Preparatory Mathematical Analysis (MPSI) Course
This Preparatory Mathematical Analysis (MPSI) Course provides a rigorous foundation in linear ordinary differential equations (ODEs), stability analysis, and numerical methods. Students master exponential and trigonometric solutions, convert higher-order equations to systems, apply Euler's method with error estimation, and use Taylor expansions for precise modeling. Ideal for advanced math preparation, it builds intuition for long-term behavior and control systems.

4 to 360h flexible workload
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What will I learn?
Gain a rigorous, accelerated mastery of linear constant-coefficient ODEs, including exponential and trigonometric solutions, stability analysis, and long-time behavior. Learn to reduce higher-order equations to first-order systems, implement Euler's method manually with global error bounds, and leverage Taylor expansions featuring explicit remainder terms for high-accuracy simulations and modeling.
Elevify advantages
Develop skills
- Solve linear ODEs using real, repeated, and complex root methods efficiently.
- Analyze system stability through eigenvalues, damping, and asymptotic behavior.
- Implement Euler's method manually, computing steps, errors, and stability bounds.
- Apply Taylor expansions to construct cubic polynomials with precise remainder estimates.
- Derive rigorous bounds on solutions using exponential and derivative 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.What our students say
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