Course syllabus for Multivariable calculus

Course syllabus adopted 2025-02-22 by Head of Programme (or corresponding).

Overview

  • Swedish nameAnalys i flera variabler
  • CodeMVE760
  • Credits7.5 Credits
  • OwnerTKTKE
  • 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 43117
  • Maximum participants230
  • Open for exchange studentsNo

Credit distribution

0125 Examination 7.5 c
Grading: TH		 7.5 c

In programmes

Examiner

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 Linear algebra and differential equations.

Aim

The aim of the course, together with the other mathematics courses, is to provide a general knowledge of mathematics that is as useful as possible in further studies and technical careers. The course should provide, in a logical and coherent way, the knowledge of mathematical analysis in several variables necessary for the other courses in the Engineering Chemistry and Bioengineering programs.

Learning outcomes (after completion of the course the student should be able to)

  • explain the meaning of the basic concepts and operations of multivariable calculus
  • perform the operations and utilise this in problem solving
  • explain the relationships between the different concepts and utilise these relationships in problem solving
  • combine knowledge of different concepts in practical problem solving

Content

  • Vector-valued functions and functions in several variables, function surfaces, derivatives of vector-valued functions
  • Parameterisation of curves, arc length
  • Limits to functions in several variables, partial derivatives, gradients and directional derivatives, chain rule
  • Tangent planes and normals to function surfaces, linearising functions in several variables
  • Extreme value problems and Lagrange multipliers
  • Double integrals and multiple integrals: changing the order of integration, changing variables - especially to polar and spherical coordinates
  • Areas of curved surfaces
  • Field lines to vector fields, conservative vector fields
  • Curve integrals, surface integrals and flow integrals
  • Nabla notation, Green's formula, Gauss theorem and Stokes theorem

Organisation

The teaching is given in the form of lectures, and exercise sessions in small groups.

Literature

To be indicated on the course website before the start of the course.

Examination including compulsory elements

Written examination. Optional tests during the course that can give bonus points may occur.

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 about disability study support.