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Preparatory Mathematical Analysis (MPSI) Course

Preparatory Mathematical Analysis (MPSI) Course
4 to 360h 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, stability analysis, and long-time behavior. Learn to reduce higher-order equations to first-order systems, implement Euler's method manually with global error bounds, and leverage Taylor expansions featuring explicit remainder terms for high-accuracy simulations and modeling.

Elevify advantages

Develop skills

  • Solve linear ODEs using real, repeated, and complex root methods efficiently.
  • Analyze system stability through eigenvalues, damping, and asymptotic behavior.
  • Implement Euler's method manually, computing steps, errors, and stability bounds.
  • Apply Taylor expansions to construct cubic polynomials with precise remainder estimates.
  • Derive rigorous bounds on solutions using exponential and derivative data.

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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