Applied Computing

Recommended Prerequisites

Linear Algebra and Analytic Geometry, Calculus I and II.

Teaching Methods

Theoretical and practical sessions. The theoretical lectures are expository. The practical are intended for problem solving, both in the classroom and in the computational laboratory.

Learning Outcomes

Numerical methods and computing science are fundamental in chemical engineering. The curricular unit called Applied Computing aims to give students a solid training in numerical methods applied to chemical engineering in close connection with the computing science, reinforced by its application other disciplines of the MIEQ.

Work Placement(s)

No

Syllabus

Introduction to numerical calculus

Numerical analysis and computing science. Numerical algorithms. Types and sources of error. Conditioning and stability. Floating point arithmetic

Introduction to MATLAB®

The basics. Arrays e matrizes. Scripts and functions. Loops and conditionals. Graphics.

Non-linear equations

Closed methods: bisection, false position. Open methods: fixed-point, Newton, secant.

Systems of linear equations

Direct methods: Gauss elimination, LU factorization. Pivoting methods. Iterative methods: Jacobi, Gauss-Seidel. Conditioning, stability, and convergence.

Approximation techniques

Lagrange and Newton polynomials. Error analysis. Splines interpolation. Least squares data fitting

Numerical differentiation and integration

Finite differences and interpolation polynomials. Richardson extrapolation. Error analysis. Numerical integration: Newton-Cotes formulas, trapezoidal and Simpson rules. Romberg integration. Error analysis. Gauss quadrature.

Head Lecturer(s)

Pedro Nuno das Neves Lopes Simões

Assessment Methods

Assessment
Project: 25.0%
Mini Tests: 25.0%
Exam: 50.0%

Bibliography

• Oliveira, N.M.C. Prática de Computação. Imprensa da Universidade, Coimbra, 2006.

• Chapra, S.; Canale, R.P. Numerical methods for engineers: with programming and software applications. 4th ed., McGraw-Hill, Boston, 2002.

• Chapra, S., Applied Numerical Methods with MATLAB for Engineers and Scientists, McGraw-Hill, Boston, 2005.

• Palm, W.J. Introduction to MATLAB 7 for Engineers. McGraw-Hill, New York, 2005.

• Gerald, C.F., Wheatley, P.O. Applied Numerical Analysis, 5th ed., Addison-Wesley Publishing Company, N.Y., 1994.

• Atkinson, K. Elementary Numerical Analysis, 2nd ed., John Wiley & Sons, N.Y., 1993.

• WEBSITE DO MATLAB http://www.mathworks.com.

• Yang, W.Y.; Cao, W.; Chung, T.S.; Morris, J. Applied Numerical Methods Using MATLAB. John Wiley, New Jersey, 2005.