SF1652 Introductory Course in Mathematics 2 3.0 credits

Förberedande kurs i matematik 2

Educational level First cycle Academic level (A-D) A
Subject area Mathematics
Techonology
Grade scale P, F

Course offerings

Autumn 12 Vecka 31-52 for single courses students

Periods Autumn 12 P0 (0.5 credits), P1 (1.0 credits), P2 (1.5 credits) Application code 10001
Start date 30/07/2012 End date 2012 week: 52
Language of instruction Swedish Campus -
Number of lectures Number of exercises
Tutoring time Daytime Form of study IT based distance
Number of places * 5 - 999
*) The Course date may be cancelled if number of admitted are less than minimum of places. If there are more applicants than number of places selection will be made.

Autumn 12 Vecka 36-52 for single courses students

Periods Autumn 12 P1 (1.5 credits), P2 (1.5 credits) Application code 10049
Start date 03/09/2012 End date 2012 week: 52
Language of instruction Swedish Campus -
Number of lectures Number of exercises
Tutoring time Daytime Form of study IT based distance
Number of places * 5 - 999
*) The Course date may be cancelled if number of admitted are less than minimum of places. If there are more applicants than number of places selection will be made.

Autumn 12 Vecka 45-52 for single courses students

Periods Autumn 12 P2 (3.0 credits) Application code 10048
Start date 05/11/2012 End date 2012 week: 52
Language of instruction Swedish Campus -
Number of lectures Number of exercises
Tutoring time Daytime Form of study IT based distance
Number of places * 5 - 999
*) The Course date may be cancelled if number of admitted are less than minimum of places. If there are more applicants than number of places selection will be made.

Spring 13 Vecka 05-24 for single courses students

Periods Spring 13 P3 (1.0 credits), P4 (1.0 credits), P5 (1.0 credits) Application code 20050
Start date 28/01/2013 End date 2013 week: 24
Language of instruction Swedish Campus -
Number of lectures Number of exercises
Tutoring time Daytime Form of study IT based distance
Number of places * 5 - 999
*) The Course date may be cancelled if number of admitted are less than minimum of places. If there are more applicants than number of places selection will be made.

Spring 13 Vecka 13-24 for single courses students

Periods Spring 13 P4 (1.5 credits), P5 (1.5 credits) Application code 20051
Start date 25/03/2013 End date 2013 week: 24
Language of instruction Swedish Campus -
Number of lectures Number of exercises
Tutoring time Daytime Form of study IT based distance
Number of places * 5 - 999
*) The Course date may be cancelled if number of admitted are less than minimum of places. If there are more applicants than number of places selection will be made.
Course responsible Tommy Ekola <ekola@kth.se>

Spring 13 Vecka 22-34 for single courses students - To application

Periods Spring 13 P5 (3.0 credits) Application code 20070
Start date 27/05/2013 End date 2013 week: 34
Language of instruction Swedish Campus -
Number of lectures Number of exercises
Tutoring time Daytime Form of study IT based distance
Number of places * 5 - 999
*) The Course date may be cancelled if number of admitted are less than minimum of places. If there are more applicants than number of places selection will be made.
Apply for this course at antagning.se through this application link.
Please note that you need to log in at antagning.se to finalize your application.

Spring 13 Vecka 23-35 for single courses students - To application

Periods Spring 13 P5 (3.0 credits) Application code 40014
Start date 03/06/2013 End date 2013 week: 35
Language of instruction Swedish Campus -
Number of lectures Number of exercises
Tutoring time Daytime Form of study IT based distance
Number of places * 5 - 999
*) The Course date may be cancelled if number of admitted are less than minimum of places. If there are more applicants than number of places selection will be made.
Course responsible Tommy Ekola <ekola@kth.se>
Apply for this course at antagning.se through this application link.
Please note that you need to log in at antagning.se to finalize your application.

Spring 13 Vecka 25-35 for single courses students - To application

Periods Spring 13 P5 (3.0 credits) Application code 40015
Start date 17/06/2013 End date 2013 week: 35
Language of instruction Swedish Campus -
Number of lectures Number of exercises
Tutoring time Daytime Form of study IT based distance
Number of places * 5 - 999
*) The Course date may be cancelled if number of admitted are less than minimum of places. If there are more applicants than number of places selection will be made.
Course responsible Tommy Ekola <ekola@kth.se>
Apply for this course at antagning.se through this application link.
Please note that you need to log in at antagning.se to finalize your application.

Autumn 13 Vecka 32-52 for single courses students - To application

Periods Autumn 13 P0 (0.5 credits), P1 (1.5 credits), P2 (1.0 credits) Application code 40041
Start date 05/08/2013 End date 2013 week: 52
Language of instruction Swedish Campus -
Number of lectures Number of exercises
Tutoring time Daytime Form of study IT based distance
Number of places * 5 - 999
*) The Course date may be cancelled if number of admitted are less than minimum of places. If there are more applicants than number of places selection will be made.
Course responsible Tommy Ekola <ekola@kth.se>
Apply for this course at antagning.se through this application link.
Please note that you need to log in at antagning.se to finalize your application.

Autumn 13 Vecka 36-52 for single courses students - To application

Periods Autumn 13 P1 (1.5 credits), P2 (1.5 credits) Application code 10048
Start date 02/09/2013 End date 2013 week: 52
Language of instruction Swedish Campus -
Number of lectures Number of exercises
Tutoring time Daytime Form of study IT based distance
Number of places * 5 - 999
*) The Course date may be cancelled if number of admitted are less than minimum of places. If there are more applicants than number of places selection will be made.
Course responsible Tommy Ekola <ekola@kth.se>
Apply for this course at antagning.se through this application link.
Please note that you need to log in at antagning.se to finalize your application.

Autumn 13 Vecka 45-52 for single courses students - To application

Periods Autumn 13 P2 (3.0 credits) Application code 10049
Start date 04/11/2013 End date 2013 week: 52
Language of instruction Swedish Campus -
Number of lectures Number of exercises
Tutoring time Daytime Form of study IT based distance
Number of places * 5 - 999
*) The Course date may be cancelled if number of admitted are less than minimum of places. If there are more applicants than number of places selection will be made.
Course responsible Tommy Ekola <ekola@kth.se>
Apply for this course at antagning.se through this application link.
Please note that you need to log in at antagning.se to finalize your application.

Autumn 13 Vecka 28-35 for single courses students - To application

Periods Autumn 13 P0 (2.0 credits), P1 (1.0 credits) Application code 40032
Start date 08/07/2013 End date 2013 week: 35
Language of instruction Swedish Campus -
Number of lectures Number of exercises
Tutoring time Daytime Form of study IT based distance
Number of places * 5 - 999
*) The Course date may be cancelled if number of admitted are less than minimum of places. If there are more applicants than number of places selection will be made.
Course responsible Tommy Ekola <ekola@kth.se>
Apply for this course at antagning.se through this application link.
Please note that you need to log in at antagning.se to finalize your application.

Learning outcomes

This course is the continuation of SF1651 Introductory Course in Mathematics and consists of three main parts each worth 1 credit.The sections go through some of the basic knowledge important to have fully updated for upcoming higher education studies. The course is web based and flexible, i.e. the student studies in a pace that suits him or her best.

After the course the student should be able to;

  • Understand the derivative as the slope of an integral
  • Understanding the derivative as the instantaneous rate of change of a physical quantity
  • Know that the derivative can be characterized with f´or df/dx and that there are functions that are not derivable
  • Derivate xa, ln x, ex, cos x, sin x, tan x and sums/differences of such terms
  • Decide the tangent and normal of an integral
  • In principle derivate any elementary function 
  • Understand the definition of strictly increasing function, strictly decreasing function, local maximum, local minimum, global maximum, global minimum
  • Decide the areas where a function is strictly increasing and decreasing by studying the derivatives character
  • Decide the local maximum and minimum points and terrace point by studying the character of the derivative
  • Sketch the function curve by making a character table of the derivative
  • Know where the local/global maximum and minimum points occur
  • Decide local maximum and minimum points character by looking at the character of the second order derivative
  • Interpret integrals as area and understand other interpretations of integrals
  • Decide primitive function for and decided integral of xa, l/x, ex, cos x, sin x and the sum/difference of such terms
  • Calculate the area under a curve and between two curves
  • Know that some functions primitive functions can’t be described as a analytically closed expression, e.g. ex², (sin x)/x, sin sin x
  • Understand the origin of the formula for variable substitution
  • Solve simpler integration problems which need rewriting and/or substitution in one step
  • Describe how the integration boundaries change during variable substitution and when a variable substitution is allowed
  • Understand the origin of the formula for partial integration
  • Solve integration problems which need partial integration in one or two steps
  • Solve integration problems which need partial integration followed by a substitution (or the other way round)
  • Calculate expressions that contain complex numbers and are built up of the four rules of arithmetic
  • Solve complex first degree equations
  • Transform some complex numbers between the form a+ib and polar form
  • Calculate powers of complex numbers with de Moivres formula
  • Calculate roots of some complex numbers by rewriting them into polar form
  • Solve bionomic equations
  • Completing the square of complex second degree expressions
  • Solve complex second degree equations and factorize complex second degree expressions
  • Perform polynomial division
  • Understand the connection between factors and zero of polynomial
  • Know that a polynomial equation of degree n has n roots (counted with multiplicity)
  • Know that real polynomial equations have conjugated roots

Course main content

  • Derivatives
    Introduction, rules of differentiation, maximum and minimum problems
  • Integrals
    Introduction, variable substitution, partial integration
  • Complex numbers
    Calculations with complex numbers, polar form, exponentiation and roots, complex polynomials

Eligibility

  • General requirements i.e. completed upper secondary education including documented proficiency in Swedish and English (for courses given in Swedish) or including documented proficiency in English (for courses given in English).
  • Specific requirements: knowledge of Mathematics corresponding to Mathematics C

Literature

Elektroniskt kursmaterial som ligger gratis åtkomligt på nätet för den som anmäler sig till kursen.

Examination

  • TEN1 - Examination, 1.0 credits, grade scale: P, F
  • TEN2 - Examination, 1.0 credits, grade scale: P, F
  • TEN3 - Examination, 1.0 credits, grade scale: P, F

Offered by

SCI/Mathematics

Contact

RCN, info@rcn.kth.se

Examiner

Roy M Skjelnes <skjelnes@kth.se>

Version

Course plan valid from: Spring 13.
Examination information valid from: Autumn 07.