Preparatory Mathematical Analysis (MPSI) Course
This Preparatory Mathematical Analysis (MPSI) Course equips you with mastery over linear ordinary differential equations (ODEs), stability analysis, and numerical techniques. Gain solid intuition for exponential and trigonometric solutions, precise error estimation, and models ready for advanced mathematical control applications, ensuring reliable high-precision outcomes in mathematical modelling.

flexible workload of 4 to 360h
valid certificate in your country
What will I learn?
The Preparatory Mathematical Analysis (MPSI) Course offers a swift, rigorous route to mastering linear constant-coefficient ODEs, their exponential and trigonometric solutions, and asymptotic long-time behaviour. Participants practise reducing higher-order equations to first-order systems, manually implementing Euler’s method, estimating global errors accurately, and leveraging Taylor expansions with explicit remainder bounds to achieve dependable, high-precision mathematical modelling skills.
Elevify advantages
Develop skills
- Solve linear ODEs using real, repeated, and complex root methods swiftly.
- Analyse stability by interpreting eigenvalues, damping, and long-term behaviour.
- Apply Euler's method: compute steps manually, assess errors, and determine stability limits rigorously.
- Employ Taylor expansions: construct cubic polynomials with precise remainder bounds efficiently.
- 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 workloadWhat our students say
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