### MTH5102 Calculus III

Syllabus includes:
Elements of vector calculus (scalar and vector fields; gradient, divergence and curl; vector integrals: line, surface and volume; integral theorems: Divergence, Stokes, Green), elements of Fourier series (Dirichlet and Parseval's theorem; full, half, and arbitrary range Fourier series) and an introduction to Laplace equation.
Module website

Module website

Module website

### Scientific Programming in Fortran 90 (slides in spanish)

This is a basic course on the programming language Fortran 90 (numerical data, conditional sentences, iterative structures, arrays, intrinsic functions, I/O, and modular programming).
1. Introducción al Fortran 90
2. Datos numéricos
3. Sentencias condicionales
4. Estructuras iterativas
5. Datos tipo array: asignación dinámica de memoria
6. Funciones intrínsecas
7. Entrada y salida de datos
8. Formatos de escritura
10. Programación modular: subrutinas y funciones

### Numerical Analysis and Scientific Computing (slides in spanish)

This is a practical course on numerical analysis, focused on algorithms to numerically solve and/or calculate: nonlinear equations, numerical derivatives, numerical integration, linear systems of equations (exact and iterative methods), nonlinear systems of equations, interpolation and approximation, and ordinary differential equations. The course is practical, and focuses more on the implementation of the algorithms in Fortran 90 than in the theory behind these algorithms.
1. Introducción al Cálculo Numérico con Fortran
2. Resolución de ecuaciones no lineales
3. Integración y derivación numérica
4. Resolución de sistemas lineales: métodos exactos e iterativos
5. Resolución de sistemas no lineales
6. Interpolación polinómica
7. Resolución de ecuaciones diferenciales ordinarias

### Complex systems (slides in spanish)

This is an introductory course to the fascinating field of complex systems. Syllabus includes topics such as elements of statistical physics and critical phenomena, fractal geometry, nonlinear dynamics and chaos, complex networks, signal processing and data analysis.
1. Introducción a las ciencias de la complejidad
2. La fiaacutesica de los sistemas complejos
3. Geometría fractal
4. Dinámica no lineal y caos
5. Redes complejas