# SF0002 Introductory Course in Mathematics 2 3.0 credits

#### Förberedande kurs i matematik 2 ### Offering and execution

Course offering missing for current semester as well as for previous and coming semesters

## Course information

### Content and learning outcomes

#### Course contents *

• 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

#### Intended learning outcomes *

This course is the continuation of SF0001 Introductory Course in Mathematics and consists of three main parts. 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 Disposition

No information inserted

### Literature and preparations

#### Specific prerequisites *

Completed upper secondary education including documented proficiency in Swedish corresponding to Swedish 3/Swedish B  and English corresponding to English 6/English A.

#### Recommended prerequisites

No information inserted

#### Equipment

No information inserted

#### Literature

The course material will be published on the internet and is freely accessible for course participants.

### Examination and completion

P, F

#### Examination *

• INL1 - Assignment, 3.0 credits, Grading scale: P, F

Based on recommendation from KTH’s coordinator for disabilities, the examiner will decide how to adapt an examination for students with documented disability.

The examiner may apply another examination format when re-examining individual students.

The last day to submit assignments is September 15 and the last day to supplement submitted assignments is September 30.

#### Other requirements for final grade *

All computer tests and assignments passed.

#### Opportunity to complete the requirements via supplementary examination

No information inserted

#### Opportunity to raise an approved grade via renewed examination

No information inserted

### Further information

#### Course web

Further information about the course can be found on the Course web at the link below. Information on the Course web will later be moved to this site.

Course web SF0002

SCI/Mathematics

#### Main field of study *

No information inserted

#### Education cycle *

Pre-university level