✩ Language: English

✩ Place: Czech Technical University in Prague, Prague, Czech Republic

✩ Category: Theory + Labs

✩ Credits: 7 credits

✩ Classes: Tuesday 14.30 – 16.00 (Lecture) ★ Wednesday 9.15 – 10.45 (Lecture) ★ Wednesday 11.00 – 12.30 (Practice)

✩ When: Summer Term 2025 – 2026 (February 16 – May 24, 2026)

✩ Syllabus

• Lectures
  • Solving ODEs by separation. Slope field, stability of equilibria
  • Erros in computing
  • Approximating derivative, order of the method
  • Numerical solution of differential equations (Euler, Rugen-Kutta)
  • Linear ODEs – homogeneous and non-homogeneous (method of undetermined coefficients, variation method)
  • Numerical solution of higher order ODEs
  • Numerical methods for finding roots of functions (bisection, Newton, iteration)
  • Finite methods of solving systems of linear equations (GEM, LU decomposition). Complexity of algorithm. Stability
  • Iteration methods for solving systems of linear equations (Gauss-Seidel)
  • Systems of ODEs. Stability of solutions
  • Numerical methods for determining eigenvalues and eigenvectors of matrices
  • Applications of differential equations
• Tutorials
  • Separation
  • Analysis of solutions (stability, slope field and stability)
  • Getting to know the system, error in calculations
  • Numerical integration
  • Numerical solution of differential equations
  • Homogeneous linear differential equations
  • Equations with quasipolynomial right hand-side. Method of undetermined coefficients
  • Numerical methods for finding roots of functions
  • Homogeneous systems of linear ODEs
  • Systems of linear ODEs
  • Systems of linear ODEs numerically
  • Eigenvalues and eigenvectors of matrices numerically
  • Review of differential equations

✩ Evaluation system

★Lectures: attendance is not mandatory, but highly recommended. 

★Practice: attendance is mandatory, 2 absences are tolerated.

★Midterm: it can yield up to 20 points, 10 is the minimum for passing it.

★Homeworks: 10 accepted homeworks is one of the requirements for zápočet (assessment).

★Zápočet (assesment): participation in labs + at least 10 points from the midterm + completing at least 10 homeworks.

★Final exam: it has 2 parts, a written test (mandatory) and an oral exam (optional). Only students with zápočet will be admitted to the final exam. Written test will consist of 4 problems for 20 points each, with 90 minutes allowed for solving them. Oral exam will look at theory, it can bring up to 10 points and allows students to improve their grade. It can be taken only by students who already passed the final based on their tests (see below). 

★Grading: The grade is based on 3 inputs: 

S is the points earned in the midterm decreased by 10, yielding a number from the range 0–10; 

P is the points from the written test (range 0–80); and 

U is the points from the (optional) oral exam (range 0–10). 

The grade is determined by the following algorithm: 

1) If a student did not score at least 40 pts on the final written test, the student failed the exam. 

2) Assume that a student scored at least 40 pts on the final written test. If the sum P + S is not at least 50, the student failed the exam. 

3) Assume that a student scored at least 40 pts on the final written test and also P + S is at least 50. Then the student passed the exam, we set U = 0 and the student can try to improve this number with the oral exam. 

The grade is then determined by the total P + S + U according to the following key:

➤ 50 – 59 points: E

➤ 60 – 69 points: D

➤ 70 – 79 points: C 

➤ 80 – 89 points: B

➤ 90 – 100 points: A

❖ You have at most 3 attempts to pass the final exam, each is entirely independent.

❖ Repeating the exam is obvious in case you fail, but you can also refuse a grade when you are not happy with it, then you are assigned the grade F and you can try again (if you still have attempts left).

❢❢ The midterm and the final test are subject to the following rules: No textbooks, no notes, no calculators, no cellphones are allowed.