## 27006 - Calculus II

### Syllabus Information

2017/18
Subject:
27006 - Calculus II
Faculty / School:
Degree:
453 - Degree in Mathematics
ECTS:
15.0
Year:
2
Semester:
Annual
Subject Type:
Compulsory
Module:
---

### 5.1. Methodological overview

#### There are three different types of classes received by the students.

Master classes which are dedicated to theorical concepts and fundamental exercises.

Practical classes. Students practice and  strengthen concepts and ideas which they have learnt.

Computer lessons. Students use computers to solve different types of exercises proposed in the subject.

In the web pages  http://www.unizar.es/analisis_matematico/docencia.html and  https://moodle2.unizar.es/ are avaible additional information and material.

### 5.3. Syllabus

Functions of several variables

1. Continuity and differentiability of real-valued and vector-valued functions. Functions of class C^p. Relative extrema.

2. Implicit and inverse function theorems, change of variables. Manifolds and  the Lagrange multipliers rule.

3. Integration in R^n (an approach to Lebesgue's method). Iterated integrals and differentiation under integral sign.

4. Integration of functions and of 1-differential forms on paths. Poincaré's lemma.

5. Integration of functions and differential forms on surfaces in R^3. Riemann-Green, divergence and Stokes theorems.

### 5.4. Course planning and calendar

#### Calendar

There are six hours per week in first semester and four hour per week in the second one, following the official timetable given by the Faculty of Science in the University of Zaragoza.

In these hours there are included two hours per week in the first semester and one hour and a half in the second semester dedicated to solve exercises in the classroom.

Computer lessons take place in the second semester in fixed timetible.

### 5.5. Bibliography and recommended resources

• Apostol, Tom M.. Análisis matemático / Tom M. Apostol . - 2a ed., [reimp.] Barcelona, [etc.] : Reverté, cop.1988
• Browder, Andrew. Mathematical analysis : an introduction / Andrew Browder New York [etc.] : Springer, cop. 1996
• Bombal Gordon, Fernando. Problemas de análisis matemático. Vol. 1, Espacios métricos y normados. El espacio Rn / Bombal, Rodríguez, Vera . - [2a. ed. reimp.] Madrid : AC, D.L.1993
• Bombal Gordon, Fernando. Problemas de análisis matemático. Vol. 2, Cálculo diferencial / Bombal, R. Marín, Vera . - [1a. ed., reimp.] Madrid : AC, D.L. 1995
• Bombal Gordon, Fernando. Problemas de análisis matemático. Vol. 3, Cálculo integral / Bombal, R. Marín, Vera . - 1a ed., 2a reimp. Madrid : AC, 1994
• Demidovich, B.P.. 5000 problemas de análisis matemático / B. P. Demidóvich ; traducido del ruso por Emiliano Aparicio Bernardo . - 5ª ed. Madrid : Paraninfo, 1993
• Pastor, Eduardo. Teoría y problemas de cálculo integral / Eduardo Pastor, Victor Varela . - [1a. ed.] Madrid : Crisser, D.L. 1974
• Fleming, Wendell H.. Functions of several variables / Wendell Fleming . - 2nd. ed. New York, [etc] : Springer-Verlag, 1977