Mathematical Tools I
Code: 106803Credits: 6
| Degree programme | Type | Course |
|---|---|---|
| Nanoscience and Nanotechnology | FB | 2 |
Contact lecturer
- Name :
- Francisco Javier Bafaluy Bafaluy
- Email :
- javier.bafaluy@uab.cat
Teaching staff
- Albert Beardo Ricol
Group languages
You can consult this information at the end of the document.
Prerequisites
There are none. The contents and the methods introduced in this course assume knowledge of the first year Mathematics courses: Fonaments de Matemàtiques and Càlcul.
Objectives
The aim of the course is to enable the students to use some mathematical tools which are necessary for the study and modeling of nanosystems: analysis and resolution of ordinary and partial differential equations.
Learning outcomes
- CM06 (Identify the mathematical nature of certain physical and chemical phenomena, in order to abstract the essential variables that describe them.) Identify the mathematical nature of certain physical and chemical phenomena, in order to abstract the essential variables that describe them.
- CM07 (Solve real-world problems that occur in the field of science and technology using mathematical tools and methods.) Solve real-world problems that occur in the field of science and technology using mathematical tools and methods.
- KM10 (Identify the basic tools and notions of statistical data processing.) Identify the basic tools and notions of statistical data processing.
- SM09 (Express oneself clearly using basic mathematical language.) Express oneself clearly using basic mathematical language.
- SM10 (Solve simple problems related to matrix calculus, linear equations and first order differential equations.) Solve simple problems related to matrix calculus, linear equations and first order differential equations.
- SM12 (Use graphical and numerical methods to explore, describe and interpret data.) Use graphical and numerical methods to explore, describe and interpret data.
Contents
I. INTEGRATION ON CURVES AND SURFACES
- Line and surface integrals
- Vector Analysis: Theorems of Green, Gauss and Stokes
II. ORDINARY DIFFERENTIAL EQUATIONS
- First order differential equations
- Second order linear equations
- Laplace Transforms
III. PARTIAL DIFFERENTIAL EQUATIONS
- Fourier series
- Boundary conditions
- Heat conduction equation
- Wave and Laplace equations
Learning activities and methodology
| Title | Hours | ECTS | Learning outcomes |
|---|---|---|---|
| Personal study | 32 | 1.28 | CM06 |
| Problems classes | 12 | 0.48 | CM07, KM10 |
| Problem solving | 60 | 2.4 | CM07, SM09, SM10, SM12 |
| Theory classes | 36 | 1.44 | CM06, SM09, SM12 |
| Practical classes | 4 | 0.16 | CM07, KM10, SM09, SM10, SM12 |
- Theory classes: The concepts and methods of the different subjects will be introduced, with a variety of examples.
- Problems classes: Teachers will solve selected exercises from a collection that will be available to the students beforehand.
- Practical classes: They will be held in a computer classroom. Activities will be proposed to be carried out by means of an adequate software. The results of this practical work must be presented within a given deadline.
- Autonomous work: It is imperative that students complement face-to-face activities with autonomous, individual or group work; to practice the resolution of problems is especially important.
Assessment
Continuous assessment activities
| Title | Weight | Hours | ECTS | Learning outcomes |
|---|---|---|---|---|
| Results of the practical sessions | 10% | 0 | 0 | CM07, KM10, SM09, SM12 |
| Delivery of solved problems | 10% | 0 | 0 | CM07, SM09, SM10 |
| Partial exams: | 80% | 6 | 0.24 | CM06, CM07, SM09, SM10 |
Partial exams: Two partial tests will be carried out, with a weight in the final evaluation of 40% each. At the end of the course, a re-evaluation exam for this 80% will be held for students who need it.
Practical sessions and delivery of solved exercises: The remaining 20% will come from the evaluation of the delivered problems and from the results of the practical sessions in equal parts. The presentation of the results of the practical sessions will be mandatory.
Re-evaluation: There will be a re-evaluation for one or both partial exams. Only students who have completed 2/3 of the assessment activities, this means both term tests, may opt for the re-evaluation.
The student who carries out evaluation activities that involve less than 50% of the total evaluation will be considered \"not assessable\".
Single Assessment:
Students following the single evaluation modality must take a final test similar to the partial exams but comprising all the subject matter. This test will be carried out on the same day that the second partial exam and it will account for a 90% of the grade.
The results of the practical sessions is also mandatory, in the same dates as the other students, and will account for the remaining 10% of the grade.
If necessary, students could take the same recovery exam as the rest of the students.
Use of AI:
In this course, the use of Artificial Intelligence (AI) technologies is permitted exclusively for bibliographic or information searches. For graded assignments, it is essential to clearly identify which parts were generated using this technology, specify the tools used, and include a critical reflection on how these tools influenced the process and the final result of the activity. Lack of transparency regarding the use of AI in these activities will be considered a breach of academic integrity and could result in a partial or full penalty on the assignment grade, or more severe sanctions in cases of serious misconduct.
Bibliography
- Salas, Saturnino L. & Etgen, Garret J. & Hille, Einar. (2011). Calculus : una y varias variables. Volumen II. (4ª ed.) Reverté. Available online.
- Boyce, William E. & DiPrima, Richard C. (2010)., Ecuaciones diferenciales y problemas con valores en la frontera (5ª ed.) Limusa Wiley. Available in the library.
- Logan, J. David. (2011), A First Course in Differential Equations (2a ed.) Springer Available online
- Logan, J. David. (2004), Applied Partial Differential Equations, (2nd ed.) Springer Available in the library.
Course groups and languages
The information provided is provisional until November 30. After this date, you will be able to consult the language of each group through this link. To access the information, you will need to enter the course CODE
| Type of teaching | Group | Language | Semester | Shift |
|---|---|---|---|---|
| (TE) Theory | 1 | Catalan | first semester | afternoon |
| (PAUL) Classroom practices | 1 | Catalan | first semester | afternoon |
| (PLAB) Practical laboratories | 1 | Catalan | first semester | morning-mixed |
| (PLAB) Practical laboratories | 2 | Catalan | first semester | morning-mixed |