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## Syllabus for

MVE255 - Calculus in several variables

Owner: TKMAS
7,5 Credits
Grading: TH - Five, Four, Three, Not passed
Education cycle: First-cycle
Major subject: Mathematics
Department: 11 - MATHEMATICAL SCIENCES

Teaching language: Swedish

 Course module Credit distribution Examination dates Sp1 Sp2 Sp3 Sp4 Summer course No Sp 0108 Examination 7,5 c Grading: TH 7,5 c 31 May 2016 pm SB, 05 Apr 2016 am H, 26 Aug 2016 am SB

#### In programs

TKMAS MECHANICAL ENGINEERING, Year 1 (compulsory)
TIMAL MECHANICAL ENGINEERING - Production Engineering, Year 3 (elective)
TKDAT COMPUTER SCIENCE AND ENGINEERING, Year 3 (elective)
TKDES INDUSTRIAL DESIGN ENGINEERING, Year 3 (elective)
TKITE SOFTWARE ENGINEERING, Year 2 (elective)
TKITE SOFTWARE ENGINEERING, Year 3 (compulsory elective)

#### 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, linear algebra and programming in Matlab.

#### 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 meaning of the concepts of calculus in several variables.
• account for the relations between these concepts and to use them in problem solving.
• implement the Newton method and the method of gradients in MATLAB functions.
• solve optimization problems with constraints.
• account for the basic ideas of the finite element method.
• use the finite element method in MATLAB.
• use MATLAB for solving problems.

#### Content

The space Rn, open, closed, compact sets.
Functions from Rn to Rm, curves and surfaces.
Limits, continuity, differentiability, the chain rule.
Partial derivative, linearization, Jacobi matrix, gradient, tangent plane, directional derivative, differentials.
Functional matrix, functional determinant.
Numerical solution of systems of nonlinear equations.

Extreme values, optimization in compact sets, optimization with constraints. Numerical optimization: Newton's method and the method of gradients.

Double and triple integrals. Polar and spherical coordinates, substitution of variables. Computation of volume, center of mass, area of a curved surface.

Line integral. Green's formula.

Introduction to partial differential equations: Laplace and Poisson equations, finite element method.

MATLAB applications from mechanics.

#### Organisation

Instruction is given in lectures and classes. More detailed information will be given on the course web page before the start of the course.

#### Literature

T. Kolsrud, T. Lindström och K. Hveberg, Flervariabelanalys med linjär algebra, Prentice Hall 2012.
S. Larsson, Randvärdesproblem och finita elementmetoden, kompendium, 2014.

#### 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.

Page manager Published: Thu 04 Feb 2021.