Course syllabus for Multivariable calculus

The course syllabus contains changes
See changes

Course syllabus adopted 2019-02-19 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 53111
  • Maximum participants200
  • Open for exchange studentsNo

Credit distribution

0115 Laboratory 1.5 c
Grading: UG		 1.5 c
0215 Examination 6 c
Grading: TH		 6 c
  • 19 Mar 2021 pm J
  • 10 Jun 2021 am J
  • 27 Aug 2021 am J

In programmes

Examiner

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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/bioteknik

Literature

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 syllabus contains changes

  • Changes to course rounds:
    • 2020-11-19: Examinator Examinator changed from Thomas Wernstål (twernst) to Maria Roginskaya (maria) by Viceprefekt/adm
      [Course round 1]