# Coursebooks

## Analysis II (English)

Mountford Thomas

English

#### Summary

The course studies fundamental concepts of analysis and the calculus of functions of several variables.

#### Content

-The Euclidean space R^n.

-Vector functions and curves

-Differentiation of functions of several variables.

-Multiple integrals

-Ordinary differential equations.

#### Keywords

Euclidean vector space, partial derivative,differential, Jacobian, Hessian, Taylor expansion, gradient, chain  rule, implicit function theorem, Lagrange multipliers, multiple integrals, ordinary differential equation

#### Learning Prerequisites

##### Required courses

Analysis I, Linear Algebra I

##### Important concepts to start the course

-calculus of functions of one variable

-concepts of convergence

-vector space, matrices, eigenvalues

#### Learning Outcomes

• The goal of this course consists as for Analysis 1 is that students acquire the following capacities:
• Consolidate the skills and knowledge they acquired in Analysis 1.
• Reason
• rigorously and to analyse problems
• Choose
• appropriate analytical tools for problem solving.
• Conceptualize problems
• Apply
• efficiently mathematical concepts for problem solving by means of examples and exercises
• Analyze
• and to solve new problems.
• Master the basic tools of analysis
• Master the basic tools of elementary ordinary differential equations, the Euclidean space R^n and functions of several variables

#### Teaching methods

Ex cathedra lectures, exercises sessions in the classroom.

Written exam

#### Supervision

 Office hours No Assistants Yes Forum No Others Tutoring of exercises other measures to be defined

#### Resources

##### Bibliography

Jacques Douchet and Bruno Zwahlen: Calcul différentiel et intégral. PPUR, 2011.

### Reference week

MoTuWeThFr
8-9CE4 BCH2201
9-10
10-11CE1105
CM1100
CM1120
CO122
CO123
CO124

11-12
12-13
13-14
14-15
15-16
16-17
17-18
18-19
19-20
20-21
21-22

Lecture
Exercise, TP
Project, other

### legend

• Autumn semester
• Winter sessions
• Spring semester
• Summer sessions
• Lecture in French
• Lecture in English
• Lecture in German