Course syllabus adopted 2024-02-02 by Head of Programme (or corresponding).
Overview
- Swedish nameFlervariabelanalys
- CodeTMA044
- Credits7.5 Credits
- OwnerTKELT
- 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 50141
- 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 |
|---|---|---|---|---|---|---|---|
| 0114 Laboratory 1.5 c Grading: UG | 1.5 c | ||||||
| 0214 Examination 6 c Grading: TH | 6 c |
|
In programmes
- TKELT - ELECTRICAL ENGINEERING, Year 1 (compulsory)
- TKMED - BIOMEDICAL ENGINEERING, Year 1 (compulsory)
Examiner
Håkan Samuelsson Kalm- Full Professor, 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
Calculus in one variable and Linear algebra. The student should also have basic knowledge of a computational tool and the ability to use it in problem solving in Calculus and Linear algebra.Aim
The purpose of the course is to, together with the other math courses in the program, provide a general knowledge in the mathematics 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)
- account for the basic concepts and calculations of multivariable analysis, perform the operations and use this knowledge in problem solving.
- account for the connections between the different concepts and use these connections in problem solving.
- use and combine different concepts in problem solving.- use computational tools in problem solving.
More detailed learning outcomes are found in course-PM, see the course home page.
Content
Functions from Rn to Rm, curves and surfaces.Limits, continuity, partial derivatives, differentiability, the chain rule, gradients, directional derivatives, tangent lines/planes, differentials.
Jacobian matrices/determinants.
Extreme values, optimization on compact domains, optimization with constraints, Lagrange multipliers. Numerical methods for optimization.
Multiple integration, improper integrals.
Polar and spherical coordinates, change of variables in double and triple integrals.
Some applications: volumes, center of mass, area of surfaces.
Lineintegrales and Green's theorem.
Surface and flux integrals, divergence and curl, Gauss' divergence theorem, Stokes's theorem.
Short introduction to partial differential equations: the Laplace and wave equations.
Numerical methods for problem solving using computational tools.
Organisation
Instruction is given in lectures and classes. More detailed information will be given on the course web page before start of the course:http://www.chalmers.se/math/SV/utbildning/grundutbildning-chalmers/arkitekt-och/elektroteknik
Literature
Literature will be written at the course web pagehttp://www.chalmers.se/math/SV/utbildning/grundutbildning-chalmers/arkitekt-och/elektroteknik
before the start of the course
Examination including compulsory elements
Written examination. To pass the course it is also necessary to pass computer exercises.
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.