Course syllabus adopted 2025-02-18 by Head of Programme (or corresponding).
Overview
- Swedish nameMatematisk analys i flera variabler
- CodeMVE765
- Credits7.5 Credits
- OwnerTIEPL
- 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
- Maximum participants10
- Minimum participants1
- 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 |
|---|---|---|---|---|---|---|---|
| 0125 Examination 7.5 c Grading: TH | 7.5 c |
In programmes
Examiner
Elin Götmark- 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
The courses MVE570 Mathematical analysis in several variables and MVE575 Calculus, or corresponding knowledge.Aim
The course will provide knowledge in multivariate analysis. It should also create the necessary knowledge for mathematical treatment of technical problems in professional practice and provide basic knowledge for further studies.Learning outcomes (after completion of the course the student should be able to)
- demonstrate some geometric understanding in several variables, for example by switching between treating surfaces as graphs, parameterised surfaces and level surfaces,
- calculate different types of limits and derivatives for functions of several variables, interpret these geometrically, and use them for example to decide continuity, find tangent planes, and use the implicit function theorem,
- solve optimization problems by locating and classifying critical points, and by means of Lagrange multipliers, if there are equality constraints,
- calculate multiple integrals with repeated single integrals and by changing variables, and use these to calculate areas and volumes,
- calculate line and surface integrals of vector fields, decide if a vector field is conservative, and use Gauss and Stoke's theorems,
- define basic concepts and prove certain theorems in the course.
Content
Parametrization of curves and surfaces. Level curves and level surfaces. Limits in several variables. Partial derivatives, differentiability, gradients, directional derivative, functional matrices. Classification of stationary points. Chain rule in several variables. Something of partial differential equations. Optimization on compact sets, optimization with equality constraints, and simple optimization problems on non-compact sets. Implicit function theorem.Integration in two and several variables, in terms of multiple integrals and repeated single integrals. Changes in coordinates, especially polar and spherical coordinates. Applications of integrals on areas, volumes, and center of mass. Generalized double integrals. Vector fields, especially conservative ones. Line and surface integrals. Green's, Gauss', and Stoke's theorems.
Organisation
The teaching is organised in the form of lectures, exercises and computer labs.Literature
Published on the course website before the start of the course.Examination including compulsory elements
The examination consists of a written exam at the end of the course, and computer exercises. During the course, there may be optional assignments that give bonus points on the 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 about disability study support.