Calculus
Code: 103796 ECTS Credits: 6| Degree | Type | Year |
|---|---|---|
| 2500895 Electronic Engineering for Telecommunication | FB | 1 |
| 2500898 Telecommunication Systems Engineering | FB | 1 |
Contact
- Name:
- Gil Solanes Farres
- Email:
- gil.solanes@uab.cat
Teachers
- Josep Maria Burgues Badia
- Laura Rodriguez Cima
- Carmelo Puliatti
- Alba Aguilera Montserrat
- Gil Solanes Farres
Teaching groups languages
You can view this information at the end of this document.
Prerequisites
Although there are no official prerequisites, it is essential that students have a very good command of the most basic notions of mathematics. It will also be of great use to them if they already have consolidated knowledge of Calculus taught in High School: limits, continuity and derivability of real functions of a real variable; notions of integral calculus. People who do not have a minimum background in previous mathematics will have to make an effort to worry about solving these deficiencies.
Objectives and Contextualisation
Reach a sufficient level in the calculation of a variable to deal with phenomena and solve the mathematical problems raised in engineering that can be described in these terms.
Support the parts of the other subjects of the degree that require mastery of real functions of a variable. Achieve a sufficient level in the use of complex numbers and above all in trigonometry.
Competences
- Electronic Engineering for Telecommunication
- Communication
- Develop personal attitude.
- Develop personal work habits.
- Develop thinking habits.
- Learn new methods and technologies, building on basic technological knowledge, to be able to adapt to new situations.
- Work in a team.
- Telecommunication Systems Engineering
- Communication
- Develop personal attitude.
- Develop personal work habits.
- Develop thinking habits.
- Learn new methods and technologies, building on basic technological knowledge, to be able to adapt to new situations.
- Work in a team.
Learning Outcomes
- Apply, in the problems that arise in engineering, knowledge about linear algebra, geometry, differential geometry, differential and integral calculus, differential and partial derivative equations, numerical methods, numerical algorithms, statistics and optimisation.
- Apply, to the problems that arise in engineering, knowledge of linear algebra, geometry, differential geometry, differential and integral calculus, differential and partial derivative equations, numerical methods, numerical algorithms, statistics and optimisation.
- Communicate efficiently, orally and in writing, knowledge, results and skills, both professionally and to non-expert audiences.
- Develop curiosity and creativity.
- Develop scientific thinking.
- Develop the capacity for analysis and synthesis.
- Manage available time and resources.
- Manage available time and resources. Work in an organised manner.
- Prevent and solve problems.
- Resolve the mathematical problems that can arise in engineering.
- Work autonomously.
- Work cooperatively.
- Work in an organised manner.
Content
1. Complex numbers.
1.1 Trigonometric functions. Addition formulae. Identities. Trigonometric inverse functions.
1.2 Trigonometric equations.
1.3 Complex numbers. Sum, product and the invers. Square roots. Second degree equations.
1.4 Module and argument. Euler's formula.
1.5 Polynomials, roots and factorization. Fundamental theorem of Algebra.
2. Continuity
2.1 Continuity and limits.
2.2. Fundamental theorems of continuous functions. Exponential and logarithmic functions.
3. Differential calculus.
3.1 Derivatives of functions. Algebraic rules of derivation. Chain rule. Derived of the inverse.
3.2 Mean value theorem and consequences. Intervals of monotony.
3.3 Relative and absolute extremes. Optimization.
3.4 Calculation of limits using derivation.
3.5 Taylor's formula.
4. Integral Calculus.
4.1 Notion of Riemann integral.
4.2 Fundamental Theorem of Calculus. Barrow's theorem.
4.3 Calculation of primitives.
4.4 Applications of integrals.
5. Differential equations.
5.1 Notion of differential equation.
5.2 Solving the equations of separate variables.
5.3 First order linear equations.
5.4 Second order linear with constant coefficients.
5.5 Examples of applications of the differential equations.
Activities and Methodology
| Title | Hours | ECTS | Learning Outcomes |
|---|---|---|---|
| Type: Directed | |||
| Theoretical classes and exercise classes | 45 | 1.8 | 1, 2, 10 |
| Type: Supervised | |||
| Supervised special sessions | 24 | 0.96 | 1, 2, 10 |
| Type: Autonomous | |||
| Personal work | 76 | 3.04 | 5, 6, 9, 10, 11 |
The subject has two hours of theory per week. They will be taught in the traditional way with a blackboard. The theory teacher will give the main ideas about the various topics by showing examples and exercises.
The student will receive lists of exercises and problems that we will work on in the weekly problem class. Previously, during your off-site activity, you will have read and thought about the proposed exercises and problems. In this way, their participation in the classroom can be guaranteed and the assimilation of procedural content will be facilitated.
Throughout the semester, there will be 5 seminar sessions (the last one is assessed) devoted to subjects of independent interest but related to the contents of the course.
The Virtual Campus will be the means of communication between teachers and students. It will be important to consult it every day.
The students will have a tutoring and counseling service both online and in the office. It is recommended to use this aid for monitoring the course.
Note: 15 minutes of a class will be set aside, within the calendar established by center/degree, for students to complete the teacher evaluation and subject/module evaluation surveys.
Annotation: Within the schedule set by the centre or degree programme, 15 minutes of one class will be reserved for students to evaluate their lecturers and their courses or modules through questionnaires.
Assessment
Continous Assessment Activities
| Title | Weighting | Hours | ECTS | Learning Outcomes |
|---|---|---|---|---|
| Evaluation of seminars | 15% | 1 | 0.04 | 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13 |
| Midterm Exam 1 | 40% | 2 | 0.08 | 1, 3, 4, 5, 6, 8, 9, 10, 11, 12, 13 |
| Midterm Exam 2 | 45% | 2 | 0.08 | 1, 4, 6, 10 |
In order to avoid possible confusions and errors of legal interpretation, see the Catalan version.
Bibliography
1. F. Carreras, M. Dalmau, F. J. Albéniz, J. M. Moreno, Ecuaciones diferenciales, Ed. UAB, 1994.
2. N. Levinson i R. M. Redheer, Curso de variable compleja (Capítol 1) Ed. Reverté, 1981.
3. D. Pestana, J. Rodríguez, E. Romera, E. Touris, V. Álvarez, A. Portilla. Curso Práctico de Cálculo y Precálculo, Ed. Ariel, 2000.
4. S.L. Salas, E. Hille, Calculus Vol. 1, Ed. Reverté, 2002.
5. D. G. Zill, Ecuaciones Diferenciales con aplicaciones de modelado (6a ed.), International Thomson cop., 1997.
Software
There are no computer practice classes in the subject, so no study of computer programs will be done. Despite this, it will be recommended to use mathematical manipulation programs such as Maxima or Wolfram Alpha.
Language list
| Name | Group | Language | Semester | Turn |
|---|---|---|---|---|
| (PAUL) Classroom practices | 311 | Catalan | first semester | morning-mixed |
| (PAUL) Classroom practices | 312 | Catalan | first semester | morning-mixed |
| (PAUL) Classroom practices | 331 | Catalan | first semester | morning-mixed |
| (PAUL) Classroom practices | 332 | Catalan | first semester | morning-mixed |
| (PAUL) Classroom practices | 351 | Catalan | first semester | afternoon |
| (PAUL) Classroom practices | 352 | Catalan | first semester | afternoon |
| (SEM) Seminars | 311 | Catalan | first semester | morning-mixed |
| (SEM) Seminars | 312 | Catalan | first semester | morning-mixed |
| (SEM) Seminars | 313 | Catalan | first semester | morning-mixed |
| (SEM) Seminars | 314 | Catalan | first semester | morning-mixed |
| (SEM) Seminars | 315 | Catalan | first semester | morning-mixed |
| (SEM) Seminars | 316 | Catalan | first semester | morning-mixed |
| (SEM) Seminars | 317 | Catalan | first semester | morning-mixed |
| (SEM) Seminars | 318 | Catalan | first semester | morning-mixed |
| (SEM) Seminars | 319 | Catalan | first semester | afternoon |
| (SEM) Seminars | 320 | Catalan | first semester | afternoon |
| (SEM) Seminars | 321 | Catalan | first semester | afternoon |
| (SEM) Seminars | 322 | Catalan | first semester | afternoon |
| (TE) Theory | 31 | Catalan | first semester | morning-mixed |
| (TE) Theory | 33 | Catalan | first semester | morning-mixed |
| (TE) Theory | 35 | Catalan | first semester | afternoon |