Titular Professors
Professors
Trigonometry, basic functions and derivation.
Students taking this subject will acquire the knowledge and will develop the following skills:
1. Global basic knowledge of real variable function analysis and its application. Limit calculus, function studies, integral calculus and general convergence problem solving.
2. Understand and associate basic demonstrations.
3. Problem analysis and synthesis capabilities.
4. Engineering problem solving using mathematical tools.
1. The numbers
1.1. Various number introduction, and their characteristics.
1.2. Real numbers. Properties.
1.3. Imaginary numbers.
2. Functions
2.1. Basic functions. Definition and properties.
2.2. Limits.
2.3. Continuous functions: definitions, properties and basic theorems for interval continuous functions.
3. Differential calculus
3.1. Definition and meaning.
3.2. Differential functions theorems and their applications
4. Function representation
4.1. Cartesian axis.
4.2. Polar axis.
5. Riemann integral calculus
5.1. Definition and properties. Geometric interpretation
5.2. Fundamental calculus theorem
5.3. Infinite integrals. Definition and basic calculus.
6. Integral calculus
6.1. Immediate integral calculus
6.2. Change of variable and parts integral calculus
6.3. Rational integral calculus
6.4. Trigonometrical integral calculus
6.5. Irrational integral calculus
7. Integral calculus applications
7.1. Length calculus
7.2. Area calculus
7.3. Volume calculus
8. Numerical sequences
8.1. Real number secuences. Concept of limit.
8.2. Calculus of limits.
9. Numerical series
9.1. Definition and properties. Convergence of series
9.2. Nonnegative number series. Convergent criteria.
9.3. General number series. Absolute convergence.
10. Function series
10.1. Punctual convergence. Examples.
10.2. Potency series
10.3. Fourier series and their applications to engineering.
The methodology divides the classes in two ways: lectures and sessions dedicated to problem solving using the theoretical concepts taught in the lectures.
1. Lectures
The teacher explains the various theoretical concepts in the lectures: this includes theorems, criteria and all kind of mathematical demonstrations for mathematical methods to be known. In these sessions, the teacher also solves some exercises using direct applications for the taught concepts.
2. Exercises sessions
The exercises sessions intend that the student learns to solve more elaborate examples using the theoretical concepts taught in the lectures. They take place in the same class and during the time for the subject´s lectures. The problems solved by the teacher are more difficult than the ones in the lecture, and they intend to help students to link concepts in the subject and also in other subjects.
3. Exercises to solve at home
Apart from the exercises solved in class the student must solve other exercises at home. The objective of these exercises is to consolidate the theoretical basis given in the lectures and give the student the tools to solve engineering problems using mathematics.
In order to evaluate if the student has obtained all the objectives in this subject, different tests are done to obtain information from the students:
Exams
During the academic year, four main exams are done: two at the first semester and two more during de second semester.
Class tests
Class participation
The teacher has an observation checklist where he notes down the student´s different attitudes and behaviours during the class.
Personal or group work
The final mark the course is calculated with 50% weighting each final semester. The final mark from each semester is calculated as follows: 60% exam grade and 40% continuous assessment mark. The grade exam is calculated by weighting 30% of the control point, and a 70% final exam of the semester. The continuous assessment mark is calculated by weighting 30% mark for participation and attitude, and a 70% grade knowledge. The attitude mark is defined from class attendance and attitude. The knowledge mark is calculated from exercises, checks and questionnaires to students during the semester.
Villalbí, R. Càlcul I. Teoria i problemes. Editat per Enginyeria La Salle
Adelantado, Alsina, Guerola, Iriondo, Miralles, Meler, Matemàtiques bàsiques. Editat per Enginyeria La Salle.
García, A. i altres. Cálculo I. Teoría y problemas de Análisis Matemático en una variable. Librería I.C.A.I., 1993
Piskunov, N. Cálculo diferencial e integral. Varias editoriales
Galindo, F. , Sanz, J. , Tristán L.A., Guia práctica de cálculo infinitesimal en una variable real, Thompson 2003.
Ayres, F. Cálculo diferencial e integral. Mc Graw Hill, Schaum, 1991
Spiegel, M. Cálculo Superior. Mc Graw Hill, 1969Natella antonyan, Problemari de precalculo.
Pilar Garcia, Iniciacion a la Matematica Universitaria
Lali Barriere, Fonaments Matematics
Venancio Tomeo, Problemas resueltos de cálculo de una variable