Study programme competencies |
Code
|
Study programme competences / results
|
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 / results |
The study, representation and interpretation of elementary functions of univariate and multivariate functions. |
A15 A16 A20 A24 A25 A27
|
B1 B2 B3 B6
|
C1 C3 C6
|
Use skilfully the techniques of calculation of primitive and its applications.
|
A15 A16 A20 A24 A25 A27
|
B1 B2 B3 B6
|
C1 C3 C6
|
Set out and solve simple models that comport equations and systems of differential equations. |
A15 A16 A20 A24 A25 A27
|
B1 B2 B3 B6
|
C1 C3 C6
|
Solve problems of basic statistical methods from the descriptive point of view
|
A15 A16 A20 A24 A25 A27
|
B1 B2 B3 B6
|
C1 C3 C6
|
Contents |
Topic |
Sub-topic |
• Functions of Several Variables. |
o Graphs an Level Curves.
o Polar Coordinates. Cylindrical and Spherical Coordinates.
o Partial Derivatives. Differentiability and Gradient.
o Directional Derivatives. Repeated Partial Derivatives.
o The Chain Rule. The Jacobian Matrix. The Hessian.
o Critical Points. Maxima and Minima.
o Constrained Optimisation. Lagrange Multipliers.
o Least Squares Analysis.
|
• Multiple Integrals. |
o Repeated Integrals. Double Integrals. Triple Integrals.
o Change of Variable in Multiple Integrals.
o Curve Integrals.
o Potential Function.
o Green's Theorem.
o Surface Integrals.
o Stokes' Theorem.
|
• Ordinary Differential Equations. |
o First Order Differential Equations.
o Separable First Order Differential Equations.
o Homogeneous equations.
o Exact First Order Differential Equations.
o Linear First Order Differential Equations.
o Bernoulli Equations.
o Applications of First Order Differential Equations.
o Linear Differential Equations with Constant Coefficients.
o The Method of Undetermined Coefficients.
o Variation of Parameters.
o Linear Systems with Constant Coefficients.
|
Descriptive Statistics |
Univariate Descriptive Statistics
Bivariate Descriptive Statistics
Simple Linear Regression Analysis |
Planning |
Methodologies / tests |
Competencies / Results |
Teaching hours (in-person & virtual) |
Student’s personal work hours |
Total hours |
Guest lecture / keynote speech |
A15 A16 A24 A27 B1 B2 B3 B6 |
32 |
64 |
96 |
Problem solving |
A20 A25 B2 B3 C1 |
8 |
18 |
26 |
Supervised projects |
A15 A20 B3 B1 C1 C3 C6 |
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 |
Explanation of the contents and solution of problem from previous academic years.
|
Problem solving |
Question lists and exams from other courses that will be regularly available about different contents and requested to be solved by the students.
|
Supervised projects |
Supervised projects proposed by the teacher. They must include a theoretical abstract along with a list of solved problems on the corresponding issue.
|
Multiple-choice questions |
Exam guided to assess the knowledge of the theoretical contents explained in the keynote speeches.
|
Personalized attention |
Methodologies
|
Supervised projects |
Guest lecture / keynote speech |
Problem solving |
|
Description |
Personalized attention is designed as work of the student face to face with the teacher, so the student involvement is assumed. The way and moment of these meetings will be designated during the course according to the subject work plan.
|
|
Assessment |
Methodologies
|
Competencies / Results |
Description
|
Qualification
|
Supervised projects |
A15 A20 B3 B1 C1 C3 C6 |
Development of specific aspects with examples and solved problems. Competences A24, A27, B3 and C1 will be assessed. |
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 |
Guest lecture / keynote speech |
A15 A16 A24 A27 B1 B2 B3 B6 |
Questions to the students. |
10 |
Problem solving |
A20 A25 B2 B3 C1 |
Delivery of exercises and solved exams from previous courses. Competences A15, A16, A20, A25, B1, B2, B6 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 supervised projects nor 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
|
|
“Cálculo ”. Larson . Mcgraw-Hill “Cálculo varias variables ”. Jon Rogawski. Editotial Reverté “Ecuaciones diferenciales con aplicaciones de modelado”. Zill. Thomson-Learning. CAO ABAD, R. y otros (2001). Introducción a la estadística y sus aplicaciones. Ed. Pirámide.
MILLER, J.C. Y MILLER, J.N. (2002). Estadística para Química Analítica. Addison-Wesley Iberoamericana. TOMEO PERUCHA V. y UÑA JUÁREZ I. (2003). Lecciones de Estadística Descriptiva. Paraninfo. |
Complementary
|
(). . |
“Cálculo I”. Alfonsa García. CLGSA
“Cálculo II”. Alfonsa García. CLGSA “Problemas de funciones de varias variables ”. Alegre. PPU “Ecuaciones diferenciales”. Rainville. Prentice Hall. “Ecuaciones diferenciales”. Ayres. Mcgraw-Hill “Cálculo ”. Bradley. Prentice Hall “Cálculo ”. Finney. Addison-Wesley “Cálculus ”. Salas / Hille / Etgen. Reverté GARCÍA ÁLVAREZ-COQUE, C. Y RAMIS RAMOS, G. (2001). Quimiometría. Editorial Síntesis GONICK, L. Y SMITH, W. (2001). A estatística ¡en caricaturas! SGAPEIO
MONGAY FERNÁNDEZ, C. (2005). Quimiometría. PUV
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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 would be advisable to have knowledge of Matemáticas 1. As far as the block of Statistics is concerned, it is highly recommended the active involvement in the practicals and seminars. |
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