Calculus of One Variable
Code: 107596Credits: 6
| Degree programme | Type | Course |
|---|---|---|
| Physics | FB | 1 |
Contact lecturer
- Name :
- Francisco Javier Bafaluy Bafaluy
- Email :
- javier.bafaluy@uab.cat
Teaching staff
- Alvaro Corral Cano
Group languages
You can consult this information at the end of the document.
Prerequisites
There are no requirements.
Objectives
The basic concepts of real variable calculus are introduced: limits, continuity, derivative, integration and power series.
The student will learn the practcal techniques of calculus.
Learning outcomes
- CM09 (Justify the use of calculus in one and several variables and differential equations in the resolution of general problems.) Justify the use of calculus in one and several variables and differential equations in the resolution of general problems.
- CM10 (Adapt the basic mathematical strategy when approaching a given problem from an analytical point of view.) Adapt the basic mathematical strategy when approaching a given problem from an analytical point of view.
- KM09 (Identify the basic concepts of limits, continuity, derivatives and integrals, vector and subspace space, linear and scalar product and the methodology of matrix diagonalisation.) Identify the basic concepts of limits, continuity, derivatives and integrals, vector and subspace space, linear and scalar product and the methodology of matrix diagonalisation.
- SM07 (Apply the mathematical knowledge acquired to the resolution of mathematical and physical problems with mathematical representation.) Apply the mathematical knowledge acquired to the resolution of mathematical and physical problems with mathematical representation.
Contents
- Real numbers, induction.
- Elementary functions and inverse function.
- Number sequences and limits.
- Limits and continuity of functions.
- Derivatives and applications.
- Riemann integral.
- Integration and applications.
- Improper integrals.
- Number series.
- Power series.
Learning activities and methodology
| Title | Hours | ECTS | Learning outcomes |
|---|---|---|---|
| Problem solving | 50 | 2 | CM10, SM07 |
| Personal study | 42 | 1.68 | KM09, SM07 |
| Practical classes | 13 | 0.52 | CM10, SM07 |
| Seminars | 8 | 0.32 | CM09, CM10, SM07 |
| Theory classes | 28 | 1.12 | CM09, KM09 |
Theory classes: presentation of the subject's theoretical framework and problem-solving tools.
Practical Classes: instructors will demonstrate solutions to selected problems from a collection available on the Virtual Campus; students should work through these problems before the class.
Seminars: the students will work in small groups to solve exercises related to a given topic under the supervision of an instructor; at the end of the session each group will present their reults.
Assessment
Continuous assessment activities
| Title | Weight | Hours | ECTS | Learning outcomes |
|---|---|---|---|---|
| First term exam | 40% | 3 | 0.12 | CM10, KM09, SM07 |
| Final term exam | 40% | 3 | 0.12 | CM10, KM09, SM07 |
| Re-evaluation | 80% (only the partial exams can be re-evaluated) | 3 | 0.12 | CM10, KM09, SM07 |
| Delivery of exercises | 20% | 0 | 0 | CM09, CM10, SM07 |
The evaluation is based on two tests with a global weight of 80% and on the assessment of the student work in the seminar sessions with a global weight of 20%.
The re-evaluation allows only to improve the qualification of the tests, the qualification of the seminars work is not recoverable.
In order to qualify for the re-evaluation it will be necessary to have completed at least the two partial exams.
Single Assessment:
The students following the single evaluation modality must take a final test that will be similar to the two partial tests. This exam will take place at the same day, hour and location as the corresponding exam of the continuous evaluation.
If necessary they could take the re-evaluation, that will be the same as for 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
Theory:
* Spivak, M. Calculus, Reverté (2013). Available online
* Brokate, N.; Manchanda, P.; Siddiqi, A.H.; Calculus for Scientists and Engineers, Springer (2019). Available online
* Salas, S. L; Hille, E.; Etgen, G. J. Calculus. Una y Varias Variables. Volumen I. Reverté (2018). Available online
* Méndez, A.,Càlcul en una variable real, UAB (2024) Available online
Exercicis (llibres amb exercicis resolts i per resoldre):
* Aryes, F. y Mendelson, E. Cálculo diferencial e integral, McGraw-Hill (1990). Available in the library
* Demidovich, B.P., 5000 problemas de análisis matemático, Paraninfo (2000). Available in the library
Software
No specific software will be used.
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 | morning-mixed |
| (PAUL) Classroom practices | 1 | Catalan | first semester | morning-mixed |
| (TE) Theory | 2 | Catalan/Spanish | first semester | afternoon |
| (PAUL) Classroom practices | 2 | Catalan/Spanish | first semester | morning-mixed |
| (SEM) Seminars | 11 | Catalan | first semester | morning-mixed |
| (SEM) Seminars | 12 | Catalan | first semester | morning-mixed |
| (SEM) Seminars | 21 | Catalan | first semester | afternoon |
| (SEM) Seminars | 22 | Catalan | first semester | afternoon |