Course code: 250206 |
Subject title: MATHEMATICS II |
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Credits: 6 |
Type of subject: Basic |
Year: 1 |
Period: 2º S |
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Department: Estadística, Informática y Matemáticas |
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Lecturers: |
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PORTERO EGEA, LAURA [Mentoring ] | ESTEVAN MUGUERZA, ASIER (Resp) [Mentoring ] |

- 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.

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 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.

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 |

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.

- 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.

**Access the bibliography that your professor has requested from the Library.**

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.