ECTS credits ECTS credits: 4.5
ECTS Hours Rules/Memories Student's work ECTS: 74.25 Hours of tutorials: 2.25 Expository Class: 18 Interactive Classroom: 18 Total: 112.5
Use languages Spanish, Galician
Type: Ordinary Degree Subject RD 1393/2007 - 822/2021
Departments: Mathematics
Areas: Geometry and Topology
Center Faculty of Pharmacy
Call: First Semester
Teaching: Sin docencia (Extinguida)
Enrolment: No Matriculable | 1st year (Yes)
- To teach to use the necessary mathematical tools (derivatives, integrals and differential equations of first order and first grade) to study the various disciplines that make up the Degree of Pharmacy, to enable them to solve simple mathematical problems arising in different contexts (Biology, Chemistry, Physics, Pharmacokinetics, ...)
- To provide the background needed (Descriptive Statistics and Data Analysis, Probability Theory, Random Variables and Probability Distributions) to make them accessible to basic statistical methods commonly used today in pharmaceutical research.
- To initiate the student in the use of mathematical software.
CHAPTER 1: DIFFERENTIATION
1.1 Introduction. The derivative (geometric and physical interpretation), Leibniz notation. Computing derivatives
1.2 Graphing
1.3 Optimization: Maxima and minima problems
CHAPTER 2: INTEGRATION
2.1 Area problem
2.2 Definite integrals, properties
2.3 Indefinite Integrals. Fundamental theorem of calculus
2.4 Mean value of a function
2.5 Improper Integrals
CHAPTER 3: DIFFERENTIAL EQUATIONS
3.1 Differential Equations: concept. General solution and initial conditions
3.2 Differential equations in separate variables
3.3 Linear Differential Equations
3.4 Applications of differential equations: Newton's law of cooling. Radioactive decay. Applications to population models. Applications to different models in the administration of medicines
CHAPTER 4: DESCRIPTIVE STATISTICS
4.1 Definition and objectives of Statistics. The statistics in pharmaceutical research
4.2 Design of the study, population and sample
4.3 Types of data. Presentation of data, frequency tables
4.4 Characteristic measures of a distribution (of central tendency, position, dispersion and shape)
4.5 Graphical representations of data: stem and leaf diagrams, bar charts, histograms, box plots
CHAPTER 5: PROBABILITY
5.1 Introduction and interpretation of probabilities
5.2 Experiment random. Sample space. Events
5.3 Definition and properties of probability
5.4 Conditional probability. Independent Events
5.5 Theorem of total probabilities and Bayes rule
CHAPTER 6: RANDOM VARIABLES AND PROBABILITY DISTRIBUTIONS
6.1 Concept of random variable. Classes of random variables
6.2 Discrete probability distributions: Probability mass function. Distribution function. Mean.Variance
6.3 Binomial Distribution
6.4 Poisson Distribution
6.5 Continuous Probability Distributions: Density Function. Distribution function.Mean. Variance
6.6 Normal distribution. Tipification of a variable. Normal Approximation of a Binomial variable
6.7 Distributions associated with the Normal: the distribution “ t of Student”, “Pearson chi-square” distribution,” F of Fisher-Snedecor” distribution.
– Cao Abad R., Francisco Fernández M., y otros, “Introducción a la estadística y sus aplicaciones” Ed. Pirámide (Grupo Anaya, S. A.), Madrid, 2001.
– Larson, Hostetler, Edwards, “Cálculo con geometría analítica. Volumen I” Octava edición. McGrw–Hill Interamericana, Madrid, 2006.
– Milton, J.S.,“Estadística para Biología y Ciencias de la Salud” Tercera edición. McGraw-Hill Interamericana, Madrid, 2001.
– Murray R. Spiegel, “Ecuaciones diferenciales aplicadas” Ed. Dossat S. A., Madrid, 1983.
– James Stewart, “Cálculo: Conceptos y contextos” Internacional Thompson Ed., 1999.
– Valderrama Bonnet, M. J., “Métodos matemáticos aplicados a las Ciencias Experimentales” Ediciones Pirámide S. A., Madrid, 1989.
Competences to be achieved by the student with the subject:
- Transversal competences:
(CI01) Analysis and synthesis capacity
(CI07) Basic Computer Skills
(CI08) Information management skills (ability to search and analyze information from diverse sources)
(CI09) Troubleshooting
(CI10) Decision making
(CP01) Critical and self-critical capacity
(CP02) Teamwork
(CS01) Ability to apply knowledge in practice
(CS03) Ability to learn
- Specific competences:
(FM01) Apply mathematics knowledge to the pharmaceutical sciences
(FM02) Apply computational techniques and data processing, in relation to information regarding physical, chemical and biological data
(FM04) Evaluate scientific data related to medicines and health products
(FM05) Use statistical analysis applied to the pharmaceutical sciences
Since the course is essentially practical, emphasis will be put on developing the contents with simplicity without sacrificing accuracy.
- Magisterial lectures in large groups: In each class a time will be devoted to the introduction or illustration of some theoretical question, and the rest to the resolution of problems and exercises related to that issue.
- Interactive lectures in a small group: Some problems will be proposed to the students, corresponding to the contents of each one of the agenda items. The student will try, with the help of what worked in the previous section, solve them, or if necessary, solve them in the classroom, with their active participation. These lectures will be compulsary.
- Interactive computer classes in small group: To solve practical cases the student will learn to use MAPLE program that will facilitate the calculations and the study of various graphical representations of functions. Data entry and coding (practical cases with EXCEL). These lectures will be compulsary.
- The tutorials in small groups will be devoted, individually or in groups, to solve the particular doubts as they arise, and individual monitoring of each student.
The mark of each student will be obtained through continuous assessment and final exams set in the calendar of the Faculty. The examination will consist of problem solving.
Continuous assessment will be made by checking written controls, participation of students in the classroom and tutorial.
The mark of the student will be the sum of the 80% of the final exam mark and the 20% of the the continuous assessment.
WORK IN THE CLASSROOM
Magisterial lectures in big group 23
Interactive lectures in small group 11
Computer practises with small group 6
Tutoring in small groups or individualized 5
Total hours of classroom work 45
PERSONAL WORK STUDENT
Individual study or in group 45
Writing exercises, conclusions or other work 16,5
Computer practises 6
Total working hours of the student 67,5
The course devotes a lot of time to solving exercises. Obviously, it is considered a fundamental aspect in the learning of the subject, so that it is recommended:
- Try to solve the problems of the exercise sheets
- Use the literature to consolidate the knowledge and techniques for solving the problems given in the exercise sheets
- Going to the tutorials to be able to solve any doubts that arise along the course.
– To use the web site virtual of the USC to accede to the didactical material.
Jose Manuel Carballes Vazquez
Coordinador/a- Department
- Mathematics
- Area
- Geometry and Topology
- Phone
- 881813146
- xm.carballes [at] usc.es
- Category
- Professor: University Lecturer
Juan Francisco Torres Lopera
- Department
- Mathematics
- Area
- Geometry and Topology
- Phone
- 881813137
- juanfrancisco.torres [at] usc.es
- Category
- Professor: University Lecturer
Modesto Ramon Salgado Seco
- Department
- Mathematics
- Area
- Geometry and Topology
- Phone
- 881813154
- modesto.salgado [at] usc.es
- Category
- Professor: University Lecturer
Victor Sanmartin Lopez
- Department
- Mathematics
- Area
- Geometry and Topology
- victor.sanmartin [at] usc.es
- Category
- Professor: LOU (Organic Law for Universities) PhD Assistant Professor
Diego Mojon Alvarez
- Department
- Mathematics
- Area
- Geometry and Topology
- diego.mojon.alvarez [at] usc.es
- Category
- Ministry Pre-doctoral Contract
Angel Cidre Diaz
- Department
- Mathematics
- Area
- Geometry and Topology
- angel.cidre.diaz [at] usc.es
- Category
- Ministry Pre-doctoral Contract
| Monday | |||
|---|---|---|---|
| 12:00-13:00 | Grupo A /CLE_01 | Spanish | 5035 Plant Physiology Classroom |
| Tuesday | |||
| 12:00-13:00 | Grupo A /CLE_01 | Spanish | 5035 Plant Physiology Classroom |
| Wednesday | |||
| 12:00-13:00 | Grupo A /CLE_01 | Spanish | 5035 Plant Physiology Classroom |
| Thursday | |||
| 12:00-13:00 | Grupo A /CLE_01 | Spanish | 5035 Plant Physiology Classroom |
| Friday | |||
| 12:00-13:00 | Grupo A /CLE_01 | Spanish | 5035 Plant Physiology Classroom |