Preparatory Mathematical Analysis (MPSI) Course
This Preparatory Mathematical Analysis (MPSI) Course equips you with skills to master linear ordinary differential equations (ODEs), stability analysis, and numerical methods. You will gain strong intuition for exponential and trigonometric solutions, error estimation, and reliable models essential for advanced mathematical studies and control systems.

flexible workload from 4 to 360h
valid certificate in your country
What will I learn?
The Preparatory Mathematical Analysis (MPSI) Course provides a rigorous, fast-paced introduction to linear constant-coefficient ODEs, their exponential and trigonometric solutions, and asymptotic behaviour. Learners will convert higher-order equations into first-order systems, implement Euler’s method manually, estimate global errors accurately, and apply Taylor expansions with explicit remainder terms for precise modelling in mathematical applications.
Elevify advantages
Develop skills
- Solve linear ODEs using real, repeated, and complex root methods.
- Analyse stability through eigenvalues, damping, and long-term behaviour.
- Apply Euler's method by hand-computing steps, errors, and stability limits.
- Use Taylor expansions to build 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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