| TNIU23 |
Calculus in one variable II, 6 ECTS credits.
/Envariabelanalys II /
For:
BI
FT
SL
|
| |
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:
The student should after the course be able to: - define, descirbe and combine basic analytical notions like indefinite- and definite integrals, Maclaurin- and Taylorpolynomials, differential equations,
- understand the content of most relevant theorems of analysis (like main theorem of analysis, main theorem of integral calculus, Taylor theorem),
- understand the ideas of proofs of some of these theorems,
- calculate integrals of various functions by an appropriate choice of integration method
- apply integral calculus for calculations of various geometric quantities (like area of figures or volume of three-dimensional objects) by choosing suitable methods,
- apply integral calculus for calculations of various features (like expecte value, standard deviation or quantiles) of one-dimensional continuous stochastic variables,
- approximate functions with Maclaurin- or Taylorpolynomials,
- handle some simple differential equations and apply them for mathematical modelling of simple systems.
|
|
Prerequisites: (valid for students admitted to programmes within which the course is offered)
Calculus part 1
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:
The course is given in a series of lectures and tutorials and is examined by a written exam TEN1. A bonus-point system based on an optional written test is applied.
|
|
Course contents:
Primitive functions and basic integration methods. Definite integrals and main theorem of analysis. Geomtric applications of integral calculus. Application of integrals in statistics: evaluations of expected value, standard deviation and quantiles for continous stochastic variables. Approximation of functions through Maclaurin- and Taylorexpansions. Differential equations: first order separable and linear differential equations and linear differential equations of second order.
|
|
Course literature:
Göran Forsling, Mats Neymark, �?�Matematisk analys. En variabel�?�. Förlaget: Liber AB, ISBN: 978-91-47-10023-1.
Göran Forsling, �?��-vningar i analys i en variabel�?�, Matematiska Institutionen, LiU, 2001.
|
|
Examination: |
|
Written examination
Optional written test
|
6 ECTS
0 ECTS
|
| |
|
|
Course language is Swedish.
Department offering the course: ITN.
Director of Studies: George Baravdish
Examiner: Peter Holgersson
Link to the course homepage at the department
Course Syllabus in Swedish
|