## BE5B01DEN - Differential equations & Numerical methods

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 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.

**!!**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.

• 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