Preparatory Mathematical Analysis (MPSI) Course
Master linear ODEs, stability, and numerical methods in this Preparatory Mathematical Analysis (mpsi) Course. Build strong intuition for exponential and trigonometric solutions, error bounds, and control-ready models used in advanced mathematics.

from 4 to 360h flexible workload
valid certificate in your country
What will I learn?
The Preparatory Mathematical Analysis (mpsi) Course gives you a fast, rigorous path to mastering linear constant-coefficient ODEs, exponential and trigonometric solutions, and long-time behavior. You practice converting higher-order equations to first-order systems, applying Euler’s method by hand, estimating global error, and using Taylor expansions with explicit remainder bounds for reliable, high-precision modeling.
Elevify advantages
Develop skills
- Solve linear ODEs: master real, repeated, and complex root techniques fast.
- Analyze stability: read eigenvalues, damping, and long-term system behavior.
- Apply Euler method: hand-compute steps, errors, and stability limits with rigor.
- Use Taylor tools: build P3 polynomials and sharp remainder error bounds quickly.
- Bound solutions: derive tight exponential and derivative estimates from 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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