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🎓 General Prerequisites
🎓 General Prerequisites
This course assumes that the student is able to:
- 🔹 Use the fundamental tools of mathematical analysis and algebra (limits, derivatives, matrices, etc.).
- 🔹 Apply basic numerical methods (interpolation, approximation, numerical computation).
- 🔹 Solve mathematical problems independently.
- 🔹 Reason rigorously and logically, justifying each step of a mathematical argument.
📘 Chapter 1: Interpolation and Polynomial Approximation – Prerequisites
- 🔹 Recognize the fundamental properties of polynomials (degree, roots, algebraic operations).
- 🔹 Analyze the convergence of simple numerical sequences.
- 🔹 Understand the notions of equidistant and sampled points within an interval.
- 🔹 Solve linear systems with n unknowns.
📗 Chapter 2: Numerical Integration and Differentiation – Prerequisites
- 🔹 Apply the rules of differential calculus (derivation, continuity, differentiability).
- 🔹 Use the properties of definite integrals and antiderivatives.
- 🔹 Estimate approximation errors using bounds or orders of magnitude.
- 🔹 Handle continuous functions on closed intervals.
📙 Chapter 3: Solving Ordinary Differential Equations (ODEs) – Prerequisites
- 🔹 Define the basic elements of an ODE (order, general solution, initial conditions).
- 🔹 Use the properties of continuous and differentiable functions.
- 🔹 Apply classical analytical methods of resolution for simple cases.
- 🔹 Analyze sequence convergence and the concept of limit.
💡 Note: It is highly recommended to master basic programming skills or to be familiar with numerical computation software (Python, Matlab, Scilab, etc.) in order to implement and test the numerical methods covered in this course.
