## Public University of Navarre

Academic year: 2023/2024 | Previous academic years:  2022/2023  |  2021/2022  |  2020/2021  |  2019/2020
 Course code: 250206 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 ] ESTEVAN MUGUERZA, ASIER (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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English.

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### Evaluation

Continuous assessment is considered along the semester based on the following activities:

 Learning outcome Assessment activity Weight (%) Resit assessment It allows test resit O1, O2 Midterm exam A on lessons 1 and 2 15 Yes (final exam) none O3, O4 Midterm exam B on lessons 3 and 4 15 Yes (final exam) none O1, O2, O3, O4, O5 Exam C on lessons 1,2,3,4 and 5 70 Yes (final exam) 3/10

In order to pass the subject, the following conditions must be fulfilled:

• the mean of exams A, B and C is more than 5.
• the mark of the final first exam (exam C) covering the whole course (to be scheduled during the resit assessment period) is not less than 3.

Otherwise, the mark of the final second exam should be more than 5.

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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:

• 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.

• 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.

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### Location

Lecture room building at Arrosadia Campus.

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