Syllabus for |
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| MVE085 - Mathematical analysis in several variables |
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| Syllabus adopted 2011-02-22 by Head of Programme (or corresponding) |
| Owner: TKVOV |
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7,5 Credits |
| Grading: TH - Five, Four, Three, Not passed |
| 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
| Course 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 |
| 0105 |
Examination |
7,5 c |
Grading: TH |
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7,5 c
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29 Oct 2015 am V, |
04 Jan 2016 am M, |
26 Aug 2016 am SB |
In programs
TKVOV CIVIL ENGINEERING, Year 2 (compulsory)
TIBYL BUILDING AND CIVIL ENGINEERING, Year 3 (elective)
TKITE SOFTWARE ENGINEERING, Year 3 (compulsory elective)
TKDAT COMPUTER SCIENCE AND ENGINEERING, Year 3 (elective)
Examiner:
Forskarassistent
Dennis Eriksson
Go to Course Homepage
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
Pre knowledge Analysis in one variable, 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)
After this course the student should - be able to account for the basic concepts of calculus in several dimensions and of numerical analysis. - be able to explain the connections between these concepts and use the connections in problem solving. - be able to use and combine different concepts in problem solving. - have deepend the ability to use the software MATLAB in problem solving.
Content
The space Rn, open/closed/compact sets, Functions from Rn to Rm, curves and surfaces, Limits, continuity, differentiability, the chain rule, Partial derivatives, gradient and tangent plane, differentials, Functional matrices, functional determinant, Numerical solution of non-linear systems of equations, Extremal values, optimization on compact domains, optimization with constraints. Applications for V-engineers. Numerical optimization. Double and tripple integrals, generalized double integrals, Polar and spherical coordinates, substitution of variables, Computations of volumes and areas of curved surfaces, Curve integrals and Greens formula. Surface and flux integrals, divergence and curl, Gauss' divergence theorem, Stokes's theorem. System of ODE, numerical solutions with V-applications. General comments on PDE: The Laplace and the Poisson equations, numerical solutions. Applications of Matlab.
Organisation
The teaching consists of lectures and tutorial sessions for smaller groups and numerical laborations. More information is given on the course website before the start of the course.
Literature
Literature will be announced on the course web page before start of the course.
Examination
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.