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Graduate courses

Departments' graduate courses for PhD-students.

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Syllabus for

Academic year
TMV151 - Calculus in a single variable  
Matematisk analys i en variabel
 
Syllabus adopted 2019-02-21 by Head of Programme (or corresponding)
Owner: TKMAS
7,5 Credits
Grading: TH - Five, Four, Three, Fail
Education cycle: First-cycle
Major subject: Mathematics
Department: 11 - MATHEMATICAL SCIENCES


Teaching language: Swedish
Application code: 55156
Open for exchange students: No
Only students with the course round in the programme plan

Module   Credit distribution   Examination dates
Sp1 Sp2 Sp3 Sp4 Summer course No Sp
0108 Examination 7,5c Grading: TH   7,5c   16 Jan 2020 pm H   06 Apr 2020 pm DIST   17 Aug 2020 am J

In programs

TKMAS MECHANICAL ENGINEERING, Year 1 (compulsory)

Examiner:

Axel Målqvist

  Go to Course Homepage

Replaces

TMV150   Calculus in a single variable


Eligibility:

In order to be eligible for a first cycle course the applicant needs to fulfil the general and specific entry requirements of the programme(s) that has the course included in the study programme.

Course specific prerequisites

Introductary course in mathematics and programming in Matlab.

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)

  • show advanced knowledge of elementary functions.
  • define the concept of the integral and explain the connection between the derivative and the integral.
  • implement the Riemann sum as a MATLAB-function
  • apply and motivate methods for computing integrals, both analytically and numerically.
  •  explain the meaning of an ordinary differential eqation (ODE) and derive ODEs from a describing text.
  •  apply and motivate analytical as well as numerical methods for solving ordinary differential equations including reformulation of higher order ODEs to a system of first order ODEs.
  • implement Euler's method as a MATLAB function.
  • use built-in Matlab functions for solving differential equations that are part of the standard MATLAB distribution.
  • derive Laplace transforms and use tranforms for solving ODEs.
  • combine knowledge of different concepts in practical problem solving.

Content

Antiderivatives and integrals, methods of integration, integration of rational functions and some elementary functions.
Generalised integrals. Numerical integration.

Applications of integration: Area, volume, center of gravity, arc length, area and volume of solids of rotation.

Ordinary differential equations: General non-linear frirst order system. Constructing solutions by approximation.
Implementation in MATLAB. Rewriting a higher order differential equation as a system of first order differential equations.
Analytical solution of separable and linear differential equations. Second order linear equations with constant coefficients. Linear equations of higher order. Vectors in two and three dimensions. Dot product, cross product, area and volume. Laplace transforms.

Organisation

The material is presented in the form of lectures as well as classes and computer labwork in smaller groups.
Detailed information will be given on the course homepage at the start of the course.

Literature

The main textbook will be announced on the course web page two weeks before the course begins. 

Lecture notes.

Examination including compulsory elements

Detailed information concerning the examination will be given on the course homepage at the start of the course.
Examples on possible forms of examination include:
  • selected assignments may be presented orally or in writing during the course,
  • project work, individually or in groups,
  • written or oral exam during and/or after the course.
  • problems/assignments solved using the computer presented in writing and/or at the computer.


Published: Wed 26 Feb 2020.