Preparatory Mathematical Analysis (MPSI) Course
This Preparatory Mathematical Analysis (MPSI) Course equips you with mastery over linear ordinary differential equations (ODEs), stability analysis, and numerical methods. Gain strong intuition for exponential and trigonometric solutions, rigorous error bounds, and models ready for advanced mathematical applications and control systems, all through a fast-paced, rigorous approach.

4 to 360 hours flexible workload
valid certificate in your country
What will I learn?
Dive into the Preparatory Mathematical Analysis (MPSI) Course for a swift, rigorous journey to mastering linear constant-coefficient ODEs, including exponential and trigonometric solutions plus long-time behaviour. Hone skills in reducing higher-order equations to first-order systems, manually applying Euler’s method with global error estimates, and leveraging Taylor expansions featuring explicit remainder bounds for precise, high-accuracy 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 the 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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