Competencies / Study results |
Code
|
Study programme competences / results
|
A3 |
CE3 - Reconocer y analizar problemas físicos, químicos, matemáticos, biológicos en el ámbito de la Nanociencia y Nanotecnología, así como plantear respuestas o trabajos adecuados para su resolución, incluyendo el uso de fuentes bibliográficas. |
A7 |
CE7 - Interpretar los datos obtenidos mediante medidas experimentales y simulaciones, incluyendo el uso de herramientas informáticas, identificar su significado y relacionarlos con las teorías químicas, físicas o biológicas apropiadas. |
B2 |
CB2 - Que los estudiantes sepan aplicar sus conocimientos a su trabajo o vocación de una forma profesional y posean las competencias que suelen demostrarse por medio de la elaboración y defensa de argumentos y la resolución de problemas dentro de su área de estudio |
B4 |
CB4 - Que los estudiantes puedan transmitir información, ideas, problemas y soluciones a un público tanto especializado como no especializado |
B5 |
CB5 - Que los estudiantes hayan desarrollado aquellas habilidades de aprendizaje necesarias para emprender estudios posteriores con un alto grado de autonomía |
B6 |
CG1 - Aprender a aprender |
B7 |
CG2 - Resolver problemas de forma efectiva. |
B8 |
CG3 - Aplicar un pensamiento crítico, lógico y creativo. |
B9 |
CG4 - Trabajar de forma autónoma con iniciativa. |
B10 |
CG5 - Trabajar de forma colaborativa. |
B11 |
CG6 - Comportarse con ética y responsabilidad social como ciudadano/a y como profesional. |
B12 |
CG7 - Comunicarse de manera efectiva en un entorno de trabajo. |
C3 |
CT3 - Utilizar las herramientas básicas de las tecnologías de la información y las comunicaciones (TIC) necesarias para el ejercicio de su profesión y para el aprendizaje a lo largo de su vida |
C7 |
CT7 - Desarrollar la capacidad de trabajar en equipos interdisciplinares o transdisciplinares, para ofrecer propuestas que contribuyan a un desarrollo sostenible ambiental, económico, político y social. |
C8 |
CT8 - Valorar la importancia que tiene la investigación, la innovación y el desarrollo tecnológico en el avance socioeconómico y cultural de la sociedad |
C9 |
CT9 - Tener la capacidad de gestionar tiempos y recursos: desarrollar planes, priorizar actividades, identificar las críticas, establecer plazos y cumplirlos |
Learning aims |
Learning outcomes |
Study programme competences / results |
Identify the different types of differential equations and problems associated with them. Especially those originating in nanoscience and nanotechnology |
A3 A7
|
B2 B4 B6 B7 B8 B9
|
C3 C9
|
Know and acquire fluency in the techniques to obtain analytical and numerical solutions of models based on ordinary differential equations |
A3 A7
|
B2 B4 B6 B7 B8 B9 B12
|
C7 C8 C9
|
Know and acquire fluency in the techniques to obtain analytical and numerical solutions of models based on partial differential equations |
A3
|
B2 B5 B10 B11
|
C3 C7 C8 C9
|
Have criteria to choose the most efficient analytical and numerical techniques for models of real problems, especially those related to nanoscience and nanotechnology. |
A3
|
B2 B4 B5 B6 B7 B8 B9 B10 B11 B12
|
C3 C7 C8 C9
|
Manage software tools that implement the methodologies studied and know how to analyze the results |
A3 A7
|
B2 B4 B5 B6 B7 B9 B10 B12
|
C3 C9
|
Contents |
Topic |
Sub-topic |
Unit 1: First order ordinary differential equations |
- Initial value problem
- Analytic resolution
- Mathematical models
- Numerical resolution: Explicit Euler, Implicit Euler, Heun, Runge-Kutta.
- Aplications |
Unit 2: Systems of differential equations |
- Systems of differential equations
- Analytic resoluiton
- Estability
- Mathematical models
- Numerical schemes: Explicit Euler, Implicit Euler, Heun, Runge-Kutta.
- Applications |
Unit 3: Second order ordinary differential equations
|
- Initial value problem.
- Analytic resolution. Laplace transform, Fourier transform.
- Mathematical models.
- Numerical resoltion
- Aplications
- Contour problems
- Analytic resolution.
- Numerical resolution. Finite difference method.
- Sturm-Liouville problems. Numerical approximation of eigenvalues and eigenfunctions
- Aplications |
Unit 4: Partial differential equations |
- 1D Heat equation. Analític resolution using separation of variables. Numerical resolution using finite difference.
- 1D wave equation: Analític resolution using separation of variables. Numerical resolution using finite difference.
- Schrödinger equation. Analític resolution using separation of variables. Numerical resolution using finite difference.
- Laplace and Poisson equation. Analític resolution using separation of variables. Numerical resolution using finite difference.
- 2D Heat equation.Analític resolution using separation of variables. Numerical resolution using finite difference.
- Aplications. |
Planning |
Methodologies / tests |
Competencies / Results |
Teaching hours (in-person & virtual) |
Student’s personal work hours |
Total hours |
Guest lecture / keynote speech |
A3 B2 B4 B5 B6 B7 B11 C8 |
28 |
56 |
84 |
ICT practicals |
A3 A7 B2 B4 B10 C3 C7 C9 |
12 |
26 |
38 |
Problem solving |
A7 B8 B12 |
8 |
13 |
21 |
Mixed objective/subjective test |
B7 B9 C9 |
3 |
0 |
3 |
|
Personalized attention |
|
4 |
0 |
4 |
|
(*)The information in the planning table is for guidance only and does not take into account the heterogeneity of the students. |
Methodologies |
Methodologies |
Description |
Guest lecture / keynote speech |
Exhibition of the contents specified in the program of the subject, for which audiovisual media (tablet) will be used. |
ICT practicals |
Interactive practices in which relevant problems in the field of Science and Engineering will be solved, using Python programming language. |
Problem solving |
Sessions where relevant problems in the field of Science and Engineering will be presented, which will be solved both analytically and numerically. The student must be able to reach the solution of any problem using pencil and paper or alternatively using computer tools (using Python), and compare the results. |
Mixed objective/subjective test |
Development of issues and problems of the subject. |
Personalized attention |
Methodologies
|
Problem solving |
ICT practicals |
|
Description |
- The diversity of the students and their training make it advisable to have personalized guidance, which could be carried out through tutorials.
- Practices with ITC tools in problem solving, or teachers will help students to develop two stated problems, as well as applications to problems in the field of Science and Engineering.
- With the aim of preparing students for the different continuous assessment tests, as well as the final test; group defenses will be carried out, of the problems raised. Its realization will be set jointly between teachers and students. They will take place in the teachers' office. The defenses will be distributed in groups, in four sessions of 10 minutes (for each one of the groups).
- The specific personalized attention measures for "Students with recognition of part-time dedication and academic waiver of attendance exemption" for the study of the subject, the continuous evaluation of the practices through ITC and the resolution of problems carried out attending, as far as possible, to your particular circumstances. |
|
Assessment |
Methodologies
|
Competencies / Results |
Description
|
Qualification
|
Mixed objective/subjective test |
B7 B9 C9 |
Test that includes the resolution of questions and problems of the subject (by hand and/or Python) |
50 |
Problem solving |
A7 B8 B12 |
Rosolution of practical problems |
25 |
ICT practicals |
A3 A7 B2 B4 B10 C3 C7 C9 |
Resolution of practical problems using the Python programming language |
25 |
|
Assessment comments |
The final qualification of the subject consists of three parts: - Qualification of internships through ICT (CP): between 0 and 2.5 points
- Problem Solving Qualification (CR): between 0 and 2.5 points
- Mixed test qualification (CE): between 0 and 5 points.
The final qualification will be the sum of three parts: Final_Note= CP + CR + CE, if the qualification of the mixed test (CE) is greater than 1.3 (over 5 points). In other case, the final qualification will be the mark obtained on the mixed test, CE.
The qualification of the practices through ICT (CP) + the resolution of problems (CR), constitute the note of Continuous Evaluation (EV), EV = CP + CR. The qualifications of practices through ICT (CR) and problem solving (CP) will be kept on the second opportunity of the evaluation, that is, the EV note will be kept for the second opportunity. The evaluation of CP + CR will be carried out by solving four small mixed tests, in which the student will have to solve problems of the subject by hand and with Python. The qualifications of practices through ICT (CR) and problem solving (CP) will be retained in the second opportunity of the evaluation. With the aim of preparing students for the different continuous assessment tests, as well as the final test; during the course, group defenses will be carried out, of the problems raised. These defenses allow up to two points to be recovered from the evaluation (if the final grade of the mixed test (CE) is greater than 1.3 points - out of 5 points). The score corresponding to these works will only be taken into account in the first and second opportunity. Students who do not show up for the final mixed test will be considered as "Not presented". All previous observations are applicable to students who request the early December call. All aspects related to “academic dispensation”, "dedication to study", "permanence" and "academic fraud" are governed in accordance with the current academic regulations of the UDC.
|
Sources of information |
Basic
|
Richard G. Rice, Duong D. Do (2012). Applied Mathematics And Modeling For Chemical Engineers (2º ed). John Wiley & Sons
Wei-Chau Xie (2014). Differential Equations for Engineers (2º ed). Cambridge University Press
Stephen Lynch (2018). Dynamical Systems with Applications using Python. Springer
Dennis G. Zill (2018). Ecuaciones diferenciales con problemas con valores en la frontera (9ª ed). Cengage
C. Henry Edwards, David E. Penney (2017). Ecuaciones diferenciales y problemas con valores en la frontera. Cómputo y modelado (4ª ed). Pearson Education
William E. Boyce, Richard C. DiPrima, Douglas B. Meade (2017). Elementary Differential Equations and Boundary Value Problems, (11ª Ed). Willey |
|
Complementary
|
George F. Simmons (2016). Differential Equations with Applications and Historical Notes. Chapman and Hall/
William E. Boyce, Richard C. DiPrima, Douglas B. Meade (2017). Elementary Differential Equations and Boundary Value Problems, Student Solutions Manual, (11ª Ed). Wiley
Steven C. Chapra , Raymond P. Canale (2015). Métodos Nméricos para Ingenieros (7ª ed). McGraw-Hill
J. C. Butcher (2016). Numerical Methods for Ordinary Differential Equations, (3ª ed). Wiley
Victor Henner, Alexander Nepmnyashchy, Tatyana Belozerova, Mikhain Khenner (2023). Ordinary Differential Equations. Analytical Methods and Applications. Springer
Svein LingeHans, Petter Langtangen (2017). Programming for Computations - Python A Gentle Introduction to Numerical Simulations with Python. Springer // Github: https://github.com/hplgit |
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Recommendations |
Subjects that it is recommended to have taken before |
Numerical and Statistical Methods/610G04013 | Fundamentals of Mathematics/610G04001 | Advanced Calculus /610G04009 | Fundamentals of Computing Science/610G04010 |
|
Subjects that are recommended to be taken simultaneously |
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Subjects that continue the syllabus |
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Other comments |
- It is recommended to have knowledge of the second year of high school. In particular, differential and integral calculus.
- Daily study of the contents treated in the classroom, complementing them with the recommended bibliography.
- Gender perspective: as stated in the transversal competences of the title (C4), the development of a critical, open and respectful citizenship with diversity in our society will me promoted, highlighting the equal rights of students without discrimination based on gender or sexual condition. An inclusive language will be used in the material and during the development of the lessons.
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