Course syllabus for Multivariable analysis

Course syllabus adopted 2025-02-13 by Head of Programme (or corresponding).

Overview

  • Swedish nameFlervariabelanalys
  • CodeMVE035
  • Credits6 Credits
  • OwnerTKTFY
  • Education cycleFirst-cycle
  • Main field of studyMathematics, Engineering Physics
  • DepartmentMATHEMATICAL SCIENCES
  • GradingTH - Pass with distinction (5), Pass with credit (4), Pass (3), Fail

Course round 1

  • Teaching language Swedish
  • Application code 57133
  • Maximum participants130
  • Open for exchange studentsNo
  • Only students with the course round in the programme overview.

Credit distribution

0105 Examination 6 c
Grading: TH		 6 c

In programmes

Examiner

Eligibility

General entry requirements for bachelor's level (first cycle)
Applicants enrolled in a programme at Chalmers where the course is included in the study programme are exempted from fulfilling the requirements above.

Specific entry requirements

The same as for the programme that owns the course.
Applicants enrolled in a programme at Chalmers where the course is included in the study programme are exempted from fulfilling the requirements above.

Course specific prerequisites

Linear algebra MVE670 and Real analysis TMA976 or equivalent courses.

Aim

The course will provide familiarity with the most basic theories in mathematical analysis in several variables and shed light on their applications in physics and technology.

Learning outcomes (after completion of the course the student should be able to)

After completing the course, students should be able to explain the meaning of and the connection between the basic concepts of mathematical multivariable calculus and be able to apply their knowledge in practical problem solving.

Content

Functions of several variables. Partial derivatives, differentiability, the chain rule, directional derivative, gradient, level sets, tangent planes, change of variables in PDEs, the implicit and inverse function theorems. Taylor's formula for functions of several variables, characterization of stationary points and optimization. Double integrals, iterated integration, Fubinis theorem, change of variables, level sets, triple integrals, generalized integrals. Space curves. Line integrals, Green's formula in the plane, potentials and exact differential forms. Surfaces in R3, surface area, surface integrals, divergence and curl, Gauss' and Stokes' theorems. Some physical problems leading to partial differential equations. Partial differential equations of the first order. Differentiating under the integral sign. Extreme value problems for functions of several variables, Lagrange's multiplier rule.

Organisation

The teaching is organized into lectures and exercise sessions. There are voluntary electronic tests yielding bonus points.

There are also mandatory blackboard presentations. The students are divided into groups of 6. Each group presents a week of lecture material at the blackboard and writes a report.

Literature

A. Persson, L.-C. Böiers: Analys i flera variabler, Studentlitteratur, Lund. Övningar till Analys i flera variabler, Institutionen för matematik, Lunds tekniska högskola. OTHER LITERATURE L. Råde, B. Westergren: BETA - Mathematics Handbook, Studentlitteratur, Lund.

Examination including compulsory elements

A written examination.
Mandatory blackboard presentations.
Bonus point-yielding tests.

The course examiner may assess individual students in other ways than what is stated above if there are special reasons for doing so, for example if a student has a decision from Chalmers about disability study support.