| 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 | ||
| O estudo, representación e interpretación de funcións elementais de unha e varias variables. | A15 A16 A20 A24 A25 A27 |
B1 B2 B3 B6 |
C1 C3 C6 |
| Utilizar con destreza as técnicas de cálculo de primitivas e as súas aplicacións. | A20 A24 A25 A27 |
B1 B2 B3 B6 |
C1 C3 C6 |
| Resolver sistemas de ecuacions lineais e operar con cálculo matricial | A20 A24 A25 A27 |
B1 B2 B3 B6 |
C1 C3 C6 |
| Plantexar e resolver modelos sinxelos que conleven ecuacións e sistemas de ecuacións diferenciais. | 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. |
| • 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 | A15 A16 A24 A25 B1 B2 B3 C1 C3 C6 | 32 | 64 | 96 |
| Problem solving | A15 A20 B1 B2 B3 | 8 | 18 | 26 |
| Supervised projects | A15 A27 B2 B3 B6 | 8 | 16 | 24 |
| Multiple-choice questions | B2 B3 | 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 se poñen 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 |
|
|
| Assessment | |||
| Methodologies | Competencies | Description | Qualification |
| Guest lecture / keynote speech | A15 A16 A24 A25 B1 B2 B3 C1 C3 C6 | Questions to the students. | 10 |
| Multiple-choice questions | B2 B3 | 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 | A15 A27 B2 B3 B6 | Development of specific aspects with examples and solved problems. Competence B3 will be assessed. | 10 |
| Problem solving | A15 A20 B1 B2 B3 | 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 To get a NO SHOW mark, the student will not be able to attend the final multiple-choice questions exam. The Regarding 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 |
Bradley (). Cálculo. Prentice Hall
Finney (). Cálculo. Addison-Wesley
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 | |
|
É conveniente ter coñecementos de matemáticas de 2 bacharelerato, si non os ten recomendase facer o curso de nivelación. |