BE5B01DEN - Differential equations & Numerical methods

Exams: Mondays May 27 and June 3 and 10, 9:00 in room340. Online office hours on the preceding Sundays at 20:00.

Exam special: Follow this link to find a road map to the math department.

Goodies:
syllabus - the most important information about the course.
• Information on midterm. Sample midterm.
Information on the final.
Sample final test. See also Special: recording of a practice final session.
Make-up homeworks in case you missed some of the earier ones and arranged with the instructor to submit them later.
• 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.
You will find study resources below.

Consultations: Every Monday at 20:00 on MS Teams.

Weekly plan with slides that you can print and take with you to lectures (this is strongly recommended so that you do not have to copy that much).

Week 13 (May 13—17): eigenvalues and eigenvectors numerically.
• This is the last week of instruction and it is a consolidating week.
• Please watch videos https://www.youtube.com/watch?v=RQwjixQZmBw (the first 55 minutes are key) and https://www.youtube.com/watch?v=uJTVnPg-U44. This wil not be at the exam, but you will quite likely encounter these mothods later on in your studies.
• Printable slides: the same as previous week.
Lectures are online, but there will be the practical class (lab) on Wednesday at 11:00. We will be talking about exams, do some review, you will have a chance to ask questions and perhaps complete homeworks if needed.
• Homework #13 does not exist, start reviewing for the exam.
If you miss a class: This week's topics can be found in video 12 and 4.

Week 12 (May 6—10): systems linear equations: iteration.
This week there are changes due to calendar modifications!!
• Please watch video https://www.youtube.com/watch?v=w69tCnhPSHc. You may also need to look at the previous video 8c if you are not familiar with norms.
• Printable slides: the same as previous week.
• There is a national holiday on Wednesday. In place of the practical class please watch this recording. Please send me your Homework 11 by e-mail.
Homework #12, bring your work to practical class in week 13.
Worksheet #12 for Maple in case you want to play.
If you miss a class: This week's topics can be found in videos 8c (just for information, notions will be needed) and 8d.
Week 11 (April 29—May 3): systems linear equations: Gaussian elimination.
This week there are changes due to calendar modifications!! Since there is a state holiday on Wednesday, we will go online this whole week.
• For the lecture, watch : https://www.youtube.com/watch?v=AcCO-nVWPZg (this is important), and just for information here: https://www.youtube.com/watch?v=h5HL--o_-ko.
• Printable slides: matrices numerically and here a compact version.
• In place of the practical class please watch this recording. Please send me your Homework 9 by e-mail.
Homework #11, bring your work to practical class in week 12. Solution is here.
Worksheet #11 for Maple in case you want to play.
If you miss a class: This week's topics can be found in videos 8a and 8b (just for information).

Week 10 (April 22—26): non-homogeneous systems of ODEs, stability of solutions, numerical solution of systems, applications.
Tuesday's lecture is cancelled, but there are classes on Wednesday (midterm!).
• Printable slides: the same as previous week.
• There si no homework, study for the midterm that will be given at the practical class (come on time, test will take some 50 minutes and then we will do a bit of work). Homework #9 is due to week 11.
If you miss a class: This week's topics can be found in videos 9c (up to 0:37:43), 9d (up to 0:39:45, but the rest is also interesting), 10, and 11 (as much as you want).

Week 9 (April 15—19): systems of linear ODEs (homogeneous).
• Printable slides: systems of ODEs and here a compact version.
Homework #9, bring your work to practical class in week 11. Solution is here.
!!In week 10 the midterm will take place in the lab.
If you miss a class: This week's topics can be found in videos 9a and 9b.

Week 8 (April 8—12): finding roots via fixed points.
• Printable slides: the same as previous week.
Homework #8, bring your work to practical class in week 9. Solution is here.
Worksheet #8 for Maple in case you want to play.
If you miss a class: This week's topics can be found in video 7d.

Week 7 (April 1—5): finding roots directly.
• Printable slides: roots of functions and here a compact version.
Homework #7, bring your work to practical class in week 8. Solution is here.
Worksheet #7 for Maple in case you want to play.
If you miss a class: This week's topics can be found in video 7a, also 7b (applications up to 0:24:30) and 7c are of interest.

Week 6 (March 25—29): linear ODE.
• Printable slides: the same as previous week.
Homework #6, bring your work to practical class in week 7. Solution is here.
If you miss a class: This week's topics can be found in videos 5c and 5e; 5d may help when practicing.

Week 5 (March 18—22): linear ODE (homogeneous).
• Printable slides: linear ODE and here a compact version.
Homework #5, bring your work to practical class in week 6. Solution is here.
If you miss a class: This week's topics can be found in video 5a (you can skip the proof from 0:38:37 to 0:54:04) and 5b.

Week 4 (March 11—15): solving ODE numerically.
• Printable slides: ODE numerically and here a compact version.
Homework #4, bring your work to practical class in week 5. Solution is here.
Worksheet #4 for Maple in case you want to play.
If you miss a class: This week's topics can be found in videos 3a (up to 1:21:53) and 3b (beginning up to 0:22:30 is optional).

Week 3 (March 4—8): errors, derivative and integral numerically.
• Printable slides: error in calculations and here a compact version; derivative and integral and here a compact version.
Homework #3, bring your work to practical class in week 4. Solution is here.
Worksheet #3 for Maple in case you want to play.
If you miss a class: This week's topics can be found in videos 1a, 1c (recommended to at least skim, it helps in understanding the rest), 1d (part from 0:28:15 to 0:52:10 is optional) and 1f (you can skip proofs and focus on the basic three methods).

Week 2 (February 26—March 1:): variation, analysis.
• Printable slides: the same as previous week.
Homework #2, bring your work to practical class in week 3. Solution is here.
If you miss a class: This week's topics can be found in videos 2b and 2d (up to 1:05:57).

Week 1 (February 19—23): separable equations.
• Printable slides: ODE of order 1 and here a compact version.
Homework #1, bring your work to practical class in week 2. Solution is here.
If you miss a class: This week's topics can be found in videos 2a (at least up to 1:34:45) and 2f (as much as you want).
 

Resources:

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

In case you miss class:
• Videolectures for this course can be found in this Youtube playlist. A detailed description of contents can be found here.
Here you find recorded online practice classes from the covid lockdown days that were re-edited to fit better the way we do practice classes now.

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.
 • 8. assessing suitability of methods.
 • numerical mathematics.

Maple:
If you want to play with numerical mathematics using Maple worksheets, you will need Maple and install in it the library NumericalMethods. To install it, 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