## Public University of Navarre

Academic year: 2021/2022 | Previous academic years:  2020/2021  |  2019/2020  |  2018/2019  |  2017/2018
 Course code: 250206 Subject title: MATHEMATICS II Credits: 6 Type of subject: Basic Year: 1 Period: 2º S Department: Estadística, Informática y Matemáticas Lecturers: ROLDAN MARRODAN, ANGEL TEODORO   [Mentoring ] PORTERO EGEA, LAURA (Resp)   [Mentoring ]

Partes de este texto:

### 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 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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### 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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### 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:
• 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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English.

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### Location

Lecture room building at Arrosadia Campus.

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