BE5B01DEN - Differential equations & Numerical methods

DEN: coronaversion

Information about the setup of the course and some coronaspecifics of assessment can be found here.

Resources:
• Videolectures for this course can be found in this Youtube playlist. A detailed description of contents can be found here.
Here is the contents of the seminar recordings.
• For other documents (syllabus, textbook etc.) see below.

Exams The KOS dates are only for on-side exams (in Prague), unless specified otherwise in the remark cell. If you have trouble getting to Prague and need to arrange for a distance exam, contact me by e-mail.

Week 13 (May 10 – 16):
• Before Wednesday, watch the first 38 minutes of the lecture 12 on numerical approach to eigenvalues and eigenvectors. It will not be on a test, but it is highly relevant to the topics of the past few weeks, and we will talk about it on the seminar.
To broaden your horizons, look at the video 04 on interpolation.
Slides for the lecture are the same as the previous week.
• If you want, solve the homework 13A (results on page 2).
• On Wednesday at 9:15 visit the seminar on Teams. Here is the (edited) recording and slides. And here a bonus debate about exams.
• Solve the obligatory homework 13B. Then submit it by Sunday midnight in a suitable form into the appropriate Assignment in teams and look forward to comments and exams.
Here you find an official solution.
• On Thursday 12:45 you can visit the consultation hours and ask about things that are not clear to you. Actually, this week the main topic is a practice exam.
Bonus: an edited recording of the consultation.

Week 12 (May 3 – 9):
• Before Wednesday, watch the lecture 08c.
Slides for the lecture are the same as the previous week.
• If you want, solve the homework 12A (results on page 2).
• On Wednesday at 9:15 visit the seminar on Teams. Here is the (edited) recording and slides.
• Solve the obligatory homework 12B. Then submit it by Sunday midnight in a suitable form into the appropriate Assignment in teams and look forward to comments.
Here you find an official solution.
• On Thursday 12:45 you can visit the consultation hours and ask about things that are not clear to you.
Bonus: an edited recording of the consultation.
If you feel like playing with Maple, you can try to go through this worksheet.

Week 11 (April 26 – May 2):
• Before Wednesday, watch the lecture 08a, where the LUP part is for your information.
Also the video 08b is for your information, but you should atke away some idea of the new notions, because we will use norms and the spectral radius the following week.
Slides for the lectures can be found here.
• If you want, solve the homework 11A (results on page 2).
• On Wednesday at 9:15 visit the seminar on Teams. Here is the (edited) recording and slides.
• Solve the obligatory homework 11B. Then submit it by Sunday midnight in a suitable form into the appropriate Assignment in teams and look forward to comments.
Here you find an official solution.
• On Thursday 12:45 you can visit the consultation hours and ask about things that are not clear to you.
Bonus: an edited recording of the consultation.
If you feel like playing with Maple, you can try to go through this worksheet.

Week 10 (April 19–25):
Beware! On Wednesday April 21, the midterm will be given at 9:15 during the regular seminar on Teams, see information and Sample midterm.
The official solution.
After the test there will also be a talk about nonhomogeneous systems.
Here is the (edited) recording and slides.
During the week, look at the following videos:
09b on nonhomogeneous systems. It will not be at the exam, but you should be aware of this. Seeing it before the seminar is helpful but not crucial. Slides are the same as the previous week.
09c on stability of stationary solutions. The important bit that you will need for the exam is around 55:00, and it is a good idea to see the stuff before that as well.
– applications can be found in video 11 If you do not watch at least the first one, you will be missing out on something inteesting (this was actually done before the current problems).
• If you want, solve the homework 10A (results on page 2, this time also with solution).
• The obligatory homework 10B for this week is cancelled.
• Consultations for this week are cancelled.

Week 9 (April 12–18):
Warning! The next Wednesday (April 21), during the seminar we will have the midterm test, see information and Sample midterm.
• Before Wednesday, watch the lecture 09a.
Slides for the lecture can be found here.
• If you want, solve the homework 09A (results on page 2).
• On Wednesday at 9:15 visit the seminar on Teams. Here is the (edited) recording and slides.
• Solve the obligatory homework 09B. Then submit it by Sunday midnight in a suitable form into the appropriate Assignment in teams and look forward to comments.
Here you find an official solution.
• On Thursday 12:45 you can visit the consultation hours and ask about things that are not clear to you.
Bonus: an edited recording of the consultation.

Week 8 (April 5–11):
• Before Wednesday, watch the lecture 07c.
Slides for the lecture are the same as the previous week.
• If you want, solve the homework 08A (results on page 2).
• On Wednesday at 9:15 visit the seminar on Teams. Here is the (edited) recording and slides.
• Solve the obligatory homework 08B. Then submit it by Sunday midnight in a suitable form into the appropriate Assignment in teams and look forward to comments.
Here you find an official solution.
• On Thursday 12:45 you can visit the consultation hours and ask about things that are not clear to you.
Bonus: an edited recording of the consultation.
If you feel like playing with Maple, you can try to go through this worksheet.

Week 7 (March 29– April 4):
• Before Wednesday, watch the lecture 07a and the bonus 07ax.
Slides for the lectures can be found here.
• If you want, solve the homework 07A (results on page 2).
• On Wednesday at 9:15 visit the seminar on Teams. Here is the (edited) recording and slides.
• Solve the obligatory homework 07B. Then submit it by Sunday midnight in a suitable form into the appropriate Assignment in teams and look forward to comments.
Here you find an official solution.
• On Thursday 12:45 you can visit the consultation hours and ask about things that are not clear to you.
Bonus: an edited recording of the consultation.
If you feel like playing with Maple, you can try to go through this worksheet.

Week 6 (March 22–28):
• Before Wednesday, watch the lecture 05b. The part about variation is just for your information. The guessign method is crucial; if you have trouble with it, stere si a special training video 05c that could help.
Linear equations are quite useful; when you have some spare time, you may enjoy watching 11 from time 51:44.
Slides for the lectures are the same as the previous week.
• If you want, solve the homework 06A (results on page 2).
• On Wednesday at 9:15 visit the seminar on Teams. Here is the (edited) recording and slides.
• Solve the obligatory homework 06B. Then submit it by Sunday midnight in a suitable form into the appropriate Assignment in teams and look forward to comments.
Here you find an official solution.
• On Thursday 12:45 you can visit the consultation hours and ask about things that are not clear to you.
Bonus: an edited recording of the consultation.

Week 5 (March 15–21):
• Before Wednesday, watch the lecture 05a. You can skip the proof of dimension n and the bonus. The key part is the procedure for solving equations, but I also strongly recommend to pay attention to the proof that the set of solutions is a linear space, especially if you aim for a good grade.
The topic for this week si a bit lighter, so to round it up I recommend that you check out video 02d with applications of ODEs.
Slides for the lectures can be found here.
• If you want, solve the homework 05A (results on page 2).
• On Wednesday at 9:15 visit the seminar on Teams. Here is the (edited) recording and slides.
• Solve the obligatory homework 05B. Then submit it by Sunday midnight in a suitable form into the appropriate Assignment in teams and look forward to comments.
Here you find an official solution.
• On Thursday 12:45 you can visit the consultation hours and ask about things that are not clear to you.
Bonus: an edited recording of the consultation.

Week 4 (March 8–14):
• Before Wednesday, watch the lectures 03a (the implicit Euler method is just for information) and 03b.
Slides for the lectures can be found here.
• If you want, solve the homework 04A (results on page 2).
• On Wednesday at 9:15 visit the seminar on Teams. Here is the (edited) recording and slides.
• Solve the obligatory homework 04B. Then submit it by Sunday midnight in a suitable form into the appropriate Assignment in teams and look forward to comments.
Here you find an official solution.
• On Thursday 12:45 you can visit the consultation hours and ask about things that are not clear to you.
Bonus: an edited recording of the consultation.
If you feel like playing with Maple, you can try to go through this worksheet.

Week 3 (March 1–7):
• Before Wednesday, watch the lectures 01a (you can skip the proof of relative error for rounding), 01b (you can skip the deducing part between 0:28 and 0:52), and 01c (you can skip the proofs of error order for the trapezoid and Simpson methods, but check out their geometric interpretation and experiments).
Slides for the lectures can be found here, here and here.
• If you want, solve the homework 03A (results on page 2).
• On Wednesday at 9:15 visit the seminar on Teams. Here is the (edited) recording and slides.
• Solve the obligatory homework 03B. Then submit it by Sunday midnight in a suitable form into the appropriate Assignment in teams and look forward to comments.
Here you find an official solution.
• On Thursday 12:45 you can visit the consultation hours and ask about things that are not clear to you.
Bonus: an edited recording of the consultation.
If you feel like playing with Maple, you can try to go through this worksheet.

Week 2 (February 22–28):
• Before Wednesday, watch the lecture 02b.
Slides for the lectures are the same as can be found previous week.
• If you want, solve the homework 02A (results on page 2).
• On Wednesday at 9:15 visit the seminar on Teams. Here is the (edited) recording and slides.
• Solve the obligatory homework 02B. Then submit it by Sunday midnight in a suitable form into the appropriate Assignment in teams and look forward to comments.
Here you find an official solution.
• On Wednesday 11:00 or Thursday 12:45 you can visit the consultation hours and ask about things that are not clear to you.

Week 1 (February 15–21):
• There are two introductions, pick whichever you feel like or watch both: 00, 000.
Definitely watch the lecture 02a, the key part is up to 1:16, then there are two more examples that are recommended but not crucial.
Then watch the lecture 02c, the last example is optional but recommended again.
Slides for the lectures can be found here, a compact version without white spaces for your notes is here.
• If you want, solve the homework 01A (results on page 2).
• On Wednesday at 9:15 visit the seminar on Teams. Here is the (edited) recording and slides.
• Perhaps you should really try homework A, although it is just optional, but you definitely should solve the obligatory homework 01B. Then submit it by Sunday midnight in a suitable form into the appropriate Assignment in teams and look forward to comments.
Here you find an official solution.
• If you feel any uneasiness regarding the topics, organization of the course or life in general, visit consultations on Teams at the time when the practical classes are scheduled (Wednesday 11:00 or Thursday 12:45) and ask. We will try to answer, at least the math questions we can usually handle.

 


Goodies:
syllabus - the most important information about the course.
Schedule of classes - weekly outlines of lectures and a special printable version of slides. We strongly recommend that you print them and take them with you to lectures.
• Information on midterm. Sample midterm.
Information on the final.
Sample final test.
• And if you survive three years here, you will want to look at outline of knowledge that is expected from you when you go for the final state examination.

Important information for the start: The classes take place at room 459, where every student has a terminal connected to the kepler server. A basic manual is here. You can do all the work for the course without having an account, just log-in as a guest.

Lecture notes for the course: Ordinary Differential Equations and Numerical Mathematics.

Solved problems: Here you will find problems of key types with detailed solutions.
 • 1. analysis of solutions.
 • 2. separable equations.
 • 3 & 4. linear equations.
 • 5. variation.
 • 6. & 7. systems.
 • numerical mathematics.

Practice problems: Most of them are of the right difficulty for exams.
 • 1. analysis of solutions.
 • 2. separable equations.
 • 3. homogeneous linear equations.
 • 4. linear equations.
 • 5. variation.
 • 6. homogeneous systems.
 • 7. systems.
 • numerical mathematics.

Maple:
If you want to use the library NumericalMethods on your computer, download the files
NumericalMethods.mla (library of procedures)
NumericalMethods.hdb (Help library) or NumericalMethods.help (Help library for version 18 or later)
and put them into the library folder of your Maple, the traditional place is .../Maple/lib/. Additional info can be found on the page Resources on Maple