Course syllabus for Single and multivariable calculus

Course syllabus adopted 2023-02-10 by Head of Programme (or corresponding).

Overview

  • Swedish nameMatematisk analys i en och flera variabler
  • CodeMVE630
  • Credits7.5 Credits
  • OwnerTKDES
  • 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 56122
  • Maximum participants60
  • Open for exchange studentsNo
  • Only students with the course round in the programme overview.

Credit distribution

0120 Examination 7.5 c
Grading: TH		 7.5 c
  • 17 Jan 2025 am J
  • 16 Apr 2025 am J
  • 22 Aug 2025 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

TMV176 or corresponding

Aim

The purpose of the course is, together with the other math courses in the program, to provide a general knowledge in the single and multivariable 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)

  • have deepened knowledge of elementary functions.  
  • have attained good knowledge about the integral and its relation to differentiation.  
  • be acquainted to both analytical and numerical methods for calculating integrals.  
  • have a good understanding of the meaning of an ordinary differential equation.  
  • be familiar with both analytical and numerical methods for solving ordinary differential equations.  
  • be familiar with how functions can be approximated by polynomials and represented by power series.  
  • be able to use and combine different concepts in problem solving.  
  • have basic knowledge of functions in several variables 
  • be able to calculate partial derivatives and double integrals.

Content

Antiderivatives and integrals, methods of integration, integrals of rational functions. Improper integrals. Applications of integration: Area, volume, centre of mass, arc length, area and volume of solids of revolution Numerical integration: the trapezoid rule, Simpson's rule. Taylor's formula, series and power series. Ordinary differential equations: First-order equation in general, analytical solution of separable and linear equations. Second-order linear equations with constant coefficients. Functions of several variables. Partial derivatives, optimization, double integrals.

Organisation

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

Literature

R. A. Adams, Calculus: A Complete Course, Sixth Edition, Addison Wesley, 2006. S. Larsson, Beräkningsmatematik, kompendium, 2008.

Examination including compulsory elements

Examination:  written  exam  at the end of the course.

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.