Public University of Navarre



Academic year: 2020/2021 | Previous academic years:  2019/2020  |  2018/2019  |  2017/2018 
Bachelor's degree in Computer Science at the Universidad Pública de Navarra
Course code: 250206 Subject title: MATHEMATICS II
Credits: 6 Type of subject: Basic Year: 1 Period: 2º S
Department: Estadística, Informática y Matemáticas
Lecturers:
HIGUERAS SANZ, M. INMACULADA   [Mentoring ] ROLDAN MARRODAN, ANGEL TEODORO   [Mentoring ]
PALACIAN SUBIELA, JESUS FCO.   [Mentoring ] YANGUAS SAYAS, PATRICIA   [Mentoring ]
PORTERO EGEA, LAURA (Resp)   [Mentoring ]

Partes de este texto:

 

Module/Subject matter


Module: Basic training

Subject matter: Mathematics

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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 Self-learning

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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  On-site hours  Off-site hours
 A-1: Theoretical lectures 45  
 A-2: Practical lectures 15  
 A-3: Self-study   80
 A-4: Exams and assessment 5  
 A-5: Tutoring 5  
 TOTAL 70 80

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Relationship between formative activities and proficiencies/learning outcomes

Proficiency Activities
G8 A-1, A-2, A-3, A-5
G9 A-1, A-2, A-3, A-5
FB1 A-1, A-2, A-3, A-4, A-5
FB3 A-1, A-2, A-3, A-5
T1 A-1, A-2, A-3, A-5
T3  A-1, A-2, A-4
T4  A-2, A-4, A-5
T8 A-2, A-3

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Languages


English.

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Evaluation

Learning outcome Assessment activity Weight (%) Resit assessment
O1-O3 Midterm exam A on lessons 1 and 2 40 Yes (final exam)
O4-O7 Midterm exam B on lessons 3, 4 and 5 60 Yes (final exam) 

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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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Agenda

  1. Natural, integer, rational, real and complex numbers. Functions of a real variable. Limits and continuity. Weierstrass and Bolzano theorems. Bisection method.
  2. Differential Calculus. Derivatives of functions of one real variable. Mean value theorems. Extrema. Newton-Raphson method.
  3. Integral Calculus.  The Riemann integral. Fundamental theorems of calculus. Integration techniques. Numeric integration.
  4. Sequences and series. Definitions and notation. Monotone sequences. Limit of a sequence.  Numerical series. Convergence.  Power series. Applications.
  5. Differential calculus in Rn. 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. Addison-Wesley.
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. McGraw-Hill.

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Location


Lecture room building at Arrosadia Campus.

 

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