## BE5B01DEN - Differential equations & Numerical methods

**Exam** dates (three Mondays) are entered into the system, you can sing up for the exams.

Consultations are held every Sunday before exam week at 18:00 on 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.

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 15—19):** eigenvalues and eigenvectors numerically.

• Printable slides: the same as previous week.

**The practical class (lab)** will be held at the lecture time on Wednesday at 9:15 for all students of this course. We will be talking about exams.

• 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.

**Week 12 (May 8—12):** systems linear equations: iteration.

This week there are changes due to calendar modifications (that in this course we will ignore)!!

• On Monday or Tuesday, please watch video 8c in place of the cancelled lecture.

• Printable slides: the same as previous week.

• As a replacement for Wednesday practical class, either drop by on Thursday at 12:15 to room 202b (and bring homework 11), or watch recording of practical class 12 and send homework 11 by e-mail by Thursday midnight.

• Homework #12, bring your work to practical class in week 13.

• Worksheet #12 for Maple in case you want to play.

**Week 11 (May 1—5):** systems linear equations: Gaussian elimination.

This week there are changes due to calendar modifications!!

• We will have a standard lecture on Tuesday at 14:30.

• Printable slides: matrices numerically and here a compact version.

• On Wednesday we will have the practical class already at 9:15, and it will be a joint class for those who normally come on Wednesday at 11:00 and Thursday at 12:45. Homework #9 is due, bring it with you.

• 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 video 8a.

**Week 10 (April 24—28):** non-homogeneous systems of ODEs, stability of solutions, numerical solution of systems, applications.

• Printable slides: the same as previous week.

• There si no homework, study for the **midterm** that will be given at the practical class. Homework #9 is due to week 11.

If you miss a class: This week's topics can be found in videos 9b, 9c, 10, and 11.

**Week 9 (April 17—21):** 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 video 9a.

**Week 8 (April 10—14):** 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 7c.

**Week 7 (April 3—7):** 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 and 7ax, bonus is 7b.

**Week 6 (March 27—31):** 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 video 5b, bonus in 5c.

**Week 5 (March 20—24):** 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.

**Week 4 (March 13—17):** 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 1:04:30) and 3b (up to 0:40:42).

**Week 3 (March 6—10):** 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, 1b (at least up to 28:14) and 1c (you can skip proofs).

**Week 2 (February 27—March 3:):** 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 2c and 2b (up to 55:53).

**Week 1 (February 20—24):** 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 1:24) and 2d (as much as you want).

**Resources:**

**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.

• 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

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.