2019-2020 / MATH0006-3

# Introduction to numerical analysis

20h Th, 20h Pr

### Number of credits

 Bachelor of Science (BSc) in Engineering 4 crédits Master of Science (MSc) in Geological and Mining Engineering, professional focus in geometallurgy (EMERALD) (Erasmus mundus) 5 crédits Master of Science (MSc) in Geological and Mining Engineering 5 crédits

English language

### Organisation and examination

Teaching in the first semester, review in January

### Units courses prerequisite and corequisite

Prerequisite or corequisite units are presented within each program

### Learning unit contents

Numerical analysis is at the boundary between Mathematics and Computer Science. It consists in studying how to practically obtain in a computer different mathematical concepts studied in other courses.
There are two main types of problems studied by numerical analysis: - how to actually compute results for which an analytical expression exists but that can be obtained more or less accurately depending on the selected method - how to compute solutions of real problems for which no analytical solution is known but that can be approximated using a computer.
The course is structured in four main chapters.
Ch 1: Polynomial interpolation and regression
Ch 2: Numerical linear algebra and basic linear programming
Ch 3: Non linear systems and some basics about non linear optimization
Ch 4: Numerical derivation and integration

### Learning outcomes of the learning unit

At the end of the course, the student will have to

• master the main numerical methods to approximate derivatives, definite integrals, linear and nonlinear systems, eigenvalues, regressions,
• understand the bases of linear optimization and the simplex algorithm,
• be able to analyze the behaviour of these numerical methods and in particular to be able to discuss their stability, their order of convergence and their conditions of application,
• be able to apply these methods to academic and simple practical instances.

### Prerequisite knowledge and skills

An introductory course on linear algebra and calculus.

### Planned learning activities and teaching methods

The course is organized as follows: 10 lectures and 8 tutorials.

### Mode of delivery (face-to-face ; distance-learning)

face-to-face

The syllabus is available at the CdC.

### Assessment methods and criteria

A written exam. One theoretical question accounts for 25% of the final grade, the rest being exercises.

### Organizational remarks

The theoretical lectures are taught in English.