Course syllabus adopted 2023-02-10 by Head of Programme (or corresponding).
Overview
- Swedish nameMatematisk analys i flera variabler
- CodeMVE615
- Credits6 Credits
- OwnerTKAUT
- Education cycleFirst-cycle
- Main field of studyMathematics
- DepartmentMATHEMATICAL SCIENCES
- GradingTH - Pass with distinction (5), Pass with credit (4), Pass (3), Fail
Course round 1
- Teaching language Swedish
- Application code 47126
- 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 |
|---|---|---|---|---|---|---|---|
| 0120 Examination 6 c Grading: TH | 0 c | 0 c | 0 c | 6 c | 0 c | 0 c |
|
In programmes
Examiner
Hossein Raufi- Senior Lecturer, Algebra and Geometry, 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
Analysis in one variable, linear algebra.Aim
The aim of the course, together with the other math courses in the program, is to provide a general knowledge in the mathematics and numerical analysis required in further studies as well as in the future professional career.Learning outcomes (after completion of the course the student should be able to)
After completion of this course, the student should be able to- describe the significance and meaning of the fundamental concepts of mathematical analysis in several variables
- describe the relations between the different concepts
- use the concepts to solve mathematical problems
Content
The space Rn, open/closed/compact sets. Functions from Rn to Rm, curves and surfaces. Limits, continuity, differentiability, the chain rule. General comments on PDE: The Laplace and the Poisson equations. Partial derivatives, gradient and tangent plane, differentials. Functional matrices, functional determinant. Extremal values, optimization on compact domains, optimization with constraints. Double and triple integrals, generalized double integrals. Polar and spherical coordinates, substitution of variables. Computations of volumes and areas of curved surfaces. Curve integrals and Greens formula. Divergence and Gauss theorem. Curl and Stokes theorem.
Organisation
The teaching consists of lectures and exercise sessions. More detailed information will be available on the course webpage before the course starts.
Literature
Information is given on the course website before the start of the course.
Examination including compulsory elements
The examination consists of a written or oral exam.
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 on educational support due to disability.