Study Guide@lith
 

Linköping Institute of Technology

 
 
Valid for year : 2017
 
TNA004 Calculus II, 6 ECTS credits.
/Analys II/

For:   ED   KTS   MT  

 

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
  • explain Taylors formula and the concepts series, power series and convergence of series.
  • make comparisons metween sums and integrals
  • use expressions for, and calculate, geometrical quantities such as plane areas, arc length, surface area, volumes of solids of revolution and areas of surfaces of revolution
  • utilize ordinary differential equations (linear of first order: linear and separable and linear equations of higher order with constant coefficients, serie solutions) and integral equations
  • use Taylors Theorem in approximating functions with polynomial, calculating limits and estimation errors and estimate local properties of functions.
  • carry out convergence tests for improper integrals, series and power series and find derivatives and antiderivatives for power series
  • 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)
Analysis I

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.

Organisation:
Lectures and problem classes.

Course contents:
Applications of integrals - Improper integrals: definition and calculations, area, length of curves, volume of solids of revolution, area of surfaces of revolution. Generalised integrals. Estimation of sums. The formulas of Taylor and Maclaurin. The Maclaurin expansion of elementary functions. Applications, e.g. estimation of errors and finding limits. Ordinary differential equations. Equations of the first order: linear and separable equations. Integral equations. Linear equations of higher order with constant coefficients. Serie solutions. Applications will be given of mathematical models from various fields. Series.

Course literature:
Forsling, G. and Neymark, N.: Matematisk analys, en variabel. Liber.

Examination:
Written examination
6 ECTS
 



Course language is Swedish.
Department offering the course: ITN.
Director of Studies: George Baravdish
Examiner: Sixten Nilsson
Link to the course homepage at the department


Course Syllabus in Swedish

Linköping Institute of Technology

 


Contact: TFK , val@tfk.liu.se
Last updated: 05/30/2017