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Preparatory Mathematical Analysis (MPSI) Course

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

What will I learn?

The Preparatory Mathematical Analysis (MPSI) Course offers a rapid, rigorous journey to expertise in linear constant-coefficient ODEs, their exponential and trigonometric solutions, and asymptotic behaviour. Learners will convert higher-order equations into first-order systems, perform hand calculations with Euler’s method, assess global errors, and leverage Taylor series expansions with explicit remainder terms for accurate, high-fidelity simulations and predictions.

Elevify advantages

Develop skills

  • Solve linear ODEs using real, repeated, and complex root methods efficiently.
  • Analyse stability by interpreting eigenvalues, damping, and long-term behaviour.
  • Implement Euler's method manually, computing steps, errors, and stability limits accurately.
  • Apply Taylor expansions to construct cubic polynomials with precise remainder bounds.
  • Derive tight bounds on solutions using exponential and derivative estimates from given 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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