Computational Modelling of Materials

General characterization

Prerequisites

To have basic knowledge of Mathematics, Materials Science and Computation (not restrictive).

Bibliography

• Steven C. Chapra, Applied numerical methods with MATLAB for engineers and scientists, 2ª ed., Mc-Graw Hill, New York, 2008

• Desmond J. Higham & Nicholas J. Higham,  Matlab guide, 2ª ed., SIAM, Philadelphia, 2005

• Steven C. Chapra & Raymond P. Canale, Numerical methods for engineers, 2ª ed., Mc-Graw Hill, New York, 1988 (edição mais recente 7ª ed)

• John H. Mathews & Kurtis D. Fink, Numerical methods : using MATLAB, 4ª ed., Pearson, New Jersey, 2004

Teaching method

The course will be given in a classroom equipped with computers (one computer per student).

Initial presentation of the subjects followed by immediate application or simultaneous execution of commands.

Resolution of training questionnaires.

Software used:

- Visual Basic for Applications (VBA/excel).

- MatLab.

Evaluation method

Pratical evaluation

- Course attendance (As) and Project grade (NP)

- Conditions to access continuous evaluation
          NP >= 9,5
          As >= 2/3 of the class

Continuous evaluation (AC)
-Theoretical
         Grade of 1st test (T1)
         Grade of 2nd test (T2)
- Pratical
         Project grade (NP)
- Conditions to succeed
         MT = (T1+T2)/2 >= 9,5
         NP >= 9,5

- Final grade of AC (NF)
         NF = 70% MT + 30% NP

Exam (if student fails AC)

- Exam grade (NE)
- Project grade(NP)

- Conditions to suceed
         NE >= 9,5
         NP >= 9,5

- Final grade (NF)
         NF = 70% NE + 30% NP

Subject matter

Part I A - Introduction to VBA

    - Excel as a spreadsheet. Excel functions.

    - The Visual Basic for Applications (VBA) excel environment.

    - Variables, constants, procedures and functions. Types and nature of variables.

    - Data exchange between the program and excel sheets.

    - Native VBA functions and access to excel functions

    - Flow control: Elementary and composite control instructions.

    - Manipulation and formatting of text. Text functions

    - Matrices and Arrays. Matrix operations using excel functions.

    - File operations. Write and read.

    - Execution of external programs.

    - Events

    - Graphics

    - User-created graphical interfaces (forms)

Part I B - Introduction to MatLab

    - The MatLab Environment

    - Variables, constants, operators and functions. Variable types.

    - Matrices and Arrays. Matrix and non-matrix operations. Data structures.

    - Text and graphics.

    - File operations. Recording and reading of variables.

    - Flow control: Elementary and composite control instructions.

    - Scripts and Functions

    - User-created graphical interfaces (GUIs)

Part II - Scientific Computing

    - Numerical Errors

    - Roots and relative extrema

    - Linear systems

    - Fit curves to experimental points

    - Interpolation

    - Splines

    - Numerical Integration

    - Numerical Differentiation

    - Ordinary differential equations - prob. of initial value

    - Ordinary differential equations - prob. of boundary conditions

    - Application Examples - Final Project

Programs

Programs where the course is taught: