| Competences |
| Type A | Code | Competences Specific |
| FB1 | Have the ability to solve mathematical problems that may arise in engineering. Have the ability to apply knowledge on: linear algebra; geometry, differential geometry, differential and integrated calculation, differential equations and partial derivatives, numerical methods, numerical algorithmics, statistics and optimisation. | |
| Type B | Code | Competences Transversal |
| B2 | Have knowledge in basic and technological subjects, which gives them the ability to learn new methods and theories, and the versatility to adapt to new situations. | |
| 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. | |
| Type B | Code | Learning outcomes |
| B2 |
Know and understand the basic properties of the complex numbers. Understand the basic properties of complex numbers. Understand the notions of limit, continuity and derivability of a real function of a real variable in terms of geometry and shape. Know the Taylor series of a function. Calculate the Taylor series of "elementary" functions. Approximate zeros of functions numerically. Understand the derivative as a tool for the study of dynamic processes. Understand the concept of indefinite integral. Understand the concept of definite integral in terms of geometry and shape. | |
| 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 | Presentation of the contents of the subject and taking of Contact with the level of new students. |
| Lecture | Exposition of the contents of the subject. Reinforcement of theoretical concepts with abundant practical material. |
| Problem solving, exercises in the classroom | Problem solving following previous examples. |
| Problem solving, exercises | Resolució de problemes sobre un tema concret. |
| Personal attention | Private sessions for the resolution of doubts. |
| 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. |
| Assessment |
| Methodologies | Competences | Description | Weight | ||||
| Extended-answer tests |
|
A general test relating to the entire syllabus. | 60% | ||||
| Practical tests |
|
A partial test related to the subject matter seen until the day of the test. | 40% | ||||
| Others |
| Other comments and second exam session | |||
|
Evaluation process: 1 A partial test related to the syllabus seen until the day of the test: 40% of the weight of the final grade of the subject. These two tests generate the first call. 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 quatre són llibres digitalitzats. |
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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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(*)The teaching guide is the document in which the URV publishes the information about all its courses. It is a public document and cannot be modified. Only in exceptional cases can it be revised by the competent agent or duly revised so that it is in line with current legislation.