## BE5B01DEN - Differential equations & Numerical methods

**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**.

• 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 9—13):** eigenvalues and eigenvectors numerically.

• Printable slides: the same as previous week.

**The practical class (lab)** will be held at the lecture time on Tuesday 14:30. The school is closed on Wednesday!

If you miss a class: This week's topics can be found in video 12.

**Week 12 (May 2—6):** systems linear equations: iteration.

• Printable slides: the same as previous week.

• 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 video 8c.

**Week 11 (April 25—29):** systems linear equations: Gaussian elimination.

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

• Homework #11, bring your work to practical class in week 12.

• 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 and 8b.

**Week 10 (April 18—22):** 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**. 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 11—15):** 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 video 9a.

**Week 8 (April 4—8):** 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 7c.

**Week 7 (March 28—April 1):** finding roots directly.

• Printable slides: roots of functions and here a compact version.

• Homework #7, bring your work to practical class in week 8.

• 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 21—25):** linear ODE.

• Printable slides: the same as previous week.

• Homework #6, bring your work to practical class in week 7.

If you miss a class: This week's topics can be found in video 5b, bonus in 5c.

**Week 5 (March 14—18):** linear ODE (homogeneous).

• Printable slides: linear ODE and here a compact version.

• Homework #5, bring your work to practical class in week 6.

If you miss a class: This week's topics can be found in video 5a.

**Week 4 (March 7—11):** solving ODE numerically.

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

• Homework #4, bring your work to practical class in week 5.

• 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 (February 28—March 4):** 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.

• 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 21—25:):** variation, analysis.

• Printable slides: the same as previous week.

• Homework #2, bring your work to practical class in week 3.

If you miss a class: This week's topics can be found in videos 2c and 2b (up to 55:53).

**Week 1 (February 14—18):** separable equations.

• Printable slides: ODE of order 1 and here a compact version.

• Homework #1, bring your work to practical class in week 2.

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.

• 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 is the contents of the seminar recordings, I will upload them to Teams as the school web does not allow me to put them here.