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Preparatory Mathematical Analysis (MPSI) Course

Preparatory Mathematical Analysis (MPSI) Course
from 4 to 360h flexible workload
certificate valid in your country

What will I learn?

The Preparatory Mathematical Analysis (MPSI) Course provides a rapid, rigorous route to mastering linear constant-coefficient ODEs, their exponential and trigonometric solutions, and asymptotic behaviour. Learners practise reducing higher-order equations to first-order systems, implementing Euler’s method manually, assessing global errors, and employing Taylor expansions with explicit remainder terms for accurate, high-precision modelling in mathematical contexts.

Elevify advantages

Develop skills

  • Solve linear ODEs using real, repeated, and complex root methods efficiently.
  • Analyse stability through eigenvalues, damping, and long-term behaviour.
  • Apply Euler's method by hand, computing steps, errors, and stability limits.
  • 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.
Workload: between 4 and 360 hours

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