Course syllabus for Single variable calculus

Course syllabus adopted 2021-02-26 by Head of Programme (or corresponding).

Overview

  • Swedish nameEnvariabelanalys
  • CodeMVE620
  • Credits7.5 Credits
  • OwnerTKGBS
  • 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 74122
  • Maximum participants65
  • Open for exchange studentsNo

Credit distribution

0120 Examination 7.5 c
Grading: TH		7.5 c
  • 28 Okt 2022 am J
  • 05 Jan 2023 pm J
  • 15 Aug 2023 pm J

In programmes

Examiner

Go to coursepage (Opens in new tab)

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.

Aim

The aim of the course is, together with other mathematics courses, to provide a mathematical general education useful in further studies and professional activities. The course will provide knowledge in single variable calculus necessary for other courses in the Global Systems Program.

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

  • handle logical expressions and elementary functions.
  • explain the concepts of limits, derivatives and integrals and the link between them.
  • calculate limits, derivatives and integrals.
  • carry out extreme value calculations.
  • approximate functions with polynomials and represent them as power series.
  • solve simple ordinary differential equations.
  • combine knowledge of different concepts in practical problem solving.

Content

  • Mathematical logic, sets, sequences and real numbers.
  • The function concept and elementary functions.
  • Limits and continuity.
  • Derivatives and derivation rules.
  • Extreme values, the mean value theorem and linearization.
  • Taylor polynomials and series.
  • Riemann integrals and generalized integrals.
  • The mean value theorem for integrals and the fundamental theorem of calculus.
  • Integration methods and calculation of arc length, area and volume.
  • Solution methods for some ordinary differential equations.

Organisation

The teaching consists of lectures and tutorials.

Literature

Matematisk Analys & Linjär Algebra Del I and II by S. Larsson, A. Logg och A. Målqvist

Examination including compulsory elements

Final written examination. Homework assignments giving credit points for the examination may exist.

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 on educational support due to disability.