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. Delve into exponential and trigonometric solutions, error estimation, and robust modelling essential for advanced mathematical studies and control systems, fostering deep intuition through rigorous practice.

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.What our students say
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