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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 offers a quick, rigorous route to mastering linear constant-coefficient ODEs, their exponential and trigonometric solutions, and asymptotic behaviour. Participants learn to reduce higher-order equations to first-order systems, implement Euler’s method manually, assess global errors, and apply Taylor expansions with remainder bounds for accurate, high-precision modelling in mathematical applications.

Elevify advantages

Develop skills

  • Solve linear ODEs using real, repeated, and complex root methods quickly.
  • Analyse stability by checking eigenvalues, damping, and long-term behaviour.
  • Apply Euler's method: compute steps manually, estimate errors, and check stability limits.
  • Use Taylor expansions: construct cubic polynomials with precise remainder bounds.
  • Bound solutions: obtain tight exponential and derivative estimates from given data.

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.
Workload: between 4 and 360 hours

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