XWT-20305 Mathematical Principles in Water Technology

Course

Credits 5.00

Language of instruction:

English

Assumed knowledge on:

Precalculus.

Contents:

A solid knowledge and flexible use of mathematics is required to understand and design solutions for problems in water technology.
Calculus: functions, differentiation, integrals, 1th and 2nd order differential equations, functions of 2 variables, partial differentiation, total differential, optimization.
Linear Algebra: systems of linear equations, matrix equations, solutions sets of linear systems, linear transformations, matrix operations, determinants, Eigen vectors and Eigen values, diagonalization and systems of differential equations.
Based on acquired knowledge regarding linear algebra the student will apply the theory in a powerful and general state space model representation as a main tool. Having the model, its behaviour can be analysed by analytical tools and by simulations later on in the program.

Learning outcomes:

- understand mathematical concepts and to apply mathematical knowledge, insights and methods to solve problems in technological sciences using a systematic approach;
- simplify or approach problems when analytical solutions are impossible;
- understand limits;
- critically reflect upon the results by verifying them;
- numerically calculate the solution of lower-order differential equations in Excel and Matlab and knows how to interpret the solution;
- analyse stability and stationary conditions of linear systems and understands the superposition principle;
- simulate LTI systems under some specific input functions, as impulse, step, sine wave and random binary signal;
- perform vector/matrix manipulations in Matlab;
- represent a physical (linear, first-order differential equation) model in LTI (linear, time-invariant) state-space form with matrices {A,B,C,D} and to extend this concept to a system with N tanks.

Activities:

- participating lectures/tutorials to provide some additional background material;
- self-study to prepare for the lectures/tutorials;
- performing exercises;
- computer practical's to apply the theory in a Matlab environment.

Examination:

The final exam of the course consists of:
- written exam (80%);
- computer assignment (20%).
Students need to have a minimum partial grade of 5.5 for both components.

Literature:

Stewart, J. (2007) Calculus: Early Transcendentals. 6th ed. USA:Cengage Learning Services.1308p. ISBN:10: 0495011665.
Lay, D.C. (2002). Linear Algebra and its applications, 3rd ed., Pearson Education. 576p. ISBN: 0201709708