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. Develop strong intuition for exponential and trigonometric solutions, rigorous error bounds, and models essential for advanced mathematical control systems and applications.

4 to 360 hours of flexible workload
certificate valid in your country
What Will I Learn?
Gain a rigorous, accelerated mastery of linear constant-coefficient ODEs, including exponential and trigonometric solutions plus long-time behaviour analysis. Learn to reduce higher-order equations to first-order systems, perform hand calculations with Euler’s method, estimate global errors accurately, and leverage Taylor expansions featuring explicit remainder bounds for dependable high-precision 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 manually, 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
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