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 techniques. Gain deep insights into exponential and trigonometric solutions, precise error estimation, and modelling skills essential for advanced mathematical studies and control systems.

flexible workload of 4 to 360h
valid certificate in your country
What will I learn?
The Preparatory Mathematical Analysis (MPSI) Course offers a rapid, rigorous journey to expertise in linear constant-coefficient ODEs, their exponential and trigonometric solutions, and asymptotic behaviour. Learners will convert higher-order equations into first-order systems, perform hand calculations with Euler’s method, assess global errors, and leverage Taylor series expansions with explicit remainder terms for accurate, high-fidelity simulations and predictions.
Elevify advantages
Develop skills
- Solve linear ODEs using real, repeated, and complex root methods efficiently.
- Analyse stability by interpreting eigenvalues, damping, and long-term behaviour.
- Implement Euler's method manually, computing steps, errors, and stability limits accurately.
- Apply Taylor expansions to construct cubic polynomials with precise remainder bounds.
- Derive tight bounds on solutions using exponential and derivative estimates from given data.
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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