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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?

This Preparatory Mathematical Analysis (MPSI) course offers a swift, rigorous route to mastering linear constant-coefficient ODEs, their exponential and trigonometric solutions, and asymptotic behaviour. Gain proficiency in reducing higher-order equations to first-order systems, manually applying Euler’s method with global error estimates, and leveraging Taylor expansions featuring explicit remainder terms for precise, high-fidelity modelling in mathematical applications.

Elevify advantages

Develop skills

  • Solve linear ODEs using real, repeated, and complex root methods swiftly.
  • Analyse stability via eigenvalues, damping, and long-term behaviour.
  • Implement Euler's method manually, computing steps, errors, and stability bounds rigorously.
  • Employ Taylor expansions to construct cubic polynomials with precise remainder estimates.
  • Derive tight bounds on solutions using exponential and derivative approximations.

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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