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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 13 Vecka 32-52 for single courses students

  • 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>

Autumn 13 Vecka 36-52 for single courses students

  • 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>

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>

  • Application

    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

  • 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>

Spring 14 Vecka 22-33 for single courses students - To application

  • Periods

    Spring 14 P4 (0.5 credits), P5 (2.5 credits)

  • Application code

    40004

  • Start date

    26/05/2014

  • End date

    2014 week: 33

  • 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.

  • Application

    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 14 Vecka 23-33 for single courses students - To application

  • Periods

    Spring 14 P4 (0.5 credits), P5 (2.5 credits)

  • Application code

    40005

  • Start date

    02/06/2014

  • End date

    2014 week: 33

  • 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.

  • Application

    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 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

  • 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.

Spring 13 Vecka 23-35 for single courses students

  • 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.

  • Schedule

    Schedule (new window)

  • Course responsible

    Tommy Ekola <ekola@kth.se>

Spring 13 Vecka 25-35 for single courses students

  • 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>

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.