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Preparatory Mathematical Analysis (MPSI) Course

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

What Will I Learn?

Gain a rigorous, accelerated mastery of linear constant-coefficient ODEs, including exponential and trigonometric solutions plus long-time behaviour analysis. Learn to reduce higher-order equations to first-order systems, perform hand calculations with Euler’s method, estimate global errors accurately, and leverage Taylor expansions featuring explicit remainder bounds for dependable high-precision 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 manually, 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 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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