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## Syllabus 2019-20 - 11112023 - Mathematics 2 (Matemáticas II)

- Level 1: Tutorial support sessions, materials and exams in this language
- Level 2: Tutorial support sessions, materials, exams and seminars in this language
- Level 3: Tutorial support sessions, materials, exams, seminars and regular lectures in this language

DEGREE: | Grado en Administración y dirección de empresas (11112023) |

FACULTY: | FACULTY OF LAW AND SOCIAL SCIENCES |

DEGREE: | Grado en Finanzas y contabilidad (11312021) |

FACULTY: | FACULTY OF LAW AND SOCIAL SCIENCES |

DEGREE: | Grado en Administración y dirección de empresas (11122023) |

FACULTY: | FACULTY OF LAW AND SOCIAL SCIENCES |

DEGREE: | Doble Grado en Administración y dirección de empresas y Finanzas y contabil (11912009) |

FACULTY: | FACULTY OF LAW AND SOCIAL SCIENCES |

ACADEMIC YEAR: | 2019-20 |

COURSE: | Mathematics 2 |

NAME: Mathematics 2 | |||||

CODE: 11112023 (*) | ACADEMIC YEAR: 2019-20 | ||||

LANGUAGE: English | LEVEL: 3 | ||||

ECTS CREDITS: 6.0 | YEAR: 2 | SEMESTER: PC |

NAME: JÓDAR REYES, JOAQUÍN | ||

DEPARTMENT: U124 - MATEMÁTICAS | ||

FIELD OF STUDY: 595 - MATEMÁTICA APLICADA | ||

OFFICE NO.: B3 - 037 | E-MAIL: jjodar@ujaen.es | P: 953212934 |

WEBSITE: http://www4.ujaen.es/~jjodar/ | ||

ORCID: https://orcid.org/0000-0002-8421-019X | ||

LANGUAGE: - | LEVEL: 3 |

Differential and integral Calculus of several variables with applications to economics. Introduction to differential equations.

**THEORETICAL CONTENTS**

**Unit 1.**
**Limits and continuity of real-valued functions of several
real variables**. The space R^n. Real-valued functions of
several real variables. Limits of real-valued functions of several
real variables. Continuity of real-valued functions of several real
variables.

**Unit 2. Differentiability of real-valued functions of
several real variables.** Partial derivatives. Directional
derivatives. Differential of real-valued functions of several real
variables. Applications to economics.

**Unit 3. Vector-valued functions of several real
variables.** Limits, continuity and
differentiability of vector-valued functions. The Chain
Rule. Homogeneous functions. Applications to economics.

**Unit 4. Optimization of real-valued functions of several
real variables.** Quadratic forms. Unconstrained
optimization. Optimization with equality constraints. Applications
to economics.

**Unit 5. Integration of real-valued functions of several
real variables.** Double integral construction. Double
integrals over rectangular domains. Double integrals over
general bounded regions.

**Unit 6. Introduction to differential equations.**
Basic concepts and notation. Integration methods for some types of
first and second order ordinary differential equations.
Applications to economics.

**PRACTICAL CONTENTS**

Written exercises and computer sessions related to the theoretical contents.

Lectures (M1, M3, M4, M5): Theoretical contents and related practical examples will be developed in these sessions.

Seminars (M6, M7, M8, M10, M12, M13): 15 one-hour long classroom sessions will be devoted for solving problems, with special emphasis on applications to economics. Additionally, 15 one-hour long computer lab sessions will be devoted for solving problems by using the software Mathematica.

Students with special educational needs should contact the Student Attention Service (Servicio de Atención y Ayudas al Estudiante) in order to receive the appropriate academic support

- Detail:

* S2. THEORETICAL CONCEPTS: 6.0 points (60%): Final written exam about the theoretical concepts and related exercises. Learning results R1 and R4.

* S3. CLASSROOM EXERCISES: 2 points (20%): Short classroom tests. Learning results R1, R2 and R4.

*S4. COMPUTER LAB PRACTICES: 2 points (20%): Computer exam. Computer guidelines may be used in the exam. Learning results R1, R3 and R4.

- Marks from S3 and S4 will be maintained during the current academic year (however, if a student attends a new computer exam (S4) in a new official exam call during the current academic year, the old mark from S4 will be changed by the new computer exam mark obtained). Students who attend the final written exam (S2) and/or the computer exam (S4) will appear as 'SHOWN' in the grade list for the corresponding official exam call.
- The final continuous grade will be the sum of the marks obtained from S2, S3, S4.
- Calculator is not allowed in tests and exams.
- Assessment of S2 and/or S4 could be performed during the ordinary classroom sessions if the number of students of the group allows it.

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A final alternative grade given by the sum of the marks of the final written exam (S2) and the computer exam (S4), weighted 80% and 20%, respectively, will be considered for each student at each official exam call.

The final student grade will be the maximum of the final continuous student grade and the final alternative student one at each official exam call.