General information 
Course unit name: Mathematical Models and Dynamical Systems
Course unit code: 360153
Academic year: 20182019
Coordinator: Ernest Fontich Julia
Department: Department of Mathematics and Computer Science
Credits: 6
Single program: S
Estimated learning time 
Total number of hours 150 
Facetoface learning activities 
60 
 Lecture 
30 

 Problemsolving class 
15 

 Laboratory session 
15 
Supervised project 
30 
Independent learning 
60 
Competences to be gained during study 
 
Basic knowledge and understanding of mathematics. 
 
Ability to use physical and electronic bibliographical resources. 
 
Understanding of and capacity to apply the language of mathematics. 
 
Understanding of the applications of mathematics in other branches of science and technology. 
 
Capacity to assimilate new mathematical concepts through the prior understanding of other concepts. 
 
Capacity to construct mathematical models of simple, reallife situations. 
 
Capacity to select and apply the most suitable mathematical process for each problem encountered. 
 
Ability to identify flaws in scientific reasoning. 
Learning objectives 
Referring to knowledge — Understand and interpret various mathematical models from different scientific fields (biology, physics, economics, etc.).
— Understand some of the key results of dynamic systems theory.
Referring to abilities, skills — Solve difference equations and elementary differential equations.
— Qualitatively analyse the dynamics of lowdimensional discrete and continuous systems.
— Apply dynamic systems tools in the analysis of mathematical models. 
Teaching blocks 
1. Discrete dynamical systems
1.1. Discrete evolutionary processes: application iteration
1.2. Linear difference equations
1.3. Onedimensional applications: qualitative analysis, phase portraits and bifurcation
1.4. Discrete linear systems: resolution, qualitative analysis and classification
1.5. Introduction to qualitative theory: stationary solution and stability
1.6. Applications
2. Fractals and complex dynamics
2.1. Iterated function systems
2.2. Fractal dimension
2.3. Fractals and dynamic systems
2.4. Julia and Mandelbrot sets
3. Continuous dynamic systems
3.1. Continuous evolution process: ordinary differential equations
3.2. Standard methods of solving ordinary differential equations
3.3. Onedimensional systems: qualitative analysis, phase portraits and bifurcation
3.4. Linear differential equation: resolution, qualitative analysis and classification
3.5. Introduction to qualitative theory: stationary solution and stability
3.6. Applications
Teaching methods and general organization 
The weekly timetable consists of three hours of theorypractical classes and one hour of laboratory exercises and practical work. The theorypractical classes are devoted to presenting the subject matter, which will be illustrated through examples and practical applications. Laboratory classes are dedicated to problemsolving exercises, and the occasional use of computer tools to further understanding of the concepts introduced in the theorypractical classes. 
Official assessment of learning outcomes 
Continuous assessment is based on a midsemester examination (P1) and a final examination, of two parts, at the end of the semester, from which two scores are generated (F1 and F2) corresponding to each of the parts, respectively. There is the possibility of sitting the first part of the final examination to increase the grade. A minimum grade of 3 out of 10 is required in each section in order to pass the subject. Also, part of the grade corresponds to an evaluation of the problemsolving work done in the laboratory (L) during the course. The teacher will specify the value of this component at the beginning of the course.
Examinationbased assessment Single assessment consists of a final examination (F). This option must be requested of the Secretary’s Office at the Faculty before the date set by the Board of Studies.

Reading and study resources 
Consulteu la disponibilitat a CERCABIB
Book
Student solutions manual : elementary differential equations and boundary value problems