BE5B01DEN - Differential equations & Numerical methods
Consultations: During exam weeks, office hours are held Sunday at 19:00 on MS Teams.
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.
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). A more detailed plan for the course can be found here.
Week 13 (May 12—16): eigenvalues and eigenvectors numerically.
• Printable slides: the same as previous week.
• Practical class: This Wednesday is holiday! The practical class will be held next Tuesday (May 20) instead of the lecture. If you want me to have your HW#12 earlier, you can send it by e-mail.
• There is no Homework #13, 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 5—9): systems linear equations: iteration.
• Printable slides: the same as previous week.
• Tuesday: No DEN lecture, because teaching follows Thursday's schedule.
• Practical class: Bring in your HW #11.
• 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 28—May 2): systems linear equations: Gaussian elimination.
• Printable slides: matrices numerically and here a compact version.
• Practical class: Bring in your HW #9.
• Homework #11, bring your work to practical class in week 12. Now it includes a solution.
• 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 21—25): 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.
• Practical class: midterm. 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.
• There si no homework #10, study for the midterm.
If you miss a class: This week's topics can be found in videos 9d (up to 0:39:45, but the rest is also interesting), 10, and 11 (as much as you want).
Week 9 (April 14—18): systems of linear ODEs (homogeneous and non-homogeneous).
• Printable slides: systems of ODEs and here a compact version.
• Practical class: Bring in your HW #8.
• Homework #9, bring your work to practical class in week 11. Now it includes a solution.
!!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, 9b, and 9c (up to 0:37:43).
Week 8 (April 7—11): finding roots via fixed points.
• Printable slides: the same as previous week.
• Note: There is no lecture on Tuesday! Wednesday's classes will happen as usual.
• Practical class: Bring in your HW #7.
• Homework #8, bring your work to practical class in week 9. Now it includes a solution.
• 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 (March 31—April 4): finding roots directly.
• Printable slides: roots of functions and here a compact version.
• Practical class: Bring in your HW #6.
• Homework #7, bring your work to practical class in week 8. Now it includes a solution.
• 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 24—28): linear ODE.
• Printable slides: the same as previous week.
• Practical class: Bring in your HW #5.
• Homework #6, bring your work to practical class in week 7. Now it includes a solution.
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 17—21): linear ODE (homogeneous).
• Printable slides: linear ODE and here a compact version.
• Practical class: Bring in your HW #4.
• Homework #5, bring your work to practical class in week 6. Now it includes a solution.
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 10—14): solving ODE numerically.
• Printable slides: ODE numerically and here a compact version.
• Practical class: Bring in your HW #3.
• Homework #4, bring your work to practical class in week 5. Now it includes a solution.
• 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 3—7): errors, derivative and integral numerically.
• Printable slides: error in calculations and here a compact version; derivative and integral and here a compact version.
• Practical class: Bring in your HW #2.
• Homework #3, bring your work to practical class in week 4. Now it includes a solution.
• 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 24—28:): variation, analysis.
• Printable slides: the same as previous week.
• Practical class: Bring in your HW #1.
• Homework #2, bring your work to practical class in week 3. Now it includes a solution.
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 17—21): separable equations.
• Printable slides: ODE of order 1 and here a compact version.
• Homework #1, bring your work to practical class in week 2. Now it includes a solution.
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 (including equations of order 1).
• 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 (including equations of order 1).
• 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