| Competences |
| Type A | Code | Competences Specific |
| FB1 | Be able to solve mathematical problems that may arise in engineering. Have the ability to apply knowledge on: linear algebra, differential and integral calculation, numerical methods, numerical algorithmics, statistics and optimisation. | |
| Type B | Code | Competences Transversal |
| Type C | Code | Competences Nuclear |
| Learning outcomes |
| Type A | Code | Learning outcomes |
| FB1 |
Determine the joint solution to an inequality. Work with complex numbers in their binomial, polar and exponential expressions. Solve problems of square root extraction, exponentiation and logarithmic operations with complex numbers. Solve problems of limits, continuity and derivability. Calculate the Taylor series of "elementary" functions. Apply the Taylor series when solving problem using polynomial approximation. Approximate zeros of functions numerically. Apply the Taylor series to the calculation of "indeterminate" limits. Obtain graphically the derivative of certain basic functions. Apply differential calculation to solve problems of optimisation. Graphically represent a flat curve from its analytical expression. Analyze and interpret the graphical representation of a plane curve. Calculate integrals of basic functions. Approximate a definite integral numerically. Obtain graphically the integral of certain basic functions. Apply the definite integral for the calculation of physical parameters. Apply differential and integrated calculation to problem solving in physics and technology. Know and understand the basic properties of the body of real numbers. Understands the basic properties of complex body numbers Comprèn geomètrica i formalment les nocions de límit, continuïtat i derivabilitat d'una funció real de variable real Know Taylor's development of a function. Entén la derivada com una eina per a l'estudi de processos dinàmics Understand the concept of indefinite integral. Comprèn geomètrica i formalment el concepte d'integral definida | |
| Type B | Code | Learning outcomes |
| Type C | Code | Learning outcomes |
| Contents |
| Topic | Sub-topic |
| The real number. Basic properties. | The absolute value. Inequalities. |
| The complex number. Elementary arithmetic. | Binomial, polar and exponential forms. Radical, exponential and logarithmic operations. |
| Real variable functions. | Elementary and transcendent functions. Limits and continuity. |
| Derivation of functions of a real variable | Derivation formulas. Extremes, maximums and minimums. Graphic representation. Optimization. |
| Taylor series. | Taylor series development. |
| Integration. | Primitive functions. Integration formulas. |
| Definite integral. | Geometric concept. Applications. |
| Planning |
| Methodologies :: Tests | ||||||||||
| Competences | (*) Class hours |
Hours outside the classroom |
(**) Total hours | |||||||
| Introductory activities |
|
1 | 0 | 1 | ||||||
| Lecture |
|
37 | 29 | 66 | ||||||
| Problem solving, exercises in the classroom |
|
15 | 20 | 35 | ||||||
| Problem solving, exercises |
|
15 | 20 | 35 | ||||||
| Personal attention |
|
1 | 0 | 1 | ||||||
| Extended-answer tests |
|
4 | 4 | 8 | ||||||
| Practical tests |
|
2 | 2 | 4 | ||||||
| (*) On e-learning, hours of virtual attendance of the teacher. (**) The information in the planning table is for guidance only and does not take into account the heterogeneity of the students. | ||||||||||
| Methodologies |
| Description | |
| Introductory activities | Presentació dels continguts de l'assignatura i presa de contacte amb el nivell dels nous alumnes. |
| Lecture | Exposició dels continguts de l'assignatura. Reforçament dels conceptes teòrics amb abundant material pràctic. |
| Problem solving, exercises in the classroom | Resolució de problemes seguint exemples previs. |
| Problem solving, exercises | Resolució de problemes sobre un tema concret. |
| Personal attention | Consultes privades per a la resolució de dubtes. |
| Personalized attention |
| Description |
|
Els professors, en les seves hores de consulta, atendran els alumnes. Although this course is not offered in English, foreign exchange students will receive personalised support in English and will be able to develop the evaluation activities in this language. A causa de l'emergència sanitària provocada per la COVID-19 poden haver-hi canvis que s'informaran a l'espai Moodle de cada assignatura. En general, en cas de necessitat, podran fer-se consultes via correu electrònic o via videoconferència. |
| Assessment |
| Methodologies | Competences | Description | Weight | ||||
| Extended-answer tests |
|
Two tests related to the rest of the syllabus from the real and complex numbers (30%, 50%). | 80% | ||||
| Practical tests |
|
A test regarding real and complex numbers. | 20% | ||||
| Others |
| Other comments and second exam session | |||
|
Evaluation process: 1 A test related to real and complex numbers: 20% of the weight of the final grade of the course. The evaluation in the second call will be done through a single global exam. The tests will be done without any electronic means (calculators, computers, telephones, etc ..) The tests are face-to-face. Due to the health emergency caused by the Covidien-19 there may be changes that will be reported in the Moodle space of each subject. In general, in case of need, the tests can be done in person via Moodle. |
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| Sources of information |
| Basic |
Joan Camps Sabaté, Fernando Serveto Olivé, Miguel Ángel Acebo Visanzay, Apunts de Càlcul, Universitat Rovira i Virgili, 2004
Joan Camps Sabaté, Fernando Serveto Olivé, Miguel Ángel Acebo Visanzay, Francisco García Estarlich, Càlcul: problemes i exàmens, Universitat Rovira i Virgili, 2004
Pepe Aranda, Cálculo I: Cálculo infinitesimal en una variable, Alqua, 2007
Francisco Javier Pérez González, Cálculo diferencial e integral de funciones de una variable, Universidad de Granada, 2008 |
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Els llibres "Apunts de Càlcul " i "Càlcul: problemes i exàmens", seran digitalitzats per poder ser usats com a base de classes no presencials de docència virtual. Els llibres "Cálculo I: Cálculo infinitesimal en una variable " i "Cálculo diferencial e integral de funciones de una variable", són llibres digitalitzats, són de llicència oberta Creative Commons, no comercials, poden ser obtinguts lliurement i usats en classes no presencials de docència virtual. |
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| Complementary |
Larson, R.E., Cálculo con geometría análítica, McGraw Hill, 2006
Edwards, C.H., Penney, D.E., Cálculo con trascendentes tempranas, Pearson Education, 2008
Spivak, M., Càlcul infinitesimal, Reverté, 1995
Jon Rogawski, Cálculo (Una variable), Reverté, 2012
Dennis G.Zill et altres, Cálculo diferencial, McGraw-Hill, 2016
Dennis G.Zill et altres, Cálculo Integral, McGraw-Hill, 2016 |
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| Recommendations |
| Subjects that continue the syllabus | ||
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