Public University of Navarre

Academic year: 2021/2022 | Previous academic years:  2020/2021  |  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

Partes de este texto:


Module/Subject matter

Module: Basic training

Subject matter: Mathematics


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


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.


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.



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


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






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) 



  • 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.



  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.



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.



Lecture room building at Arrosadia Campus.