ECTS credits ECTS credits: 6
ECTS Hours Rules/Memories Total: 0
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 (Extinguida)
Enrolment: No Matriculable | 1st year (Yes)
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 (36 hours + 8 hours)
LECTURE 1. DISCRET BIOLOGICAL MODELS WITH MATRICES (6 hours)
Matrices and matrix calculus. Eigenvalues and eigenvectors of a matrix. Age-structured population in discrete time: Leslie-Lewis matrix.
LECTURE 2. 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.
LECTURE 3. BIOLOGICAL MODELS WITH DIFFERENTIAL EQUATIONS (ODEs), OR SYSTEMS OF DIFFERENTIAL EQUATIONS (SODEs) (18 hours)
From the rate of change as a hypothesis to the differential equation: introduction to the modeling of a biological process by ODEs. Solving ODEs. Biological models with EDOs: Malthus's law, logistic equation and Von Bertalanffy equation. Biological models with SEDOs: compartmental models. Biological models with non linear SODEs: the Lotka-Volterra predator-prey model.
INTERACTIVE CLASSES IN COMPUTER ROOM (9 hours)
- Computer practices:
PRACTICE 1 (2 hours): Introduction to mathematical software environment MATLAB. Matrix calculus; matrix eigenvalues and eigenvectors.
PRACTICE 2 (1 hour): Elementary mathematical functions and graphical representations.
PRACTICE 3 (1 hour): Introduction to symbolic calculation with SageMath. Derivatives and integrals.
PRACTICE 4 (2 hours): Solving ODEs, or SODEs, with MATLAB.
- 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
Neuhauser, C., 2004. Matemáticas para Ciencias. 2ª ed. Madrid: Pearson Prentice Hall.
Pérez López, C., 2011. MATLAB a través de ejemplos. Madrid: Ibergaceta.
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.
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.
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.
- A VIRTUAL CLASSROOM will be operational on the MOODLE platform, available to students.
- Direct communication channels with teachers by e-mail and MS-TEAMS.
Begoña Nicolas Avila
- Department
- Applied Mathematics
- Area
- Applied Mathematics
- bego.nicolas [at] usc.es
- Category
- Professor: Temporary supply professor for IT and others
Érika Diz Pita
Coordinador/a- Department
- Statistics, Mathematical Analysis and Optimisation
- Area
- Mathematical Analysis
- Phone
- 881813202
- erikadiz.pita [at] usc.es
- Category
- Professor: LOU (Organic Law for Universities) PhD Assistant Professor
| Monday | |||
|---|---|---|---|
| 18:00-19:00 | Grupo /CLE_01 | Spanish | Classroom 03. Carl Linnaeus |
| 19:00-20:00 | Grupo /CLE_02 | Spanish | Classroom 04: James Watson and Francis Crick |
| Tuesday | |||
| 18:00-19:00 | Grupo /CLE_01 | Spanish | Classroom 03. Carl Linnaeus |
| 19:00-20:00 | Grupo /CLE_02 | Spanish | Classroom 04: James Watson and Francis Crick |
| Thursday | |||
| 18:00-19:00 | Grupo /CLE_01 | Spanish | Classroom 03. Carl Linnaeus |
| 18:00-19:00 | Grupo /CLE_02 | Spanish | Classroom 04: James Watson and Francis Crick |
| 01.08.2024 16:00-20:00 | Grupo /CLE_02 | Classroom 01. Charles Darwin |
| 01.08.2024 16:00-20:00 | Grupo /CLE_01 | Classroom 01. Charles Darwin |
| 01.08.2024 16:00-20:00 | Grupo /CLE_01 | Classroom 02. Gregor Mendel |
| 01.08.2024 16:00-20:00 | Grupo /CLE_02 | Classroom 02. Gregor Mendel |
| 01.08.2024 16:00-20:00 | Grupo /CLE_02 | Classroom 03. Carl Linnaeus |
| 01.08.2024 16:00-20:00 | Grupo /CLE_01 | Classroom 03. Carl Linnaeus |
| 06.19.2024 16:00-20:00 | Grupo /CLE_01 | Classroom 01. Charles Darwin |
| 06.19.2024 16:00-20:00 | Grupo /CLE_02 | Classroom 01. Charles Darwin |
| 06.19.2024 16:00-20:00 | Grupo /CLE_02 | Classroom 02. Gregor Mendel |
| 06.19.2024 16:00-20:00 | Grupo /CLE_01 | Classroom 02. Gregor Mendel |