Numerical Tools with Python

Code: MAT15034D

6 ECTS

Duration: 15 weeks/156 hours

Scientific Area: Informatics, Mathematics

Teaching languages: Portuguese

Languages of tutoring support: Portuguese

Regime de Frequência: B-learning

Sustainable Development Goals

Educação de qualidade - Assegurar a educação inclusiva, e equitativa e de qualidade, e promover oportunidades de aprendizagem ao longo da vida para todos.

Inovação infraestrutura - Construir infraestrutura resiliente, promover a industrialização inclusiva e sustentável, e fomentar a inovação.

Learning Goals

This Curricular Unit aims to develop and consolidate the computational implementation of numerical methods with application to problems in various scientific areas such as Engineering, Physics, Chemistry, Biology, Economics and Management. It should encourage students' ability to use computational tools as a means of calculation. It will be considered the use of a symbolic calculation program, SageMath, which will allow the implementation of scripts in the Python programming language.
At the end, students should be able to develop computational calculation programs with a view to solving concrete problems.

1. Introduction to SageMath software. Installation.
2. SageMath as a calculator: first calculations, elementary functions, Python variables, symbolic variables, first graphs.
3. Representation of floating point numbers: properties, rounding.
4. Programming and data structure: algorithms (loops, conditions and functions), lists and other data structures.
5. Analysis: symbolic expressions and simplifications, elementary mathematical functions, explicit resolution of equations. Sums, limits, sequences, series, derivatives and integrals. Solving differential equations.
6. Linear algebra: vector and matrix computation, solving linear systems, eigenvalues and eigenvectors computation, matrix decomposition.
7. Graphics: graphical representation of functions, parametric curves, curves in polar coordinates, implicitly defined curves, representation of discrete data, representation of the solution of differential equations.