Module/Subject matter
Module: Basic training
Subject matter: Mathematics
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Contents
 Functions of a real variable. Limits, continuity, differentiation.
 Integration of functions of one real variable
 Sequences and convergence. Infinite series. Taylor series.
 Functions of several variables: limits, continuity, differentiation.
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General proficiencies
General proficiencies that a student should acquire in this course:
 G8 Knowledge of basic and tecnological subjects to have the ability to learn new methods and theories, and versatility to adapt to new situations
 G9 Problem solving proficiency with personal initiative, decision making, creativity and critical reasoning. Ability to elaborate and communicate knowledge, abilities and skills in computer engineering
 T1 Analysis and synthesis ability
 T3 Oral and written communication
 T4 Problem solving
 T8 Selflearning
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Specific proficiencies
Specific proficiencies that a student should acquire in this course:
 FB1 Ability to solve mathematical problems in engineering. Ability to apply theoretical knowledge on linear algebra, differential and integral calculus, numerical methods, numerical algorithms, statistics and optimization
 FB3 Ability to understand and master the basic concepts of discrete matemathics, logic, algorithmics and computational complexity, and their applications to problem solving in engineering.
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Learning outcomes
At the end of the course, the student is able to:
 O1: Apply the basic elements of differential calculus in one variable: limits, continuity, differentiability.
 O2: Use the basic concepts of differential Calculus to find extrema of one real variable functions.
 O3: Know and apply some numerical method for solving nonlinear equations.
 O4: Apply the basic elements of integral calculus in one variables.
 O5: Understand the applications of integrals to the calculus of volumes, areas and lengths.
 O6: Use the basic concepts of sequences and series.
 O7: Apply the basic elements of differential calculus in several variables: limits, continuity, differentiability.
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Methodology
The following table shows the distribution of activities in the course:
Methodology  Activity 
Onsite hours 
Offsite hours 
A1: Theoretical lectures 
45 

A2: Practical lectures 
15 

A3: Selfstudy 

80 
A4: Exams and assessment 
5 

A5: Tutoring 
5 

TOTAL 
70 
80 
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Evaluation
Learning outcome 
Assessment activity 
Weight (%) 
Resit assessment 
O1O3 
Midterm exam A on lessons 1 and 2 
40 
Yes (final exam) 
O4O7 
Midterm exam B on lessons 3, 4 and 5 
60 
Yes (final exam) 
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Agenda
 Natural, integer, rational, real and complex numbers. Functions of a real variable. Limits and continuity. Weierstrass and Bolzano theorems. Bisection method.
 Differential Calculus. Derivatives of functions of one real variable. Mean value theorems. Extrema. NewtonRaphson method.
 Integral Calculus. The Riemann integral. Fundamental theorems of calculus. Integration techniques. Numeric integration.

Sequences and series. Definitions and notation. Monotone sequences. Limit of a sequence. Numerical series. Convergence. Power series. Applications.

Differential calculus in R^{n}. Functions, limits and continuity. Partial and directional derivatives. Maxima and Minima.
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Bibliography
Access the bibliography that your professor has requested from the Library.
Basic bibliography:
 R.A. Adams. Calculus: a complete course. AddisonWesley.
Additional bibliography:
 E. Kreyszig. Advanced engineering mathematics. John Wiley & Sons.
 B. García, I. Higueras, T. Roldán. Análisis matemático y métodos numéricos. Universidad Pública de Navarra.
 R.E. Larson, R.P. Hostetler. Cálculo y geometría analítica. McGrawHill.
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Location
Lecture room building at Arrosadia Campus.
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