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Preparatory Mathematical Analysis (MPSI) Course

Preparatory Mathematical Analysis (MPSI) Course
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.
Workload: between 4 and 360 hours

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