Study Guide@lith
 

Linköping Institute of Technology

 
 
Valid for year : 2017
 
TATA42 Calculus in one variable, 2, 6 ECTS credits.
/Envariabelanalys 2/

For:   D   DPU   EM   FyN   I   Ii   IT   KeBi   M   Mat   MED   TB   Y   Yi  

 

Prel. scheduled hours: 70
Rec. self-study hours: 90

  Area of Education: Science

Main field of studies: Mathematics, Applied Mathematics

  Advancement level (G1, G2, A): G1

Aim:
To give basic proficiency in mathematical concepts, reasoning and relations contained in single-variable calculus. To provide the skills in calculus and problem solving required for subsequent studies. After a completed course, the student should be able to
  • read and interpret mathematical text
  • quote and explain Taylor's formula and the concepts involved in numerical series and convergence of series
  • derive expressions for, and compute, geometrical quantities such as plane area, arc length, and volume and surface area of solids of revolution
  • solve ordinary differential equations (first order linear and separable equations, and higher order linear equations with constant coefficients) and integral equations
  • use Taylor expansions to approximate functions by polynomials, compute limits and rational approximations, and to investigate local properties of functions
  • carry out investigations of convergence of improper integrals, numerical series and power series
  • use power series to calculate sums and to solve differential equations
  • perform routine calculations with confidence
  • carry out inspections of results and partial results, in order to verify that these are correct or reasonable.


Prerequisites: (valid for students admitted to programmes within which the course is offered)
Calculus in one variable

Note: Admission requirements for non-programme students usually also include admission requirements for the programme and threshhold requirements for progression within the programme, or corresponding.

Supplementary courses:
Calculus in several variables, Vector analysis, Complex analysis, and Fourier analysis.

Organisation:
Lectures and problem classes.
The IT programme has a different organisation, due to the study programme syllabus.


Course contents:
Applications of integrals: plane area, arc length, volume and surface area of solids of revolution and centre of mass. Taylor's and Maclaurin's formulae: Maclaurin expansions of the elementary functions, the Lagrange and Ordo forms of the remainder term, applications, e.g. error estimates for approximations and computations of limits. Ordinary differential equations: first order linear and separable equations, integral equations, higher order linear equations with constant coefficients. Improper integrals: investigation of convergence, absolute convergence. Numerical series: investigation of convergence, absolute convergence, Leibniz criterion. Power series: radius of convergence, calculation of sums, solving differential equations

Course literature:
Forsling, G. and Neymark, N.: Matematisk analys, en variabel. Liber 2011.
Complementary material and a collection of problems edited by the Department of Mathematics.


Examination:
Written examination
6 ECTS
 



Course language is Swedish.
Department offering the course: MAI.
Director of Studies: Jesper Thorén
Examiner: Lars Alexandersson (I,Ii), Johan Thim (D,IT,U,KB,TB), Ulf Janfalk (M,DPU,EMM), Tomas Sjödin (Y,Yi, MED,Mat,FyN,FRIST)
Link to the course homepage at the department


Course Syllabus in Swedish

Linköping Institute of Technology

 


Contact: TFK , val@tfk.liu.se
Last updated: 02/02/2017