Syllabus for |
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TMA044 - Multivariable analysis
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| Flervariabelanalys |
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| Syllabus adopted 2019-02-07 by Head of Programme (or corresponding) |
| Owner: TKELT |
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7,5 Credits
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| Grading: TH - Five, Four, Three, Fail |
| Education cycle: First-cycle |
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Major subject: Mathematics
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Department: 11 - MATHEMATICAL SCIENCES
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Teaching language: Swedish
Application code: 50246
Open for exchange students: No
Only students with the course round in the programme plan
| Module |
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Credit distribution |
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Examination dates |
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Sp1 |
Sp2 |
Sp3 |
Sp4 |
Summer course |
No Sp |
| 0114 |
Laboratory |
1,5 c |
Grading: UG |
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1,5 c
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| 0214 |
Examination |
6,0 c |
Grading: TH |
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6,0 c
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30 Oct 2019 pm M
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07 Jan 2020 am SB_MU
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28 Aug 2020 am J |
In programs
TIDAL COMPUTER ENGINEERING, Year 3 (compulsory elective)
TKELT ELECTRICAL ENGINEERING, Year 2 (compulsory)
Examiner:
Daniel Persson
Go to Course Homepage
Replaces
TMA042
Mathematical methods TMA043
Multivariable analysis
Eligibility:
In order to be eligible for a first cycle course the applicant needs to fulfil the general and specific entry requirements of the programme(s) that has the course included in the study programme.
Course specific prerequisites
Calculus in one variable and Linear algebra. The student should also have basic knowledge of Matlab and ability to use Matlab 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 the software MATLAB in problem solving.
More detailed learning outcomes are found in course-PM, see the course home page.
Content
Functions from R
n to R
m, curves and surfaces.
Limits, continuity, partial derivatives, differentiability, the chain
rule, gradients, directional derivatives, tangent lines/planes,
differentials.
Jacobian matrices/determinants.
Extreme values, optimisation on compact domains, optimisation with
constraints, Lagrange multipliers. Numerical methods for optimisation.
Multiple integration, improper integrals.
Polar och 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 Matlab.
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 page
http://www.chalmers.se/math/SV/utbildning/grundutbildning-chalmers/arkitekt-och/elektroteknik
before the 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.