Identifying Data 2019/20
Subject (*) Mathematics Code 610G02003
Study programme
Grao en Bioloxía
Descriptors Cycle Period Year Type Credits
Graduate 1st four-month period
 First Basic training 6
Language
Spanish
Teaching method Face-to-face
Prerequisites
Department Matemáticas
Coordinador
Ferreiro Ferreiro, Ana María
 E-mail
ana.fferreiro@udc.es
Lecturers
Ferreiro Ferreiro, Ana María
García Rodríguez, José Antonio
Otero Verea, Jose Luis
Prieto Aneiros, Andrés
 E-mail
ana.fferreiro@udc.es
jose.garcia.rodriguez@udc.es
luis.verea@udc.es
andres.prieto@udc.es
Web
General description Esta asignatura pretende a adquisición de competencias que permitan ao alumnado desenvolver un coñecemento crítico do cáculo diferencial e integral, asi como realizar unha pequena introdución ao alxebra lineal e ás ecuacións diferenciais.

Study programme competencies
Code Study programme competences
A21 Deseñar modelos de procesos biolóxicos.
B1 Aprender a aprender.
B2 Resolver problemas de forma efectiva.
B3 Aplicar un pensamento crítico, lóxico e creativo.
B4 Traballar de forma autónoma con iniciativa.
B5 Traballar en colaboración.
B6 Organizar e planificar o traballo.
B7 Comunicarse de maneira efectiva nunha contorna de traballo.
B8 Sintetizar a información.
B9 Formarse unha opinión propia.
B10 Exercer a crítica científica.
B12 Adaptarse a novas situacións.
B13 Comportarse con ética e responsabilidade social como cidadán e como profesional.

Learning aims
Learning outcomes Study programme competences
Integration and applications A21
 B1
B2
B3
B4
B5
B6
B7
B8
B9
B10
B12
B13
Differentiation and applications A21
 B1
B2
B3
B4
B5
B6
B7
B8
B9
B10
B12
B13
Linear algebra and applications A21
 B1
B2
B3
B4
B5
B6
B7
B8
B9
B10
B12
B13
Differential equations and applications A21
 B1
B2
B3
B4
B5
B6
B7
B8
B9
B10
B12
B13

Contents
Topic Sub-topic
• Differentiation o Basic Rules of Differentiation.
o The Chain Rule.
o Differentiation Techniques.
o L'Hôpital's Rule. Taylor's Theorem.
o Applications of Differentiation.
o Maxima and Minima.
o Optimization Problems.
o The Newton-Raphson Method.
• Integration o Integration as Summation.
o Fundamental Theorem of Calculus.
o Some Basic Integrals.
o Integration by Substitution.
o Integration by Parts.
o Integration of Rational Functions.
o Geometrical Applications of Integration.
o Numerical Integration. Simpson's Rule.
o Improper Integrals.
• Linear Algebra o Systems of Linear Equations
o Elementary operations.
o The Algebra of Matrices.
o Determinants. Basic properties.
o The determinant rank.
o Eigenvalues and Eigenvectors.
o Normal forms for matrices.
o Cayley-Halmiton theorem.
• Differential Equations and Applications o First-order Differential Equations.
o Separable First-order Differential Equations.
o Linear First-order Differential Equations.
o Applications of First-order Differential Equations.
o Second-order Linear Differential Equations with Constant Coefficients.
o Homogeneous Linear Systems with Constant Coefficients.

Planning
Methodologies / tests Competencies Ordinary class hours Student’s personal work hours Total hours
Guest lecture / keynote speech A21 B2 B3 B6 B13 32 64 96
Problem solving A21 B1 B2 B3 B4 B5 B6 B7 B8 B9 B10 B12 8 18 26
Supervised projects A21 B1 B2 B3 B8 B9 B10 B12 B13 8 16 24
Objective test B1 B2 B3 B4 B8 B9 B10 B13 3 0 3
 
Personalized attention 1 0 1
 
(*)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 Concept development and problem solving.
Problem solving A variety of problems (from textbooks and exams of past academic years) will be periodically made available to students on different topics of this course. The students will have to solve them to acquire the required skills to pass this course.
Supervised projects Working on topics proposed by the teacher, a theoretical summary will be presented along with a collection of problems resolved on the corresponding topic.
Objective test Mathematical solution of questions and problems related to the topics of this course.

Personalized attention
Methodologies
Guest lecture / keynote speech
Supervised projects
Problem solving
Description
The personalized attention (described in relation to these methodologies) is planned by means of face-to-face meetings between the students and the teachers, which require an active participation of the students.

The course of these personalized activities will be indicated specifically for each type of academic activity, and they will be fixed in the semester schedule.

The personalized attention for those students with a recognized part-time enrollment, will consist in the solution of exercises (from textbooks and exams of other academic years), which will be periodically available according to the schedule of this course.

Assessment
Methodologies Competencies Description Qualification
Guest lecture / keynote speech A21 B2 B3 B6 B13 Questions to the students. 10
Supervised projects A21 B1 B2 B3 B8 B9 B10 B12 B13 Development of specific aspects with examples and solved problems. Competence B3 will be assessed. 10
Problem solving A21 B1 B2 B3 B4 B5 B6 B7 B8 B9 B10 B12 Delivery of exercises and solved exams. Competences A21 and B2 will be assessed. 10
Objective test B1 B2 B3 B4 B8 B9 B10 B13 Desenvolvemento de cuestións e resolución de problemas da materia 70
 
Assessment comments

To pass this course it will be necessary to obtain (after adding the qualifications of all the activities) a minimum mark of 50% of the total. To obtain the mark "not presented", it will be sufficient that the students do not participate in the objective test and have not been evaluated in more than 50% of the problem solving and supervised works. To pass the course in the second opportunity, either the above criterion is fullfiled or a mark higher than 50% in the objective test is obtained. Final marks are not kept from succesive academic years. However, it is possible to keep the marks of the supervised works of the
previous academic year, if the teacher agrees to this, having the
student previously demanded it..

The students which are part-time enrolled (and so they are granted with an attendance exemption), can be evaluated in a personalised way regarding the methodologies of the lectures, problem solving and supervised works. For those students which are part-time enrolled, it is compulsory to make the objective test, as well as the partial test along the course. For the first and second opportunity the criteria of evaluation for these students is the same as the criterion for full-time enrolled students (where the percentage of dispenses of assistance will be of 80%).

The objective test is equal for all the students.

The priority for obtaining qualifications "with honours", will be for the students that achieve this mark in the first opportunity.

Sources of information
Basic LARSON (2006). CALCULO. McGrawHill

Complementary Finney (). Cálculo. Addison-Wesley
Bradley (). Cálculo. Prentice Hall
Alfonsa García (). Cálculo I. CLGSA
Rogawski (2014). Cálculo, una variable. Editorial Reverté
Salas / Hille / Etgen (). Cálculus. Reverté
NEUHAUSER (2004 ). MATEMÁTICAS PARA CIENCIAS . Pearson


Recommendations
Subjects that it is recommended to have taken before

Subjects that are recommended to be taken simultaneously

Subjects that continue the syllabus

Other comments

It is convenient to have studied a mathemathics course in the last academic year at high school. For those students who have not, the nivelation course offered by the Faculty of Science is strongly recommended. 


(*)The teaching guide is the document in which the URV publishes the information about all its courses. It is a public document and cannot be modified. Only in exceptional cases can it be revised by the competent agent or duly revised so that it is in line with current legislation.