Course syllabus for Calculus in one variable

The course syllabus contains changes
See changes

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

Overview

  • Swedish nameMatematisk analys i en variabel
  • CodeTMV139
  • Credits6 Credits
  • OwnerTKAUT
  • 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 47121
  • Open for exchange studentsNo
  • Only students with the course round in the programme overview.

Credit distribution

0120 Examination 6 c
Grading: TH		 6 c
  • 13 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

Introductary Course in Mathematics.

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)

After completion of the course the student shall:

  • Understand and be able to define the concepts definite, indefinite and improper (Riemann)integral, know the basic theorems in this context, be able to prove a selection of them, and use them to solve problems.

  • Independently (without aids) be able to compute fairly complex integrals using knowledge of antiderivatives of some elementary functions, integration by parts, direct and indirect substitutions and decomposition into partial fractions.

  • Independently (without aids) be able to compute the volume of a body using the slice and shell formulas, the area of a surface of revolution and the length of a graph.

  • Understand the idea of a differential equation and its solutions as well as be able to infer such an equation from a verbal description of a simple real-world situation.

  • Independently (without aids) be able to solve linear and separable first order differential equations, and second order linear equations with constant coefficients, homogeneous as well as inhomogeneous.

  • Understand the concepts number sequence and series, their convergence, know basic theorems in this context, be able to prove some of them, and use them when solving problems.

  • Understand the concepts power series, their interval of convergence, Maclaurin- and Taylor series/polynomials of a function, be able to determine them and use them when solving problems.

  • With aid in the form of a table of Maclaurin series be able to use power series to determine limits, sums of series, approximations and solving differential equations.

Content

  • Definition and properties of determined and improper integrals.

  • Antiderivatives and their relation to determined integrals.

  • Methods for determining antiderivatives; knowledge of antiderivatives of some elementary functions, direct and indirect substitution, integration by parts and decomposition into partial fractions.

  • Computation of volumes of bodies, area of surfaces and length of graphs using integrals of functions of one real variable.

  • First order linear and separable differential equations, second order linear equations with constant coefficients. Basic modelling in connection with this.

  • Number sequences, series and criteria for their convergence.

  • Power series and their basic properties, Maclaurin and Taylor series/polynomials of functions.Using power series to determine limits, sums of series, approximations and solving differential equations.

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

Literature will be announced on the course web page before start of the course.

Examination including compulsory elements

Written final exam at the end of the course.


Non-compulsory  assignments may render bonus points to the exam. Information about this will occur on the course web page at the start of each course occation. 

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.

The course syllabus contains changes

  • Changes to course rounds:
    • 2020-09-19: Examinator Examinator changed from Stefan Lemurell (sj) to Mattias Lennartsson (matlen) by Viceprefekt/adm
      [Course round 1]