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. Learners master solving constant-coefficient ODEs with exponential and trigonometric solutions, assess long-term behavior, apply Euler's method for approximations with error control, and use Taylor expansions for high-precision modeling. Ideal for building skills essential for advanced mathematical studies and control systems.

from 4 to 360h flexible workload
valid certificate in your country
What will I learn?
Gain a swift, rigorous mastery of linear constant-coefficient ODEs, including exponential and trigonometric solutions plus long-time behavior analysis. Learn to reduce higher-order equations to first-order systems, perform hand calculations with Euler’s method, estimate global errors accurately, and leverage Taylor expansions with explicit remainder bounds for dependable, precise modeling in mathematical applications.
Elevify advantages
Develop skills
- Solve linear ODEs using real, repeated, and complex root methods efficiently.
- Analyze system stability through eigenvalues, damping, and long-term behavior.
- Implement Euler's method by hand, computing steps, errors, and stability bounds.
- Apply Taylor expansions to construct cubic polynomials with precise remainder estimates.
- Derive tight bounds on solutions using exponential and derivative data analysis.
Suggested summary
Before starting, you can change the chapters and 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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