Students will be assessed through
“continuous assessment” consisting of two parts or “stages”.

FIRST
STAGE:

Several
exams will be done by students throughout the course.

Active attendance in the class will be taken
into account for assessment (1 point at most).

In this stage, students could pass the
subject by passing the established exams.

SECOND STAGE:

Students failing the subject in the “first
stage”, will be able to pass the subject by doing a final exam consisting of
theoretical and practical questions.

The final mark will be the sum of 80% of the
final exam and 20% of the continuous assessment.

Students participating in some of the
scheduled assignments throughout the course will be assessed at
the end of the course. They will not be marked as not-presented.

SECOND OPORTUNITY: In this oportunity (July)
the same criteria as those of the second part will be considered.

Students with recognition of part-time
dedication and academic exemption from attendance will be graded under the same
conditions than other students, as explained above.

In special cases, such as,
SICUE or Erasmus students, specific exams could be established.

Learning outcomes	Study programme competences
To consolidate student’s knowledge of calculus and cover gaps in relation to some basic contents, by encouraging the relationship between theory and practice.	A1	B1 B3 B5 B7 B16	C3 C6 C7 C8
To know and to connect the basic concepts and fundamental tools of calculus, and to be fluent in mathematical language appearing in the subject.	A1	B1 B5 B7 B12 B14	C3 C6 C7 C8
To get ability of thinking in an abstract way from the concrete, and to apply abstract results to concrete situations.	A1 A8 A9	B1 B3 B5 B27	C1 C3 C6 C7 C8
To know some mathematical models required for the formulation and solving of problems in construction sector.	A1 A8 A9 A19	B1 B3 B5 B6 B7	C3 C4 C6 C7 C8
To become aware that knowledge, skills and abilities achieved through the study of this subject are fundamental for academic career and future	A1 A8 A9	B1 B2 B3 B4 B5 B6 B7 B25 B26	C3 C4 C5 C6 C7 C8
To consolidate knowledge of statistics and probability.	A1 A8 A9	B1 B3 B4 B5 B6 B7	C1 C3 C4 C7 C8
To acquire fundamental knowledge of specific and general computer applications used in construction sector.	A2	B28

Topic	Sub-topic
SUBJECT 1.- FUNCTIONS OF ONE VARIABLE	1.1.- Definition and basic concepts. 1.2.- Limit of a function at a point. Properties. Operations. Infinite limits and limits at infinity. 1.3.- Continuity. Discontinuities. Properties of continuous functions. 1.4.- Derivative. Properties. Geometrical meaning. Chain rule. Taylor polynomial. 1.5.- Interpolation.
SUBJECT 5.- STATISTICS AND PROBABILITY	5-1 STATISTICS: 5-1.1 Statistics descriptive for one variable. 5-1.2 Previous concepts. Frequency tables. 5-1.3 Graphic representation. Characteristic measurement, position, dispersion 5-1.4 Statistics descriptive for several variables. 5-1.5 Bidimensional variable. Frecuency distribution. Graphic representation. Regression and correlation 5-2 PROBABILITY: 5-2.1 Probability. Random experiment. Sample space. Events. Probability definition. 5-2.2 Conditional probability. Independent events. Product and total probabilities rules. Bayes’ theorem. 5-2.3 Probability distribution. Aleatory variable discrete and continuous. Expectation and variance. 5-2.4 Binomial distribution. Normal distribution 5-2.5 Introduction to statistical inference
SUBJECT 3.- INTEGRATION OF FUNCTIONS	3.1.- Concept of primitive. Properties. 3.2.- Methods of integration. Primitive calculus. 3.3.- Improper integrals. 34.- Geometrical applications. Areas, volumes, lengths. 3.5.- Numerical integration.
SUBJECT 4.- DIFFERENTIAL EQUATIONS. NUMERICAL METHODS.	4.1.- Definition and basic concepts. 4.2.- First order differential equations: separated variables, homogeneous, linear. 4.3.- Numerical methods: Euler, Runge-Kutta.
SUBJECT 2.- FUNCTIONS OF SEVERAL REAL VARIABLES	2.1.- Definitions and basic concepts. 2.2.- Limit. Properties. Operations. 2.3.- Continuity. 2.4.- Differentiation. Partial derivatives. Properties. 2.5.- Tangent plane and normal straight. 2.6.- Relative extremes with and without constrains. Lagrange multipliers method.
Attached: Computer programm MAXIMA	Problems may be solved assisted by the computer programm Maxima

Methodologies / tests	Competencies	Ordinary class hours	Student’s personal work hours	Total hours
Directed discussion	A1 A8 A9 A19 B1 B2 B3 B4 B5 B6 B7 B12 B14 B25 B26 B27 B28 C1 C3 C4 C5 C6 C7 C8	30	45	75
Short answer questions	A2 B1 B26 C1	1	0	1
Problem solving	A1 A8 A9 A19 B1 B16	3	0	3
Objective test	A1 B1	3	0	3
Guest lecture / keynote speech	A1 A2 B12 B25 B26	30	33	63

Personalized attention		5	0	5

(*)The information in the planning table is for guidance only and does not take into account the heterogeneity of the students.

Methodologies	Description
Directed discussion	Solving exercises during regular classes in a participatory way. Some problems will be solved assisted by the computer programm Maxima.
Short answer questions	It will be a final exam consisting of questions with alternative or short answers.
Problem solving	In the final exam, several exercises related to what was explained during the course must be solved by students.
Objective test	For the continuous assessment option, several exams must be done by students throughout the course.
Guest lecture / keynote speech	In the regular classes, the professor will explain the main concepts and results of the subject.

Methodologies	Competencies	Description	Qualification
Short answer questions	A2 B1 B26 C1	It will be an exam with several short questions.	30
Problem solving	A1 A8 A9 A19 B1 B16	It will be a final exam including several problems (practical exercises).	50
Objective test	A1 B1	These consist of several exams for students with regular attendance choosing continuous assessment.	20

Assessment comments
Students will be assessed through “continuous assessment” consisting of two parts or “stages”. FIRST STAGE: Several exams will be done by students throughout the course. Active attendance in the class will be taken into account for assessment (1 point at most). In this stage, students could pass the subject by passing the established exams. SECOND STAGE: Students failing the subject in the “first stage”, will be able to pass the subject by doing a final exam consisting of theoretical and practical questions. The final mark will be the sum of 80% of the final exam and 20% of the continuous assessment. Students participating in some of the scheduled assignments throughout the course will be assessed at the end of the course. They will not be marked as not-presented. SECOND OPORTUNITY: In this oportunity (July) the same criteria as those of the second part will be considered. Students with recognition of part-time dedication and academic exemption from attendance will be graded under the same conditions than other students, as explained above. In special cases, such as, SICUE or Erasmus students, specific exams could be established.

Basic	Frank Ayres, Jr (2010). Cálculo (5ª edición). Mc-Graw-Hill Alfonsa García y otros (2007). CÁLCULO I . CLAGSA Alfonsa García y otros (2002). Cálculo II. CLAGSA Larson - Hostetler (1999). CÁLCULO Y GEOMETRÍA ANALÍTICA. Mc Graw Hill Burgos, Juan de (2008). Fundamentos matemáticos de la Ingeniería (Álgebra y Cálculo). Madrid: García-Maroto García Merayo, Félix (1997). MÉTODOS NUMERICOS EN FORMA DE EJERCICIOS. Universidad Pontificia de Comillas

Complementary	Burden, Richard L. (2011). Análisis Numérico. México: Cengage Learning Adams, Robert A. (2009). CÁLCULO. Madrid:Prentice Hall Simmons, George F. (1996). ECUACIONES DIFERENCIALES CON APLICACIONES Y NOTAS HISTÓRICAS. Madrid: McGraw-Hill Bartoll Arnau, S. y otros (2009). FUNDAMENTOS MATEMÁTICOS EN ARQUITECTURA. Valencia: Editorial de la UPV Ramos del Olmo-Rey Cabeza J.M. (2017). Matemáticas básicas para el acceso a la universidad. Ed. Pirámide Miller, Irwin (2004). Probabilidad y estadística para Ingenieros. Barcelona: Reverté