MATH-106(en) / 6 credits

Language: English

## Summary

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

## Keywords

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

## 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

## Bibliography

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

## In the programs

• Semester: Spring
• Number of places: 230
• Exam form: Written (summer session)
• Subject examined: Analysis II (English)
• Lecture: 4 Hour(s) per week x 14 weeks
• Exercises: 2 Hour(s) per week x 14 weeks
• Semester: Spring
• Number of places: 230
• Exam form: Written (summer session)
• Subject examined: Analysis II (English)
• Lecture: 4 Hour(s) per week x 14 weeks
• Exercises: 2 Hour(s) per week x 14 weeks
• Semester: Spring
• Number of places: 230
• Exam form: Written (summer session)
• Subject examined: Analysis II (English)
• Lecture: 4 Hour(s) per week x 14 weeks
• Exercises: 2 Hour(s) per week x 14 weeks
• Semester: Spring
• Number of places: 230
• Exam form: Written (summer session)
• Subject examined: Analysis II (English)
• Lecture: 4 Hour(s) per week x 14 weeks
• Exercises: 2 Hour(s) per week x 14 weeks
• Semester: Spring
• Number of places: 230
• Exam form: Written (summer session)
• Subject examined: Analysis II (English)
• Lecture: 4 Hour(s) per week x 14 weeks
• Exercises: 2 Hour(s) per week x 14 weeks
• Semester: Spring
• Number of places: 230
• Exam form: Written (summer session)
• Subject examined: Analysis II (English)
• Lecture: 4 Hour(s) per week x 14 weeks
• Exercises: 2 Hour(s) per week x 14 weeks
• Semester: Spring
• Number of places: 230
• Exam form: Written (summer session)
• Subject examined: Analysis II (English)
• Lecture: 4 Hour(s) per week x 14 weeks
• Exercises: 2 Hour(s) per week x 14 weeks
• Semester: Spring
• Number of places: 230
• Exam form: Written (summer session)
• Subject examined: Analysis II (English)
• Lecture: 4 Hour(s) per week x 14 weeks
• Exercises: 2 Hour(s) per week x 14 weeks
• Semester: Spring
• Number of places: 230
• Exam form: Written (summer session)
• Subject examined: Analysis II (English)
• Lecture: 4 Hour(s) per week x 14 weeks
• Exercises: 2 Hour(s) per week x 14 weeks
• Semester: Spring
• Number of places: 230
• Exam form: Written (summer session)
• Subject examined: Analysis II (English)
• Lecture: 4 Hour(s) per week x 14 weeks
• Exercises: 2 Hour(s) per week x 14 weeks

## Reference week

 Mo Tu We Th Fr 8-9 9-10 10-11 11-12 12-13 13-14 14-15 15-16 16-17 17-18 18-19 19-20 20-21 21-22