# Computación I: intro to Matlab. Francesca Maria Marchetti

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1 Computación I: intro to Matlab Francesca Maria Marchetti UAM, 15 September 2014

2 Subgroup 5165 Units 1, 2, 3, 5 (control 1) Francesca Maria Marchetti Departamento de Física Teórica de la Materia Condensada Facultad de Ciencias - modulo 05 6 th floor office 606 tel.: web: 15-Sept till 11 Dec Units 4 (controls 2&3) & project Jorge Bravo Abad Departamento de Física Teórica de la Materia Condensada Facultad de Ciencias - modulo 05 5 th floor office tel.: web: 19 Jan till 17 Apr

3 Web page 1. Contacts 2. Course contents 3. Bibliography & useful links 4. Evaluation 5. Timetable & calendar 6. Complementary material: notes & handouts exercises solutions

4 Web page

5 Web page computacion1_14-15.html

6 Objectives of the course To understand how to write and use a program (in a language relevant for scientific calculations) To process, interpret, and present numerical data graphically To understand how to use computers as a tool to solve physical problems To develop to capability to model and implement a simple physical problems Public presentation of scientific results

7 Content Unit 1: Basic Numerical Concepts & First Applications Unit 2: Matrices, functions & Advanced Plotting/Scripting Unit 3: Linear Systems & Root Finding Unit 4: Probability, Data Analysis & Statistics Unit 5: Differential Equations, integration of Newton law Applications: Physical Systems

8 Unit 1 Introduction and basic concepts introduction to MATLAB MATLAB as a calculator (command line usage) variables, vectors, and (in-built) functions plotting scripts numerical derivatives numerical integration Application examples: Tiro parabolico, movimiento harmonico simple, moviemiento armonico amortiguado Posicion, aceleracion, trayectoria, energia

9 Unit 2 Matrices & functions matrix operations and representations user-defined functions loops: for & while if-else conditions representation of scalar and vector fields Application examples: translation and rotation of vectors discrete charge and mass distributions

10 Unit 3 Solving equations linear systems root finding Application examples: conservation of energy circuitos con resistencias y/o fuentes de voltaje que pueden variarse

11 Unit 5 Differential equations 1 st and 2 nd ordinary differential equations Euler method & Runge-Kutta method systems of coupled equations Application examples: Harmonic oscillator, friction, damping,... 1D equations of motion

12 Unit 4 Data analysis & statistics handling of large data sets statistical analysis of data sets data fitting probability distribution functions and random numbers Application examples: your lab (Técnicas Experimentales I) data analysis! lanzamiento de monedas, dados caminos aleatorios calculos de areas y volumenes

13 Project Physical systems Physical applications: some examples in the class, but most importantly: your very own project!!!

14 Content Unit 1: Basic Numerical Concepts & First Applications Unit 2: Matrices, functions & Advanced Plotting/Scripting Unit 3: Linear Systems & Root Finding Unit 4: Probability, Data Analysis & Statistics Unit 5: Differential Equations, integration of Newton law Applications: Physical Systems

15 Evaluation Unit 1: Basic Numerical Concepts & First Applications Unit 2: Matrices, functions & Advanced Plotting/Scripting Unit 3: Linear Systems & Root Finding Unit 4: Probability, Data Analysis & Statistics Unit 5: Differential Equations, integration of Newton law Applications: Physical Systems control #1 (common to all groups) 15% control #2 (separate for each group) 20% project 40% control #3 (common) 25%

16 When and where Grupo :30-13:30 Aula: CIE5 modulo 8 5 a planta aula 503 Sala Gauss (45 ordenadores) learning by doing: essential to also work at home

17 Why useful?..,i.e., why you should care...

18 Computation in physics Graphic representation of trajectories

19 Computation in physics Graphic representation of trajectories

20 Computation in physics Graphic representation of trajectories

21 Computation in physics Graphic representation of trajectories

22 2D and 3D plotting

23 2D and 3D plotting

24 Computation in physics Analysis of complex functions Zeros Max & min

25 Computation in physics Analysis of complex functions: energy conservation

26 Computation in physics Analysis of complex functions: energy conservation

27 Computation in physics Numerical solutions of differential equations Mechanics (Newton) Quantum mechanics (Schrödinger) Fluidodynamics (Navier-Stokes) Electrodynamics (Maxwell)

28 Pendulum Not soluble in terms of elementary functions, but you will be able to solve it numerically before the end of the course

29 Pendulum: small angle approximation Analytical solution (harmonic oscillator): compare with previous results

30 Double pendulum

32 How?

33 Matlab MATLAB = MATrix LABoratory interactive program computation and visualization...not a programming language array processing language tool to understand physics better very user friendly as well as powerful (1 million users in academia & industry only in 2004)

34 Free alternative

35 Example Graphic representation of trajectories

36 Example Graphic representation of trajectories

37 Example Graphic representation of trajectories 1. Definition of a vector t in a given interval 2. Definition of the vectors x(t) and y(t) 3. Plot

38 Bibliography launchpad.html idp=3338&id=132&texto=matlab 5. contenidos/introduccion-matlab/ 6. getstart.pdf 7. matlab70primero.pdf and many more Built-in help!!!!!

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