Universidad PÃÂºblica de Navarra - Nafarroako Univertsitate Publikoa

Public University of Navarre

Bachelor's degree in Computer Science at the Universidad Pública de Navarra
Course code: 240206	Subject title: MATHEMATICS II
Credits: 6	Type of subject: Basic	Year: 1	Period: 2º S
Department: Estadística, Informática y Matemáticas
Lecturers:
PORTERO EGEA, LAURA [Mentoring ]		QUEMADA MAYORAL, CARLOS (Resp) [Mentoring ]

Partes de este texto:

Module: Basic training

Subject matter: Mathematics.

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

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.

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:

Learning outcomes	Assessment activity	Weight	Resit available
O1-O5	First midterm exam (lessons 1, 2 and 3)	50%	Yes
O6-O7	Second midterm exam (lessons 4, 5 and 6)	50%	Yes

To pass the subject, it is necessary to have a weighted average higher than 5 across the two exams, as well as at least 4 points in each of them.

Both activities can be made up in the make-up exam.

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. Newton-Raphson 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 Rn. Functions, limits and continuity. Partial and directional derivatives. Maxima and Minima.

Basic bibliography:

R.A. Adams. Calculus: a complete course. Addison-Wesley.
E. Kreyszig. Advanced engineering mathematics. John Wiley & Sons.
J.E. Marsden, A.J. Tromba. Vector calculus. W.H. Freeman.
R.K. Nagle, E.B. Saff, A.D. Snider. Fundamentals of differential equations and boundary value problems. Addison-Wesley.

Additional bibliography:

M. Braun. Differential equations and their applications: an introduction to applied mathematics. Springer-Verlag.
R.E. Larson, R.P. Hostetler. Cálculo y geometría analítica. McGraw-Hill.
S.L. Salas, E. Hille, G.J. Etgen. Calculus: una y varias variables. Reverté.
D.G. Zill. Ecuaciones diferenciales con aplicaciones de modelado. Thomson.

English, Spanish, Euskara

Arrosadia Campus.