Identifying Data 2015/16
Subject (*) Matemáticas 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
Otero Verea, Jose Luis
Ferreiro Ferreiro, Ana María
 E-mail
luis.verea@udc.es
ana.fferreiro@udc.es
Lecturers
Calvo Garrido, María Del Carmen
Ferreiro Ferreiro, Ana María
García Rodríguez, José Antonio
Otero Verea, Jose Luis
Prieto Aneiros, Andrés
 E-mail
carmen.calvo.garrido@udc.es
ana.fferreiro@udc.es
jose.garcia.rodriguez@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
derivación e aplicacions da derivada A21
 B1
B2
B3
B4
B5
B6
B7
B8
B9
B10
B12
B13
integración e aplicacions da integral 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
Multiple-choice questions 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
Multiple-choice questions proba orientada a evaluación dos contidos teóricos que se traballan nas sesions maxistrales

Personalized attention
Methodologies
Guest lecture / keynote speech
Supervised projects
Problem solving
Description
A atención personalizada que se decribe en relación a estas metodoloxías concibense como momentos de traballo presencial para o alumnado co profesor, po lo que implican unha participación obligatoria para o alumando.

A forma e o momento en que se desarrollará indicarase en relacción a cada actividad ao largo do curso según o plan de traballo da asignatura


Assessment
Methodologies Competencies Description Qualification
Guest lecture / keynote speech A21 B2 B3 B6 B13 Questions to the students. 10
Multiple-choice questions B1 B2 B3 B4 B8 B9 B10 B13 Test with 20 questions about Mathmatics and 10 about Statistics, with 4 options, and for each 3 failed answers one correct answer will be eliminated. Competencie C6 will be assessed. 70
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
 
Assessment comments

To pass the subject it is compulsory to obtain a final mark, after
adding all the activities marks, at least 50% of the total
qualification.

To get a NO SHOW mark, the student will not be able to attend the final multiple-choice questions exam.

The
guideline to pass the subject in July is the previous one, or to get a
mark in the final multiple-choice exam not lower than 50%.

Regarding
following academic years, the teaching guides management, including the
assessment, refers only to the ongoing academic year. Therefore, all
the activities and assessment methodologies scheduled and planned for
the following year will start from zero.

Supervised projects and problem solving of part-time students will be assessed in a personalized way.

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

É conveniente ter coñecementos de matemáticas de 2 bacharelerato, si non os ten  recomendase facer o curso de 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.