Overall objectives:

1 - To grasp basic principles of various Physics study fields in order to solve computational physics problems.
2 - To know methods and algorithms used in numerical simulation in Physics.
3 - To model problems, by building and exploring physical models.
4 - To formulate and solve, using the computer, problems from various Physics study fields, approached in previous curricular units (UCs) or that are given at the same time, from the perspective of numerical solving.
5 - To begin mastering the COMSOL Multiphysics simulation platform for solving computational physics problems.

Syllabus:

1 - Physics problems as examples justifying the need to use computer-implemented numerical techniques. Solving equations (Newton's method). Systems of linear equations: Gauss and Gauss-Jordan methods; Gauss-Seidel and convergence conditions. Systems of nonlinear equations: linearization by Newton's method.
2 - Interpolation techniques (polynomials, spline, linear and polynomial regression by the method of least squares). Basis of orthogonal functions. Example of a sensor calibration.
3 - Integration (example of studying the period of a pendulum as a function of its amplitude). Linear and nonlinear dynamic systems. Solution of differential equations. Initial and boundary conditions. Euler and Runge-Kutta methods. Step adaptation strategy.
4 - Molecular Dynamics Simulations. Properties of a dilute gas. Velocity distribution. Melting transition.
5 - General methods for solving boundary condition problems. Eigenvalues. Shooting and finite difference methods.
6 - Physical problems (3-D movement: trajectories of projectiles and oscillators. Paraxial propagation of light beams. Eigenvalue equations for a vibrating string. Laplace equation for electric potential. Heat conduction equation. Diffusion equation. Poisson equation)

Literature/Sources:

R. H. Landau, M. J. P. Mejía , 1997 , Computational physics: problem solving with computers , John Wiley
S. C. Chapra, R. P. Canale , 1988 , Numerical methods for engineers , McGraw-Hill
P. L. De Vries , 1994 , A First Course in Computational Physics , John Wiley and Sons
S. E. Koonin , 1986 , .Computational Physics , Benjamin/Cummings
H. Gould, J. Tobochnik , 1996 , An Introduction to Computer Simulation Methods: applications to physical systems , Addison-Wesley
J. M. Thijssen , 2007 , ..Computational Physics , Cambridge University Press
J. E. Villate , 2015 , Métodos Numéricos , Edição do autor
N. J. Giordano, H. Nakanishi , 2006 , ...Computational Physics , Pearson/Prentice Hall

Assesssment methods and criteria:

Classification Type: Quantitativa (0-20)

Evaluation Methodology:
In theoretical classes, the methodology is mostly expositive. The contents are laid out on the board or with slides, and the equations and formulas are derived from first principles. Strong emphasis is placed on the link between physical formulas and the real world. Practical laboratory classes consist of solving some key problems, solved on the board, or in the computer, using the COMSOL Multiphysics platform and serving as a demonstration and introduction to the platform. Several problems are solved by the students independently, with individual help from the teacher whenever necessary. Classes are focused on solving problems in various Physics study fields with numerical simulation. Evaluation Model: B. Evaluation Methodology: Theoretical component: 2 written tests, without aid materials. In the examination period, 1 or 2 out of the 2 tests can be improved. Lab. component: 2 computational projects. In the examination season 1 or 2 out of the 2 projects can be improved.