Computational Modeling

Recommended Prerequisites

Análise Matemática I, II, III Algebra Linear e Geometria Analítica; Computadores e Programação; Fisica Geral I; Fisica Geral II; Electromagnetismo

Teaching Methods

Teaching Methodologies Partition of contact hours: Lectures 30h, Theoretical-Practical 0 h, Laboratory Practice 30h, Field Work 0h, Seminar 0h, Tutorial 0h, Other 0h.

Evaluation :Problem solving 60, Project 40.

The adopted strategy involves the theoretical exposition of a very broad set of methods and an evaluation process based solely on the performance of small project work and reports. In PL classes the students will solve simple engineering problems using MATLAB. These problems are direct applications of the concepts introduced in lectures. For the evaluation the student presents 5 reports. The last work represents a small project and its grade represents 40% of the final grade. The other work will contribute 15% each for the final grade (they are classified as "Problem solving" in the assessment table). All these jobs allow students to develop their research skills and work individually on advanced problem solving.

Learning Outcomes

The aim of the course is to help the students to develop the ability to identify, implement and critically analyze a numerical method (or a set of methods) to solve fundamental problems in Engineering Physics. The preferred tool is MATLAB.

Skills to develop: Skills in organization and planning; informatics knowledge regarding the scope of the study; Competence in solving problems; Competence in working in group.

Work Placement(s)

No

Syllabus

Differentiation and integration of functions of one variable; Zeros of a one variable function; Linear systems of equations; Applications: normal modes of vibration of a mechanical system. Extremes of functions of one or more variables. Applications: design of an electrical circuit and maximization of power transfer in an electric circuit. Curve fitting: numerical interpolation, linear regression and the Fourier transforms. The Monte Carlo method: integration, radioactive decay, diffusion. Random walkers and Metropolis algorithm. The Ising model. Eigenvalue problems, diagonalization of the Schrödinger equation. Differential Equations: Euler, Runge-Kutta and predictor-corrector methods. The forced and damped pendulum. Chaos. The equations of Laplace and Poisson. Finite differences. Finite elements.

Head Lecturer(s)

João Carlos Lopes Carvalho

Assessment Methods

Assessment
Project: 40.0%
Resolution Problems: 60.0%

Bibliography

Bibliografia Principal/Main Bibliography

Numerical Recipes in F77/F90/C/C++: The Art of Scientific Computing, William H. Press, Saul A. Teukolsky, William T. Vetterling, and Brian P. Flannery, Cambridge University Press, Cambridge Applied Numerical Methods for Engineers and Scientists, Singiresu S. Rao, Prentice Hall (2002), ISBN: 0-13-089480-X Numerical Methods for Engineers: With Software and Programming Applications, Steven C. Chapra and Raymond Canale, McGraw-Hill (2001), ISBN: 0072431938 Computational Physics, M. Hjorth-Jensen, http://folk.uio.no/mhjensen/fys3150/teori/indexteori.html An Introduction to Computational Physics, Tao Pang, Cambridge University Press, Cambridge (1997), ISBN: 0521485924 110