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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?

This course provides a rapid, rigorous introduction to linear constant-coefficient ODEs, covering exponential and trigonometric solutions, long-time behaviour, conversion of higher-order equations to systems, hand-computed Euler's method with global error estimates, and Taylor expansions featuring explicit remainder bounds for accurate, high-precision mathematical modelling.

Elevify advantages

Develop skills

  • Solve linear ODEs using real, repeated, and complex root methods efficiently.
  • Analyse stability through eigenvalues, damping, and long-term behaviour.
  • Implement Euler's method by hand, computing steps, errors, and stability limits.
  • Apply Taylor expansions to construct cubic 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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