This course is an introduction to the major methods in numerical analysis, insisting on those methods that play an important role in theoretical and applied physics. The course considers the following topics. Chapter 1 summarizes the properties of the continuous and discrete Fourier transform and the application to digital filtering. The second Chapter presents the basic interpolation techniques, including Shannon sampling and Splines. Chapter 3 introduces numerical integration and deals also with the Monte-Carlo method and its application to nuclear physics. Chapter 4 deals with the numerical solution of ordinary differential equations, and Chapter 5 gives a very short discussion of integral equations. Optimization methods are presented in Chapter 6, with specific details over the optimization of quadratic functions. Chapter 7 introduces unsupervised learning techniques, in particular principal component analysis and clustering methods.
GENERAL COMPETENCIES
i/ Knowledge of the basic methods in numerical analysis.
ii/ Initial experimentation with the concrete analysis and treatment of examples of simple problems in physics.
