Course syllabus adopted 2021-02-26 by Head of Programme (or corresponding).
Overview
- Swedish nameFlervariabelanalys
- CodeMVE470
- Credits7.5 Credits
- OwnerTKKMT
- 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 53127
- Maximum participants200
- Open for exchange studentsNo
Credit distribution
Module | Sp1 | Sp2 | Sp3 | Sp4 | Summer | Not Sp | Examination dates |
|---|---|---|---|---|---|---|---|
| 0115 Laboratory 1.5 c Grading: UG | 1.5 c | ||||||
| 0215 Examination 6 c Grading: TH | 6 c |
|
In programmes
- TKBIO - BIOENGINEERING, Year 1 (compulsory)
- TKKEF - CHEMICAL ENGINEERING WITH ENGINEERING PHYSICS, Year 1 (compulsory)
- TKKMT - CHEMICAL ENGINEERING, Year 1 (compulsory)
Examiner
Maria Roginskaya- 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
Knowledge equivalent to the content in the courses Single variable calculus and analytical geometry, and Linear algebra calculus.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 linear algebra and 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 the software MATLAB in problem solving
Content
- Vector valued functions and functions of severable variables, derivative of vector valued functions, parametrise curves, arc length
- Partial derivatives, gradient, directional derivatives, the chain rule
- Tangent planes och normals, linearisation in several variables
- Extreme value problems and Lagrange multipliers
- Multiple integration, interchanging order of integration, change of variables, especially into polar and spherical coordinates
- Surface area
- Field lines for vector fields, conservative vector fields
- Line integrals, surface integrals and flux integrals
- Nabla notation, Green's formula, Gauss' theorem and Stokes' theorem
- Method of steepest descent and Newton's method in Matlab
- Surface plots in Matlab, contour plots och extreme value problems
- Implementing multiple integral computations using Riemann sums
- Plotting vector fields in Matlab
Organisation
Instruction is given in lectures and classes together with computer sessions using Matlab. 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/kemiteknik http://www.chalmers.se/math/SV/utbildning/grundutbildning-chalmers/arkitekt-och/kemiteknik-med-fysik http://www.chalmers.se/math/SV/utbildning/grundutbildning-chalmers/arkitekt-och/bioteknikLiterature
Literature will be announced on the course web page before start of the course.Examination including compulsory elements
More detailed information of the examination will be given on the course web page before start of the course. Examples of assessments are:-selected exercises are to be presented to the teacher orally or in writing during the course
-other documentation of how the student's knowledge develops
-project work, individually or in group
-written or oral exam during and/or at the end of the course
-problems/exercises are to be solved with a computer and presented in writing and/or at the computer.
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.