Course syllabus adopted 2025-02-22 by Head of Programme (or corresponding).
Overview
- Swedish nameFlervariabelanalys
- CodeMVE600
- Credits7.5 Credits
- OwnerTKTEM
- 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 59114
- Maximum participants50
- Open for exchange studentsNo
- Only students with the course round in the programme overview.
Credit distribution
Module | Sp1 | Sp2 | Sp3 | Sp4 | Summer | Not Sp | Examination dates |
|---|---|---|---|---|---|---|---|
| 0119 Examination 6 c Grading: TH | 6 c | ||||||
| 0219 Intermediate test 1.5 c Grading: UG | 1.5 c |
In programmes
Examiner
Thomas Bäckdahl- Associate Professor, Analysis and Probability Theory, Mathematical Sciences
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.Specific aim for the 1.5 credit part: Provide a brief introduction to numerical analysis.
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.
For the 1.5 credit module, students should, after completing the course, be able to independently solve simple problems in numerical analysis.
For the 1.5 credit module, students should, after completing the course, be able to independently solve simple problems in numerical analysis.
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.
For the 1.5 hp module: Erroranalysis and floating point arithmetics.Numerical solution of linear and non-linear equations and systems.
Simple numerical methods for computations of derivatives and integrals.
Simple numerical methods for computations of derivatives and integrals.
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.
A mandatory test.
Mandatory black-board presentation.
Bonus point rewarding 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.