Mathematics II

At the end of Mathematics II, students are expected to be able to solve qualitative and quantitative problems according to previously developed models, to recognize and analyze new problems and plan strategies to develop them, and to relate mathematics to other disciplines.

1) Integral calculus in one variable and applications. Indefinite integral. Integration methods: change of variable, integration by parts, integration of rational functions. Definite integral. Barrow's rule. Calculation of flat areas and volumes of bodies of revolution. Improper integrals. Introduction to numerical integration in one variable.

2) Integral calculus of functions of several variables and applications.
a) Double integral on a rectangle. Properties. Iterated integration. Fubini's theorem. Double integral over more general sets.
b) Triple integral.
c) Introduction to polar, cylindrical and spherical coordinates.
d) Change of variable in double and triple integrals to polar, cylindrical and spherical coordinates.
e) Some applications of the multiple integration.

3) Differential equations and their application to the modeling of chemical processes.
a) Introduction to ordinary differential equations (ODE). Separable and linear first-order ODE. Application to the resolution of physicochemical problems.
b) Second order linear differential equations: Solving linear equations with constant coefficients. Undetermined coefficient method.

4) Sage practices applied to the contents of the subject

Basic Bibliography:
- Notes prepared by teachers and provided to the students.
- E. Steiner. “Matemáticas para las ciencias aplicadas”. Reverté. 2005.

Further reading:

- G. B. Thomas. “Cálculo: una variable", Volumen I, 12ª edición, Pearson- Addison-Wesley , 2010.
- G. B. Thomas. “Cálculo: varias variables", Volumen II, 12ª edición, Pearson- Addison-Wesley , 2010.
- R. K. Nagle, E. B. Saff, A. D. Snider. “Ecuaciones diferenciales y problemas con valores en la frontera”. Pearson, 2005.
- G. A. Anastassiou y R. A. Mezei. “Numerical analysis using Sage”. Springer, 2015.

Basic and general (see "Memoria do Grao en Química"):CB1 ,CG3, CG5.

Transverse:
CT1 - Acquire analysis and synthesis capacity.
CT4 - Be able to solve problems.
CT10 - Critical reasoning.
CT12 - Acquire autonomous learning.

Specific:
CE14 - Resolution of qualitative and quantitative problems according to previously developed models.
CE15 - Recognize and analyze new problems and plan strategies to solve them.
CE25 - Ability to relate Chemistry with other disciplines

A) Lectures in large group ("E" in the time tables):
In these classes the professor will expose of the theoretical contents of the subject, problems or general examples, for which he/she can use audiovisual and computer media. The teacher will publish on the virtual page of the subject the notes of each topic. The teacher will use the bibliography contained in the "Basic Bibliography" section.
B) Small group interactive classes (Seminars, “S” in the time tables):
In these classes applications of the theory, problems, exercises are proposed and solved. The teacher can use audiovisual media. The teacher will publish problem bulletins for each topic on the virtual page of the subject; in these classes problems of special interest will be solved. The teacher can propose the realization of small works to be collected or exposed in the class.
C) Interactive classes with a computer in a small group (Practices with a computer, “L” in the time table):
These classes take place in the computer room. In them the student learns to use the mathematical software SageMath applying it to the theoretical-practical contents of the subject. For this the student must do three guided practices (previously provided by the teacher through the virtual campus) where this software is used to illustrate examples or solve problems posed in lectures or seminars. In the last session, an individual telematic questionnaire is carried out regarding the activity carried out throughout these classes.
D) Blackboard tutorials in a very small group (“T” in the time tables):
Tutorials scheduled by the teacher and coordinated by the Faculty; they will take 1 hour for each student in the semester. In these tutorials several activities can be developed: clarify doubts about theory and exercises, supervise work or other proposed tasks.
E) Tutorials: weekly tutorial hours of the professors are published on the University website. They may be carried out entirely telematically (MS TEAMS platform) by appointment with the teacher.

The student is entitled to a call consisting of two opportunities. The qualification in the first and in the second opportunities will be done through continuous evaluation and taking an exam. The final numerical grade of the student will be the maximum of the following grades: the exam grade and the grade obtained by weighing it with the continuous evaluation, giving the latter a weight of 30%.

The final numerical grade will be calculated as follows:
Final Numerical Note = Maximum {Note A, 0.7 x Note A + 0.3 x Note B},
where
Note A is the in-person final exam (out of 10),
Note B is the mark of the continuous evaluation (out of 10), which will be calculated taking into account the personal work of the student and taking into account the following criteria:

1. Two questionnaires through the virtual campus related to the different blocks of the subject (maximum 7 points).
2. A questionnaire through the virtual campus regarding computer practices (maximum 3 points).

The student who obtains a suspense grade at the first opportunity, if presented at the second, will have the maximum grade of the two final marks obtained.
For the exclusive effect of granting the Honor qualification, not only the final numerical grade will be taken into account, but also the continuous evaluation.
The grade will be "not presented" if the student, having not carried out any evaluable academic activity, does not appear for the exams at the first and second opportunities.
Throughout the course, the evaluation of the competences will be carried out in the final exam, in the seminar classes and in the computer practices:
- in the final exam all the skills developed in the subject will be evaluated.
- In the seminar classes, the competences CG5, CT1, CT4, CT10, CT12, CE14, CE15 and CE25.
- in computer practices, skills CT1, CT4, CT10, CT12, CE14, CE15 and CE25.
The proposed evaluation system evaluates 100% of all basic, general, specific and transversal competences described previously.

REPEATER STUDENT EVALUATION SYSTEM: All repeating students have the same assessment system as ordinary students, except in relation to computer practices: the pass in the computer practices (grade equal to or greater than 1.5 in computer practices) in the 2023-24 academic year will be kept during the course 2024-25.

In cases of fraudulent performance of exercises or tests, "Normativa de avaliación do rendemento académico dos estudantes e de revisión de cualificacións" will be applied.

Class hours: 32 (L) + 12 (S) + 6 (G) +1 (T).
Study hours: 75
Final exam hours: 4
Exam preparation time: 20
Total working hours: 150

- Attendance at all teaching activities in the subject.
- Dedicate to the study of the subject a time regularly distributed throughout the semester.
- After completing the study of a topic, summarize the important calculation procedures, highlighting the basic formulas to remember.
- Check the degree of assimilation of concepts and acquisition of basic calculation techniques by solving the exercises proposed in class and in the problem bulletins.
- Make use of the tutorial schedule.