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Preparatory Mathematical Analysis (MPSI) Course

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

What will I learn?

Explore a rigorous introduction to linear constant-coefficient ODEs, their exponential and trigonometric solutions, and asymptotic behaviour in this Preparatory Mathematical Analysis (MPSI) Course. Master techniques for reducing higher-order equations to first-order systems, manual Euler method implementation with error analysis, and Taylor expansions featuring explicit remainder terms to ensure precise and reliable 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 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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