Identifying Data 2020/21
Subject (*) Mathematics 1 Code 610G01001
Study programme
Grao en Química
Descriptors Cycle Period Year Type Credits
Graduate 1st four-month period
 First Basic training 6
Language
Spanish
English
Teaching method Hybrid
Prerequisites
Department Matemáticas
Coordinador
Otero Verea, Jose Luis
 E-mail
luis.verea@udc.es
Lecturers
García Rodríguez, José Antonio
Otero Verea, Jose Luis
Suarez Taboada, Maria
 E-mail
jose.garcia.rodriguez@udc.es
luis.verea@udc.es
maria.suarez3@udc.es
Web
General description Esta asignatura pretende o desenrolo de competencias que permitan ao alumnado obter un coñecemento crítico do calculo diferencial e integral así como unha pequena introducción ao alxebra lineal e as ecuacions diferenciais.
Contingency plan MODALIDADE NON PRESENCIAL

1. Modificacións dos contidos.
Non se farán cambios.

2. Metodoloxías
* Metodoloxías de ensino que se manteñen
Traballos tutelados
Atención personalizada

* Cambio de metodoloxías de ensino

Sesión maxistral: a asistencia presencial substitúese por material (PDF, vídeos explicativos) dispoñibles en moodle.udc.es e videoconferencia pola plataforma Teams.

Resolución de problemas: computa na avaliación. A asistencia substitúese por material (PDF, vídeos explicativos) dispoñibles en moodle.udc.es e videoconferencia en grupo nos ordenadores

Proba de elección múltiple: computa na avaliación. Realizaranse os seguintes cambios:
(a) As probas relacionadas coa parte práctica de Matemáticas realizaranse mediante probas en liña en moodle.udc.es
(b) As probas relacionadas coa parte teórica da materia faranse mediante probas en liña en moodle.udc.es

3. Mecanismos de atención personalizada aos estudantes.
Correo electrónico: todos os días para facer consultas, solicitar reunións virtuais para responder a preguntas e facer un seguimento do traballo supervisado.
Moodle: diariamente, segundo as necesidades dos estudantes. Teñen foros temáticos asociados aos módulos da materia, para formular as consultas necesarias.
Equipos: unha sesión semanal en grupos grandes para avanzar no contido teórico e as tarefas supervisadas no momento asignado á materia no calendario de aulas do profesorado. Tamén pode haber sesións semanais ou como o soliciten os estudantes en pequenos grupos, para o seguimento e apoio para facer un traballo supervisado. Esta dinámica permite un seguimento normalizado e axustado das necesidades de aprendizaxe do alumno para desenvolver o traballo da materia.

4. Modificacións na avaliación.

Proba de resposta múltiple: 30%.
As outras metodoloxías: 70%

* Comentarios de avaliación:

1. Asistir e participar regularmente nas actividades da clase.

2. Enviar un traballo supervisado na data indicada.

3. Obter unha nota mínima do 50% do total.

4. A oportunidade de xullo estará suxeita aos mesmos criterios que a oportunidade de xuño.

5. Modificacións da bibliografía ou webografía.
Non se farán cambios. Xa teñen dixitalizado en Moodle todos os materiais de traballo.

Study programme competencies
Code Study programme competences
A15 Ability to recognise and analyse new problems and develop solution strategies
A16 Ability to source, assess and apply technical bibliographical information and data relating to chemistry
A20 Ability to interpret data resulting from laboratory observation and measurement
A24 Ability to explain chemical processes and phenomena clearly and simply
A25 Ability to recognise and analyse link between chemistry and other disciplines, and presence of chemical processes in everyday life
A27 Ability to teach chemistry and related subjects at different academic levels
B1 Learning to learn
B2 Effective problem solving
B3 Application of logical, critical, creative thinking
B6 Ethical, responsible, civic-minded professionalism
C1 Ability to express oneself accurately in the official languages of Galicia (oral and in written)
C3 Ability to use basic information and communications technology (ICT) tools for professional purposes and learning throughout life
C6 Ability to assess critically the knowledge, technology and information available for problem solving

Learning aims
Learning outcomes Study programme competences
The study, representation and interpretation of elementary functions of one and several variables A15
 B2
B3
 C6
Skillful use of primitive calculation techniques and their applications A15
 B2
B3
 C6
Solve systems of linear equations and operate with matrix calculus A15
 B2
B3
 C6
State and solve simple models involving equations and systems of differential equations. A15
A16
A20
A24
A25
A27
 B1
B2
B3
B6
 C1
C3
C6

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.

Integración numérica: método de Simpson.
Integrales impropias.
• 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.
• 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.

Planning
Methodologies / tests Competencies Ordinary class hours Student’s personal work hours Total hours
Guest lecture / keynote speech A15 B3 B2 C6 32 64 96
Problem solving A15 B2 B3 C6 8 18 26
Supervised projects A15 B2 B3 C6 8 16 24
Multiple-choice questions A15 A16 A20 A24 A25 A27 B1 B2 B3 B6 C1 C3 C6 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

Contingency plan (by mor do Covid19):
Teams: in weekly sessions in the time slot assigned to the subject in the faculty classroom calendar.
Problem solving Questionnaires, bulletins and exams of other courses that will be periodically made available to students on different content and that students will have to solve.

Contingency plan (by mor do Covid19):
Teams: in weekly sessions in the time slot assigned to the subject for a small group in the faculty classroom calendar.
Supervised projects Work on topics proposed by the teacher, a theoretical summary will be presented along with a bulletin of problems solved on the corresponding topic

Contingency plan (by mor do Covid19):
Teams: in weekly sessions in the time slot assigned to the subject for a small group in the faculty classroom calendar.
Multiple-choice questions Multiple choice test

Contingency plan (by mor do Covid19):
The test will be carried out via Moodle and Teams.

Personalized attention
Methodologies
Supervised projects
Description
The personalized attention described in relation to these methodologies is conceived as face-to-face moments of work for the students with the teacher, for which they imply a participation for the students; the form and the moment in which it will be carried out will be indicated in relation to each activity throughout the course according to the work plan of the subject.
The specific personalized attention measures for or "Students with recognition of part-time dedication and academic exemption from attendance exemption" for the study of the subject, will be delivery of questionnaires, bulletins and exams of other courses that will be periodically made available to the students about different contents and that the student will have to solve.

Contingency plan (by mor do Covid19)
–Email: Daily. Of use to make consultations, request virtual meetings to resolve doubts and follow up on supervised work.
–Moodle: Daily to formulate the necessary queries.
–Teams: weekly sessions in the time slot assigned to the subject in the faculty classroom calendar.


Assessment
Methodologies Competencies Description Qualification
Multiple-choice questions A15 A16 A20 A24 A25 A27 B1 B2 B3 B6 C1 C3 C6 Multiple-choice questions 60
Problem solving A15 B2 B3 C6 Delivery of exercises and solved exams. Competences A15, B2 and C3 will be assessed. 20
Supervised projects A15 B2 B3 C6 Development of specific aspects with examples and solved problems. Competence B3 will be assessed. 10
Guest lecture / keynote speech A15 B3 B2 C6 Questions to the students. 10
 
Assessment comments

To pass the course, it will be necessary to obtain, added the marks of all the activities, a minimum grade of 50% of the total. To obtain the grade of not presented, it will be sufficient that the student does not participate in the multiple-choice test and has not been evaluated in the supervised Works in more than 50%. In the second chance test, the criterion to pass the subject will be the previous one or to obtain a grade of not less than 50% in the multiple choice test. With regard to successive academic courses, the teaching-learning process, including assessment, refers to one academic course, and therefore a new course would be restarted, including all assessment activities and procedures that were scheduled for that course; however, it is allowed to request to maintain the practical qualification of a previous course.

Students enrolled in part-time regime and academic exemption from attendance exemption, can be evaluated in a personalized way regarding the methodologies of Maxistral Session, Problem Solving and Tutored Jobs. Students enrolled in part-time regimen are required to sit the multiple-choice test, as well as the partial tests throughout the course. For the first and second opportunity, the evaluation criteria for this student body is the same as for the others and the attendance waiver percentage will be 80%.

Students at the first opportunity have priority in the granting of honors.

Contingency plan (Covid19):

If the multiple-choice test is not face-to-face, it will have a percentage of 30% and the other methodologies 70%

They have priority in the granting of matrícula of honour the students at the earliest opportunity.

Sources of information
Basic LARSON (2006). CALCULO. McGrawHill
W. Keith Nicholson (2019). Linear Algebra with Applications. Lyryx Learning Team

Complementary Finney (). Cálculo. Addison-Wesley
Bradley (). Cálculo. Prentice Hall
Alfonsa García (). Cálculo I. CLGSA
Rogawski (2014). Cálculo, una variable. 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 recommend 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.