ECTS credits ECTS credits: 6
ECTS Hours Rules/Memories Student's work ECTS: 99 Hours of tutorials: 3 Expository Class: 24 Interactive Classroom: 24 Total: 150
Use languages Spanish, Galician
Type: Ordinary Degree Subject RD 1393/2007 - 822/2021
Departments: Applied Mathematics, Statistics, Mathematical Analysis and Optimisation
Areas: Applied Mathematics, Mathematical Analysis
Center Faculty of Biology
Call: First Semester
Teaching: Sin Docencia (En Extinción)
Enrolment: No Matriculable (Sólo Planes en Extinción)
This course aims to update the student on the basic infinitesimal calculus with a first approach to modeling and solving problems in ordinary differential equations arising in biology. Students, familiar or not with the simpler habitual techniques of calculus, will extend their knowledge and they will discover it as an indispensable mathematical tool to formalize and solve many problems in the field of biology.
Lectures and seminar classes (44 hours)
1. IMPORTANCE OF FUNCTIONS IN THE FIELD OF BIOLOGY (20 hours)
Potential or exponential growths and decreases. Logarithmic function: logarithmic and semi-logarithmic graphs. Contour lines. Interpretation of the Shannon diversity index. Rate of change for a variable. Monod kinetic model. Rates of change for two variables. Gradient vector field: chemotaxis. Holling's disk equation. Turn around the derivation: calculation of primitives.
2. BIOLOGICAL MODELS WITH DIFFERENTIAL EQUATIONS, OR SYSTEMS OF EQUATIONS (18 hours)
From the rate of change as a hypothesis to the differential equation: introduction to the modeling of a biological process. Solving differential equations.
Biological models of growth: Malthus's Law. Logistic equation. Von Bertalanffy equation. Systems of linear differential equations: compartmental models. Systems of nonlinear differential equations: the Lotka-Volterra predator-prey model.
3. BIOLOGICAL MODELS WITH MATRICES (6 hours)
Eigenvalues and eigenvectors of a matrix. Age-structured population: Leslie matrix.
Interactive classes in computer room (9 hours)
Computer practices:
• Introduction to the free and open source mathematical software environment SageMath. Basic arithmetic, elementary mathematical functions and graphical representations (2 hours).
• Introduction to symbolic calculation with SageMath. Derivatives and integrals (1 hour).
• Solving differentials equations, or systems of equations, with SageMath (2 hours).
• Matrices with SageMath (1 hour).
Evaluation of the contents through questionnaires in the virtual campus of the USC (2 hours).
Evaluation of computer practices through a questionnaire on the virtual campus of the USC (1 hour).
Tutoring (1 hour)
Clarify in detail the doubts that may arise on the subject, both from the point of view of the concepts and the computer tool used, also on the tasks to be carried out through the virtual course.
Basic bibliography
Bard, G.V., 2015. Sage for undergraduates. Providence, Rhode Island: American Mathematical Society.
Neuhauser, C., 2004. Matemáticas para Ciencias. 2ª ed. Madrid: Pearson Prentice Hall.
Zill, D., 2009. Ecuaciones Diferenciales con Aplicaciones de Modelado. 9ª ed. México: International Thomson Editores.
Complementary bibliography
Braun, M., 1990. Ecuaciones Diferenciales y sus Aplicaciones. México: Grupo Editorial Iberoamericana.
Derrick, W.R. e Grossman, S.I., 1997. Elementary Differential Equations. Massachutsetts: Addison-Wesley.
Edwards, C.H. e Penney, D.E., 1994. Ecuaciones Diferenciales Elementales y Problemas con Condiciones en la Frontera. 3ª ed. México: Prentice-Hall Hispanoamericana.
Nagle, R.K. e Saff, E.B., 1992. Fundamentos de Ecuaciones Diferenciales. 2ª ed. Buenos Aires: Addison-Wesley Iberoamericana.
Simmons, G.F., 2002. Ecuaciones Diferenciales con Aplicaciones y Notas Históricas. 2ª ed. Madrid: McGraw-Hill.
Stein, S.K. e Barcellos, A., 1995. Cálculo y Geometría Analítica. 5ª ed. Santa Fé de Bogotá: McGraw-Hill.
Basic and general: given on pages 13 and 14 of the Memoria do Grao en Bioloxía, 2ª ed.*
Transversal: indicated on page 14 of the Memoria do Grao en Bioloxía, 2ª ed.*
* https://www.usc.gal/export9/sites/webinstitucional/gl/servizos/sxopra/m…
Specific:
CE2 - Propose, apply and interpret mathematical models and statistical methods in the field of Biology.
- Lectures in large group.
- Computer laboratory in small groups.
- Tutorials in small group.
- In addition, students will have an on-line course, with material relating to the contents being developed in the lectures, seminar classes and computer laboratory, along with bulletins of exercises for its resolution.
METHODOLOGICAL ADAPTATIONS (In accordance with the instructions contained in the document "Guidelines for the development of safe face-to-face teaching. Course 2020-21" prepared by the "Commission for Teaching Planning", we describe below the methodological adaptations that will be carried out out in each of the three scenarios in that document)
Scenario 1 (adapted normality)
The expository lectures and interactive teaching will be face-to-face and will be complemented with the virtual course of the subject, in which the students will find various bibliographic materials. Students will perform continuous assessment tasks through the virtual course, as described in the corresponding section. The tutorials will be in person or by email.
Scenario 2 (distancing)
Partially virtual teaching, according to the distribution organized by the Faculty of Biology, with aids of virtual course. If it is not possible to maintain the required interpersonal distance, computer practices will be taught virtually. Students will perform continuous assessment tasks through the virtual course, as described in the corresponding section. The tutorials will be attended by email or through MS TEAMS.
Scenario 3 (closure)
Completely remote teaching through the virtual course of the subject. Virtual computer practices. Students will perform continuous assessment tasks through the virtual course, as described in the corresponding section. Tutoring by email or MS TEAMS.
http://www.usc.es/gl/centros/bioloxia/criteriosavaliacion.html
As can be seen from the table above, the completion of the questionnaires in the virtual course (20%), the progress of computer practices (10%) and the final exam (70%) will be taken into account in calculating the final rating. The same instruments will be used to evaluate the subject competences, according to the scheme:
- In the on-line questionnaires: CG2, CG3, CG5, CT7, CE2.
- In the evaluation of computer practices: CG2, CG3, CG5, CT7, CE2.
- In the final exam: CB1, CB2, CB5, CG2, CG3, CG5, CT1, CT2, CT8, CE2.
Lectures in large group: 36 hours
Seminar classes: 8 hours
Computer laboratory in small group: 9 hours
Tutorials: 1 hour
Exam: 3 hours
Total hours work with the teacher: 57 hours
Individual study : 46 hours
Recommended reading, library or similar activities: 5 hours
Personal work with computer: 15 hours
Writing exercises, conclusions or other works: 25 hours
Attendance at lectures, or other activities recommended: 2 hours
Total hours personal work: 93
- Diary study of contents covered in the class.
- Resolution of exercises proposed in bulletins.
- Use of the tutoring hours by teachers to solve all type of doubts about the matter.
CONTINGENCY PLAN (In accordance with the instructions contained in the document "Guidelines for the development of safe face-to-face teaching. Course 2020-21" prepared by the "Commission for Teaching Planning", we describe below the contingency plan, referred to the teaching methodology and evaluation system sections foreseen for scenarios 2 and 3)
Teaching methodology
Scenario 2 (distancing)
Partially virtual teaching, according to the distribution organized by the Faculty of Biology, with aids of virtual course. If it is not possible to maintain the required interpersonal distance, computer practices will be taught virtually. Students will perform continuous assessment tasks through the virtual course, as described in the corresponding section. The tutorials will be attended by email or through MS TEAMS.
Scenario 3 (closure)
Completely remote teaching through the virtual course of the subject. Virtual computer practices. Students will perform continuous assessment tasks through the virtual course, as described in the corresponding section. Tutoring by email or MS TEAMS.
Learning assessment system
Scenarios 2 (distancing) and 3 (closing)
The procedure will be the same as that just explained with the difference that the scheduled tests will be telematic.
Maria Del Pilar Mato Eiroa
Coordinador/a- Department
- Applied Mathematics
- Area
- Applied Mathematics
- Phone
- 881813181
- mdelpilar.mato [at] usc.es
- Category
- Professor: University Lecturer
Rodrigo Lopez Pouso
- Department
- Statistics, Mathematical Analysis and Optimisation
- Area
- Mathematical Analysis
- Phone
- 881813166
- rodrigo.lopez [at] usc.es
- Category
- Professor: University Lecturer
Daniel Cao Labora
- Department
- Statistics, Mathematical Analysis and Optimisation
- Area
- Mathematical Analysis
- Phone
- 881813174
- daniel.cao [at] usc.es
- Category
- Professor: Temporary supply professor to reduce teaching hours
Jorge Rodríguez López
- Department
- Statistics, Mathematical Analysis and Optimisation
- Area
- Mathematical Analysis
- jorgerodriguez.lopez [at] usc.es
- Category
- Professor: LOU (Organic Law for Universities) PhD Assistant Professor
| Monday | |||
|---|---|---|---|
| 12:00-14:00 | Grupo /TI-ECTS01 | Spanish | Main Hall Santiago Ramón y Cajal |
| 18:00-19:00 | Grupo /CLE_02 | Spanish, Galician | Virtual classroom |
| 19:00-20:00 | Grupo /CLE_01 | Spanish, Galician | Virtual classroom |
| Tuesday | |||
| 18:00-19:00 | Grupo /CLE_02 | Galician, Spanish | Virtual classroom |
| 19:00-20:00 | Grupo /CLE_01 | Galician, Spanish | Virtual classroom |
| Thursday | |||
| 18:00-19:00 | Grupo /CLE_01 | Galician, Spanish | Virtual classroom |
| 18:00-19:00 | Grupo /CLE_02 | Galician, Spanish | Virtual classroom |
| 01.25.2021 16:00-20:00 | Grupo /CLE_01 | Classroom 01. Charles Darwin |
| 01.25.2021 16:00-20:00 | Grupo /CLE_02 | Classroom 01. Charles Darwin |
| 01.25.2021 16:00-20:00 | Grupo /CLE_01 | Classroom 02. Gregor Mendel |
| 01.25.2021 16:00-20:00 | Grupo /CLE_02 | Classroom 02. Gregor Mendel |
| 01.25.2021 16:00-20:00 | Grupo /CLE_01 | Classroom 03. Carl Linnaeus |
| 01.25.2021 16:00-20:00 | Grupo /CLE_02 | Classroom 03. Carl Linnaeus |
| 01.25.2021 16:00-20:00 | Grupo /CLE_01 | Classroom 04: James Watson and Francis Crick |
| 01.25.2021 16:00-20:00 | Grupo /CLE_02 | Classroom 04: James Watson and Francis Crick |
| 07.05.2021 16:00-20:00 | Grupo /CLE_01 | Classroom 04: James Watson and Francis Crick |
| 07.05.2021 16:00-20:00 | Grupo /CLE_02 | Classroom 04: James Watson and Francis Crick |
| 07.05.2021 16:00-20:00 | Grupo /CLE_01 | Main Hall Santiago Ramón y Cajal |
| 07.05.2021 16:00-20:00 | Grupo /CLE_02 | Main Hall Santiago Ramón y Cajal |