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, precise error bounds, and models ready for advanced mathematical control applications, ensuring reliable high-precision modelling skills for complex systems.

from 4 to 360h flexible workload
valid certificate in your country
What will I learn?
The Preparatory Mathematical Analysis (MPSI) Course offers a swift, rigorous route to mastering linear constant-coefficient ODEs, including exponential and trigonometric solutions alongside long-time behaviour analysis. Learners practise reducing higher-order equations to first-order systems, manually implementing Euler’s method, estimating global errors accurately, and employing Taylor expansions with explicit remainder bounds to achieve dependable, high-precision modelling capabilities.
Elevify advantages
Develop skills
- Solve linear ODEs using real, repeated, and complex root methods swiftly.
- Analyse stability via eigenvalues, damping, and long-term behaviour.
- Apply Euler's method by hand, computing steps, errors, and stability limits rigorously.
- Use Taylor expansions to construct P3 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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