|OFICIAL||Physical Sciences (Mathematics)|
|Responsible unit:||Department of Chemical Engineering|
|Course/CS Responsible:||Master in Chemical Engineering|
|Acronym||No. of Students||Study Plan||Curricular Years||Credits UCN||Credits ECTS||Contact hours||Total Time|
|Fernão Domingos de Montenegro Baptista Malheiro de Magalhães|
|Fernão Domingos de Montenegro Baptista Malheiro de Magalhães||3,00|
|Maria Joana Monteiro de Carvalho Peres||4,50|
The theoretical modeling of transient physical-chemical phenomena is an important component of Chemical Engineering, which is set on the construction and resolution of mathematical models based on differential equations.
- Acquisition of fundamental knowledge in math, namely analytical and numerical resolution of differential equations.
- Development of competences in the areas of formulation, identification and modelling of engineering problems.
- Development of creative and critical thinking and for solving engineering problems. Previous knowledge Basic knowledge on math analysis and algebra: integration and differentiation, complex numbers, matrix algebra, eigen values and eigen vectors. Basic knowledge on programming: programming structures, variable indexation.
Scientific component: 90 %
Technological component: 10 %
Capability to solve ordinary differential equations (first and higher orders) using analytical and numerical methods.
Capability to formulate and implement simple mathematical models describing physical-chemical phenomena.
Capability to use computational tools for numerical resolution of differential equations.
I) Analytical resolution od differential equations
1. Introduction: Definitions. Linearity. General solution and particular solution. Existence and unicity of solution.
2. First order ordinary differential equations: Equations with separable variables. Equations reduced to separable variables by change of variable. Integrating factor method. Exact equations. Bernoulli equations.
3. Second order linear ordinary differential equations. General solution of homogeneous linear equation. D’Alembert’s method (order reduction). Homogeneous equations with constant coefficients. General solution of non-homogeneous linear equation. Method of indeterminated coefficients. Method of parameter variation.
4. Laplace transforms: Definition and properties. Inverse transform. Unit step function (Heaviside) and unit impulse function (Dirac). Application to resolution of linear ordinary differential equations.
5. Systems of linear ordinary differential equations: Method of elimination. Laplace transform method. Matrix method. Homogeneous systems. Non-homogeneous systems
6. Introduction to partial differential equations.
II) Numerical resolution of differential equations
Introduction to Scilab programming. Initial value problems. Euler method. Runge-Kutta methodAnalysis of error in mumerical resolution. Resolution of systems of differential equations. Usage of Scilab's ode function. Boundary value problems. Method of finite differences. Numerical stiffness.
Exposition of theoretical concepts and resolution of practical examples during classes. Interaction with students will be emphasized. The classe dedicated to numerical methods will all take place in computer rooms. Small evaluation tests will take place along the semester, in order to stimulate and monitor the process of aquisition of knowledge and skills by the students along that time period.
|Frequência das aulas||0,00|
Previous attendance is attributed to students who obtained a minimum grade of 6 in distributed evaluation.
Students who enter directly to the 2nd Study Cicle and did not obtain equivalence to this Curricular Unit are not subject to this restriction. Previous attendance is then attributed by performing the exam.
The final classification (CF) will be computed according to:
Conditions for course approval:
The mini-tests are mandatory for students without previous attendence of the course. In case of missing a mini-test, its repetition in a later date ill only be possible after evaluation of the properly fundamented justification.
Students who enter directly to the 2nd Study Cicle and did not obtain equivalence to this Curricular Unit have the option to not do the mini-tests.
The distributed evaluation from previous years is not maintained. Performing the mini-tests is optional for students with previous attendance. In case these students intend to perform the mini-tests, they should inform the teacher during the first week of classes, becoming in this way vinculated to the new distributed evaluation.
Improvement of classification (distributed evaluation and final exam) can be attempted in the second examination ("recurso"). The computation formula is identical to the one used in final classification described above.