 8 should also be solved using the trapez rule) and 11 p. 836; 14 p. 837.
    Lecture notes can be found here.
    Hints: Exercise 2: f(x)-p_0(x)=(x-(x_i-h/2))f'(t). Exercises 7 and 8: remember that the book uses a different notation (their m is our n).

    Lecture 18

    Lecture on Section 21.1.
    Exercises related to Lecture 18:
    Exercises: 1, 7, and 11 p. 907; 19(a) p. 908.
    Lecture notes can be found here.
    For most of the Exercises, a computer would be helpful, especially for 11 and 19(a).

    Lecture 19

    Lecture on Sections 21.2 and 21.3.
    Exercises related to Lecture 19:
    Exercises: 1 and 2 p. 912; 2 and 8 p. 919.
    Lecture notes can be found here.
    Comments on the exercises:
    Ad 21.2.1: The three numbers in parentheses are starting values you should use to initiate the Adams-Moulton method.
    Ad 21.2.2: You should find the first steps by RK4.
    Ad 21.3.2: "Calculate the errors" means solve it exactly and compare!
    Ad 21.3.8: Solve 21.3.2 with RK4 instead of Euler and see how much better it performs.

    Lecture 20

    Lecture on Sections 21.4, 20.3 and 21.5.
    Exercises related to Lecture 20:
    Exercises: 2, 13, and 15 p. 927; 4 and 16 p. 933.
    Lecture notes can be found here.

    Lecture 21

    No lecture today. A document with all headlines from all lectures can be found here.
    Exercises: any exercises that are related to the course, either from the book or from Moodle.

    Tidligere års eksamenssæt

    Matematisk Modellering og Numeriske Metoder, K3 og K5, 03.01.14.
    Matematisk Modellering og Numeriske Metoder, K5, 04.01.13.
    Matematisk Modellering og Numeriske Metoder, M3, 04.01.13.
    Matematisk Modellering og Numeriske Metoder, M3 og K5, 04.01.12.
    Matematisk Modellering og Numeriske Metoder, M3, 26.08.11.
    Matematisk Modellering og Numeriske Metoder, M3, 25.01.11.
    Matematisk Modellering og Numeriske Metoder, M3, 14.01.11.
    Partielle Differentialligninger, B3, 03.01.14.
    Partielle Differentialligninger mm., B3, 04.01.13.
    Partielle Differentialligninger mm., B3, 15.02.12.
    Partielle Differentialligninger mm., B3, 04.01.12.
    Partielle Differentialligninger mm., B3, 26.08.11.
    Partielle Differentialligninger mm., B3, 25.02.11.
    Partielle Differentialligninger mm., B3, 14.01.11.