- Unit Coordinator: Jarosław Rybicki
- ECTS Credits: 1
- Semester: 2
- Year: 2
- Campus: Gdansk University of Technology
- Language: English
- Aims:
The course aims at presentation of modern methods of thinking applied in science and technology
- Content:
1. INTRODUCTION. Ontological, psychological, semiotic, theory-cognitive terminology. Formal logic. Philosophy of logic. Methodology vs. science. Science vs. logic.
2. PHENOMENOLOGICAL METHOD. Objectivity of phenomenologists. Return to "issue in itself", intuitive cognition.
3. SEMIOTIC METHODS. Sign and its three dimensions. Formalism. Essence of formalism - calculation. Application of calculation to non-mathematical subjects. Validation of formalism. Eidetic and operational sense. Models. ArtiScial language. Syntactic rules of sense. Construction of language. Atomic and molecular expressions. Notion of syntactic category. Functors and arguments. Examples of syntactic nonsense. Semantic functions and levels Two semantic functions of sign. Designation and signiScance. Semantic levels. Language and meta-language. Semantic meaning and veriSability. Rule of verifiability. Verification levels: technical possibility, physical possibility, logical possibility, transempirical possibility. Principle of intersubjectivity. Verifiability of general clauses.
4. AXIOMATIC METHOD. Structure of indirect cognition. Law and rule. Two basic forms of inference: deduction and reduction. Reliable and unreliable rules of inference. Concept of axiomatic system. Structure of axiomatic clause system. Requirements for axiomatic system. Constitutional system. Progressive and regressive deduction. Mathematical logic. Methodological significance. Implication and derivability. Definition and creation of concepts. Basic types of definition. Real and nominal definitions. Syntactic and semantic definitions. Analytical and synthetic deSnitions. Types of syntactic definitions: clear definitions, contextual definitions, recursive definitions, definitions by axiomatic system. Semantic deictic definitions. Real definitions. Application of axiomatic method. Axiomatization of logic of Hilbert-Ackermann clauses.
5. REDUCTION METHODS. Historical introductory remarks. Concept and division of reduction. Concept of verification and explanation. Regressive reduction. Reduction sciences. Structure of natural sciences. Observation clauses. Progress in natural sciences. Verification of hypotheses. Experience and thinking. Types of explanatory sentences. Causal explanation and teleological explanation. Co-occurrence laws and functional laws. Deterministic laws and statistical laws. Authentic and non-authentic induction. Division of induction. Primary and secondary induction. Qualitative and quantitative induction. Deterministic and statistical induction. Enumerative and eliminatory induction. Postulates of determinism, closed system, relationship between laws, simplicity.
- Reading list:
J. M. Bocheński, Współczesne metody myślenia, wydawnictwo "Wdrodze", Poznań (1992)
Supplementary Literature
K. Popper, Logika odkrycia naukowego, PWN (1983)
M. Grzegorczyk, Logika matematyczna, PWN (1979)
- Code: DT0011
- Unit Coordinator: Giordano Pola
- ECTS Credits: 6
- Semester: 1
- Year: 2
- Campus: University of L'Aquila
- Language: English
- Aims:
The aim of this course is to provide students with basics about modeling, analysis and control of networked and multi-agent systems through consensus techniques.
- Content:
- Introduction to networked and multi-agent systems.
- Recalls of graph theory.
- The agreement protocol: the linear and nonlinear cases.
- Formation control.
- Reading list:
Graph Theoretic Methods in Multiagent Networks, Princeton University Press, Mehran Mesbahi & Magnus Egerstedt, 2010
- Unit Coordinator: Marcello Di Risio
- Programme: InterMaths
- ECTS Credits: 6
- Semester: 1
- Year: 2
- Campus: University of L'Aquila
- Language: English
- Delivery: In-class
- Aims:
This course aims to give a general overview of numerical modeling approaches to reproducing water-related natural hazards. Analytical solutions are outlined for validation/verification purposes. Theoretical aspects will be then applied to a series of test cases, in particular related to (i) tsunami generation, propagation, and interaction with water body boundaries, (ii) wind driven waves propagation and interaction with coastal and harbour structures, (iii) river flow and (iii) detailed simulation (i.e. CFD) of wave-structure interaction. At the end of the course the students will be able to design and perform numerical investigations in typical real cases within the frame of water-related hazard assessment studies.
- Unit Coordinator: Jan Franců
- ECTS Credits: 5
- Semester: 2
- Year: 2
- Campus: Brno University of Technology
- Language: English
- Aims:
The aim of the course is to provide students an overview of modern methods applied for solving boundary value problems for differential equations based on function spaces and functional analysis including construction of the approximate
- Content:
1. Motivation. Overview of selected means of functional analysis.
2. Lebesgue spaces, generalized functions, description of the boundary.
3. Sobolev spaces, different approaches, properties. Imbedding and trace theorems, dual spaces.
4. Weak formulation of the linear elliptic equations.
5. Lax-Mildgam lemma, existence and uniqueness of the solutions.
6. Variational formulation, construction of approximate solutions.
7. Linear and nonlinear problems, various nonlinearities. Nemytskiy operators.
8. Weak and variational formulations of the nonlinear equations.
9. Monotonne operator theory and its applications.
10. Application of the methods to the selected equations of mathematical physics.
11. Introduction to Stochastic Differential Equations. Brown motion.
12. Ito integral and Ito formula. Solution of the Stochastic differential equations.
13. Reserve.
- Pre-requisites:
Differential and integral calculus of one and more real variables, ordinary and partial differential equations, functional analysis, function spaces, probability theory.
- Reading list:
- S. Fučík, A. Kufner: Nonlinear Differential Equations, Nort Holland, 1980.
- K. Rektorys: Variational Methods in Mathematics, Science and Engineering, Dordrecht, D. Reidel Publ. Comp., 1980.
- J. Nečas: Direct Methods in the Theory of Elliptic Equations, Springer, Heidelberg 2012. B. Oksendal: Stochastic Differential Equations, Springer, Berlin 2000.
- Additional info:
The course yields overview of modern methods for solving differential equations based on functional analysis. It deals with the following topics: Survey of spaces of functions with integrable derivatives. Linear elliptic equations: the weak and variational formulation of boundary value problems, existence and uniqueness of the solution, approximate solutions and their convergence. Characteristics of the nonlinear problems. Weak and variational formulation of the nonlinear coercive problems, existence of the solution. Application to the selected nonlinear equations of mathematical physics. Introduction to stochastic differential equations.
