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Preparatory Mathematical Analysis (MPSI) Course

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

What will I learn?

The Preparatory Mathematical Analysis (MPSI) Course provides a rigorous, fast-paced introduction to linear constant-coefficient ODEs, their exponential and trigonometric solutions, and asymptotic behaviour. Learners will convert higher-order equations into first-order systems, implement Euler’s method manually, estimate global errors accurately, and apply Taylor expansions with explicit remainder terms for precise modelling in mathematical applications.

Elevify advantages

Develop skills

  • Solve linear ODEs using real, repeated, and complex root methods.
  • 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 build 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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