Numerical Methods and Optimization

year 2015/2016

Background knowledge

Students are expected to have attended introductory courses on calculus, linear algebra, and numerical analysis during their B.Sc. degree. The suggested reading below provides the list of topics students have to be familiar with.

The following preliminary test allows evaluating the level of knowledge on the subject: test.pdf

A set of additional exercise sessions on these topics will be delivered by Stefano Massei during the first semester. All students are encouraged to attend.

Suggested reading

R.L. Burden, J.D. Faires, A.M. Burden Numerical Analysis, Brooks/Cole, 2015.

Chapter 1: Mathematical Preliminaries and Error Analysis
1.1 Review of calculus
1.2 Round-off and Computer Arithmetics
1.3 Algorithms and Convergence
Chapter 2: Solutions of Equations in One Variable
2.2 Fixed-Point Iteration
2.3 Newton's Method
Chapter 3: Interpolation and Polynomial Approximation
3.1 Interpolation and Lagrange Polynomial
Chapter 6: Direct Methods for Solving Linear Systems
6.1 Linear Systems of Equations
6.2 Pivoting Strategies
6.3 Linear Algebra and Matrix Inversion
Chapter 7: Iterative Techniques in Matrix Algebra
7.1 Norm of Vectors and Matrices
7.2 Eigenvalues and Eigenvectors