Analysis II (English)

Summary

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

Content

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
• Apply the skills and knowledge they acquired in Analysis 1.
• Reason rigorously and analyse problems
• Develop appropriate analytical tools for problem solving.
• Analyze efficiently mathematical concepts for problem solving by means of examples and exercises

Teaching methods

lectures, exercises sessions in the classroom.

Assessment methods

Written exam

Supervision

Resources

Bibliography

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

Ressources en bibliothèque

• Calcul différentiel et intégral / Douchet et Zwahlen

Moodle Link

• https://go.epfl.ch/MATH-106_en