Identifying Data 2017/18
Subject (*) Mathematics Code 610G02003
Study programme
Grao en Bioloxía
Descriptors Cycle Period Year Type Credits
Graduate 1st four-month period
 First FB 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
Otero Verea, Jose Luis
Prieto Aneiros, Andrés
 E-mail
ana.fferreiro@udc.es
luis.verea@udc.es
andres.prieto@udc.es
Web
General description esta asignatura pretende o desarrollo de competencias que permitan ao alumnado desarrollar un conocemento crítico do cáculo diferencial e integral asi como unha pequena introducción ao alxebra lineal e as ecuacios 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
integración e aplicacions da integral A21
 B1
B2
B3
B4
B5
B6
B7
B8
B9
B10
B12
B13
derivación e aplicacions da derivada A21
 B1
B2
B3
B4
B5
B6
B7
B8
B9
B10
B12
B13
álxebra lineal e aplicacions A21
 B1
B2
B3
B4
B5
B6
B7
B8
B9
B10
B12
B13
ecuacions diferenciais e aplicacions 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 Techniques Differentiation.
o L'Hôpital's Rule. Taylor's Theorem.
o Applications of Differentiation.
o Maxima and Minima.
o Optimisation 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.
• Ordinary Differential Equations. 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 desarrollo dos conceptos e resolución de problemas
Problem solving Cuestionarios, boletins e exámenes de outros cursos que periódicamente ponderanse a disposición dos alumnos sobre distintos contiidos e que o alumno terá que resolver.
Supervised projects Traballo sobre temas propostos por o profesor, presentarase un resumo teórico xunto con un boletín de problemas resoltos acerca do tema correspondente
Objective test Desenvolvemento de cuestios e problemas da materia

Personalized attention
Methodologies
Guest lecture / keynote speech
Supervised projects
Problem solving
Description
The personalised attention that describes in relation to these methodologies conceive like moments of face-to-face work for the student with the professor, by what involve a participation for the student; the form and the moment in that it will develop will indicate in relation to each activity along the course according to the plan of work of the subject.
The measures of specific personalised attention for or student with recognition of dedication part time and dispenses academician of exemption of assistance for the study of the matter, will be delivery of questionnaires, bulletins and examinations of other courses that will put to disposal of the students on distinct contents and that the student will have to resolve.


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 A15, B2 and C3 will be assessed. 10
Objective test B1 B2 B3 B4 B8 B9 B10 B13 desarrollo de cuestios e problemas da materia 70
 
Assessment comments

To surpass the asignatura will be necessary to obtain, added the qualifications of all the activities, a minimum note of 50% of the total. To obtain the qualification of no presented, sera sufficient that the student do not participate in the objective proof and have not been evaluated in the Works tutelados in but of 50%. In the proof of  second opportunity the criterion to surpass the asignatura will be the previous or obtain a no inferior note to 50% in the objective proof. By what refers  to successive academic courses, the process of education-learning, included the evaluation, refers  to an academic course, and therefore  volveria to begin with a new course, included all the activities and procedures of evaluation that went programmed for said course; nevertheless it allows  request keep the qualification of practices of a previous course.

The students enrolled in regimen of partial time and academic exemption from attendance exemption, can be evaluated of personalised way regarding the methodologies of Session maxistral, Solution of problems and Works tutelados. The students enrolled in regimen of partial time is compulsory to present to the objective proof, asi as to the partial proofs along the course. For the first and second  opportunity the criteria of evaluation for this alumnado, is the same that for the others  and the percentage of dispenses of assistance will be of 80%.

The objective Proof is equal for all the students.

They have priority in the granting of matrícula of honour the students at the earliest 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 knowledges of mathematics of 2 bachillerato, if it does not have them recommends  do the course of nivelación. 



(*)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.