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Preparatory Mathematical Analysis (MPSI) Course

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

What will I learn?

This course delivers a rapid, rigorous introduction to linear constant-coefficient ordinary differential equations (ODEs), covering exponential and trigonometric solution methods, stability analysis, and numerical techniques. Learn to reduce higher-order equations to first-order systems, implement Euler's method with manual computations and global error estimates, and leverage Taylor expansions featuring explicit remainder terms for dependable, precise mathematical modeling.

Elevify advantages

Develop skills

  • Solve linear ODEs using real, repeated, and complex root methods efficiently.
  • Analyze system stability through eigenvalues, damping ratios, and asymptotic behaviors.
  • Implement Euler's method manually, computing steps, errors, and stability constraints accurately.
  • Apply Taylor expansions to construct cubic polynomials with precise remainder error bounds.
  • Derive rigorous exponential and derivative bounds for solution 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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