Preparatory Mathematical Analysis (MPSI) Course
This Preparatory Mathematical Analysis (MPSI) Course equips you with essential skills in solving linear ordinary differential equations (ODEs), analysing stability, and applying numerical methods like Euler's method and Taylor expansions. You will gain strong intuition for exponential and trigonometric solutions, error estimation, and reliable modelling techniques vital for advanced mathematics and control systems, ensuring a solid foundation through rigorous practice and precise computations.

from 4 to 360h flexible workload
valid certificate in your country
What will I learn?
This course provides a rapid, rigorous introduction to linear constant-coefficient ODEs, covering exponential and trigonometric solutions, long-time behaviour, conversion of higher-order equations to systems, hand-computed Euler's method with global error estimates, and Taylor expansions featuring explicit remainder bounds for accurate, high-precision mathematical modelling.
Elevify advantages
Develop skills
- Solve linear ODEs using real, repeated, and complex root methods efficiently.
- Analyse stability through eigenvalues, damping, and long-term behaviour.
- Implement Euler's method by hand, computing steps, errors, and stability limits.
- Apply Taylor expansions to construct cubic polynomials with precise remainder bounds.
- Derive tight bounds on solutions using exponential and derivative estimates.
Suggested summary
Before starting, you can change the chapters and workload. Choose which chapter to start with. Add or remove chapters. Increase or decrease the course workload.What our students say
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