Course syllabus adopted 2023-02-08 by Head of Programme (or corresponding).
Overview
- Swedish nameFlervariabelanalys
- CodeMVE660
- Credits6 Credits
- OwnerTKIEK
- 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 51125
- Maximum participants220
- 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 |
|---|---|---|---|---|---|---|---|
| 0121 Examination 6 c Grading: TH | 6 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
Knowledge corresponding to the courses Single variable calculus and Linear algebra in the I-program is presupposed.Aim
The multivariable calculus part gives together with the courses in single variable calculus and linear algebra the fundamentals in mathematics that are common for many programs of education both inside and outside Sweden. For a large variety of applications of mathematics it is necessary to have a background in multivariable calculus.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
Instruction is mostly given in lectures and classes. More detailed information will be given on the course web page before start of the course.Literature
The literature will be announced on the webpage of the course.Examination including compulsory elements
Written examinationsThe 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.