This course contains the first 7 chapters of a numerical analysis course given to EPFL bachelor students. Basic tools are described in Chapters 1 to 5. Numerical solution of differential equations is covered in Chapters 6 and 7. (automatic translation)
This course is based on the book "Introduction à l'analyse numérique", J. Rappaz M. Picasso, Ed. PPUR. Basic tools are described in the first 5 chapters. The last two chapters deal with the numerical solution of differential equations. More specifically, we will study the following chapters of the book:
Chapter 1: interpolation, how to approximate a function by a polynomial?
Chapter 2: how to approximate derivatives with finite difference formulas?
Chapter 3: How can integrals be approximated by quadrature formulas?
Chapters 4,5,6: how to solve (large) linear systems?
Chapter 8: How to solve nonlinear equations and systems of equations?
Chapter 9: how to approximate the solution of a differential equation (initial value problem)?
Chapter 10: How to approximate the solution of a one-dimensional boundary problem using a finite difference method? (automatic translation)
