Mat2 FunktiotLaajuus (3 op)
Tunnus: TZLM2300
Laajuus
3 op
Opetuskieli
- suomi
- englanti
Vastuuhenkilö
- Anne Rantakaulio, TKN
- Antti Kosonen, TER, TRY, TRM
- Ida Arhosalo, TSA, TAR
- Harri Varpanen, TIC
- Pekka Varis, TTV
- Kalle Niemi, TLS, TLP
Osaamistavoitteet
Opintojakson tarkoitus
Opintojaksolla laajennat tekniikan alalla tarvittavien matemaattisten työkalujen valikoimaa perehtymällä funktion käsitteeseen ja erityyppisten funktioiden käyttöön tekniikan alan ilmiöiden mallintamisessa.
Opintojakson osaamiset
EUR-ACE: Tieto ja ymmärrys
Sinulla on tieto ja ymmärrys oman teknisen erikoistumisalasi matemaattisista ja luonnontieteellisistä perusteista tasolla, joka on tarpeen ohjelman muiden oppimistavoitteiden saavuttamiseksi.
Opintojakson osaamistavoite
Opintojakson käytyäsi ymmärrät funktion käsitteen, tunnistat funktion tyypin ja ymmärrät erityyppisten funktioiden ominaisuuksia. Osaat hyödyntää yhtälöitä funktioiden tarkastelussa. Osaat käyttää erityyppisiä funktioita yksinkertaisten tekniikan alan ilmiöiden mallintamiseen.
Sisältö
- Funktion käsite ja merkinnät
- Logaritmifunktio ja -yhtälö
- Eksponenttifunktio ja -yhtälö
- Trigonometriset funktiot: sinikäyrä
- Funktioiden käyttö mallintamiseen
- Paloittain määritellyt funktiot
- Yhdistetty funktio
- Käänteisfunktio
- Funktion raja-arvo
Esitietovaatimukset
Osaat sieventää polynomi- ja rationaalilausekkeita. Ymmärrät yhtälön käsitteen ja yhtälön yleisiä ratkaisuperiaatteita.
Arviointikriteerit, tyydyttävä (1)
Arvosana 1
Ymmärrät funktion käsitteen ja merkinnät. Tunnistat perusmuotoiset alkeisfunktiot. Osaat tutkia funktion käyttäytymistä apuvälineen avulla. Osaat ratkaista perustehtäviä mallin avulla.
Arvosana 2
Ymmärrät funktion käsitteen ja merkinnät. Tunnistat perusmuotoiset alkeisfunktiot. Tiedät funktiotyyppien perusominaisuuksia. Osaat itsenäisesti ratkoa perusmuotoisia tehtäviä. Käytät merkintöjä ja käsitteitä vielä epävarmasti.
Arviointikriteerit, hyvä (3)
Arvosana 3
Osaat funktioihin liittyvät käsitteet ja merkinnät. Osaat tutkia funktion kuvaajaa funktion lausekkeen perusteella ja piirtää funktion kuvaajan ilman apuvälinettä. Osaat ratkaista funktioihin liittyvät yhtälöt ja mallintaa yksinkertaisia ilmiöitä funktiolla.
Arvosana 4
Osaat analysoida eri funktiotyyppien ominaisuuksia myös symbolimuotoisilla funktioilla. Käyttämäsi merkinnät ovat selkeitä ja perusteltuja. Ratkaiset virheettömästi funktioihin liittyviä yhtälöitä. Osaat mallintaa ilmiöitä funktiolla, mutta soveltaminen uusissa tilanteissa on vielä epävarmaa.
Arviointikriteerit, kiitettävä (5)
Arvosana 5
Osaat analysoida eri funktiotyyppien ominaisuuksia myös symbolimuotoisilla funktioilla. Käytät oikeita, täsmällisiä merkintöjä. Ratkaiset virheettömästi funktioihin liittyviä luku- ja symbolikertoimisia yhtälöitä. Osaat mallintaa ilmiöitä funktioilla ja soveltaa oppimaasi myös uusissa tilanteissa.
Lisätiedot
Opintojakso antaa hyviä matemaattisia valmiuksia myös muun korkeakoulualan kuin teknisen alan opintoja varten. Opintojakso on tarjolla myös polkuopinnoissa ja avoimessa ammattikorkeakoulussa.
Enrollment
20.11.2023 - 14.01.2024
Timing
11.03.2024 - 26.04.2024
Number of ECTS credits allocated
3 op
Mode of delivery
Face-to-face
Unit
School of Technology
Campus
Main Campus
Teaching languages
- English
Seats
0 - 30
Degree programmes
- Bachelor's Degree Programme in Purchasing and Logistics Engineering
Teachers
- Kalle Niemi
Groups
-
TLP23VSBachelor's Degree Programme in Purchasing and Logistics Engineering (AMK) vaihto-opiskelu/Exchange studies
-
TLP24VKBachelor's Degree Programme in Purchasing and Logistics Engineering (AMK) vaihto-opiskelu/Exchange studies
-
ZJATLP23S1Avoin amk, Purchasing and Logistics Engineering, Päivä
-
TLP23S1Bachelor's Degree Programme in Purchasing and Logistics Engineering
Objective
Course purpose
During this course you will expand the range of mathematical tools needed in your studies in the field of technology by studying the notion of a function and the use of functions in modelling different phenomena.
Course competences
EUR-ACE: Knowledge and understanding
You have the knowledge and understanding of mathematics and other basic sciences underlying your engineering specialisation, at a level necessary to achieve the other programme learning outcomes.
Learning outcomes
After completing this course you know the notion of a function, recognise the type of a given function and understand the properties of different kinds of functions.
Content
- The notion of a function and the notation related to functions
- Logarithmic functions and equations
- Exponential functions and equations
- Trigonometric functions: the sine curve
- The use of functions in modelling
- Piecewise defined functions
- Combined functions
- Inverse functions
- Limit of a function
Location and time
Two lessons (a 90min) per week during weeks 11-16. One rehearsal lesson and exam in week 17.
Oppimateriaali ja suositeltava kirjallisuus
Free openly licensed textbooks will be used. Links will be shared in the learning environment Moodle.
Teaching methods
Weekly lessons and weekly homework exercise, independent studying from theory material (literal and videos), exams.
Exam schedules
Times of the exams will be given in the first lesson of the course.
International connections
approx. 30 h for lessons and exams
approx. 20h independent studying of theory
approx. 30h independent studying of exercises
Evaluation scale
0-5
Arviointikriteerit, tyydyttävä (1-2)
Grade 1
You understand the notion of function and the notation related to functions. You recognise basic elementary functions. You are able to analyze functions with the help of information technology. You can solve basic tasks by using a model.
Grade 2
You understand the notion of function and the notation related to functions. You recognise basic elementary functions. You know basic properties of different types of functions. You are able to independently solve basic tasks. Your use of notation is dubious.
Arviointikriteerit, hyvä (3-4)
Grade 3
You understand the notion of function and the notation related to functions. You can analyze the graph of a function by inspecting the expression of the function and draw the graph without information technology. You are able to solve necessary function-related equations and model simple problems with functions.
Grade 4
You are able to analyze the properties of different types of functions also when the functions expressions contains parameters. Your notation is clear and valid. You solve function-related equations validly. You are able to model phenomena with functions, but you apply your knowledge uncertainly in new situations.
Assessment criteria, excellent (5)
Grade 5
You are able to analyze the properties of different types of functions also when the functions expressions contains parameters. Your notation is precise. You solve function-related equations validly. You are able to model phenomena with functions and apply your knowledge in new situations.
Qualifications
You are able to simplify polynomial and rational expressions. You understand the notion of an equation and common principles to solve equations.
Further information
The course offers good mathematical competencies for studies in other fields than technology. The course is also offered in the open university of applied sciences.
Enrollment
01.11.2022 - 05.01.2023
Timing
09.01.2023 - 19.05.2023
Number of ECTS credits allocated
3 op
Mode of delivery
Face-to-face
Unit
School of Technology
Campus
Main Campus
Teaching languages
- English
Seats
0 - 30
Degree programmes
- Bachelor's Degree Programme in Purchasing and Logistics Engineering
Teachers
- Kalle Niemi
Groups
-
TLP23VKBachelor's Degree Programme in Purchasing and Logistics Engineering (AMK) vaihto-opiskelu/Exchange studies
-
TLP22S1Bachelor's Degree Programme in Purchasing and Logistics Engineering
-
ZJATLP22S1Avoin amk, Purchasing and Logistics Engineering, Päivä
-
TLP22VSBachelor's Degree Programme in Purchasing and Logistics Engineering (AMK) vaihto-opiskelu/Exchange studies
Objective
Course purpose
During this course you will expand the range of mathematical tools needed in your studies in the field of technology by studying the notion of a function and the use of functions in modelling different phenomena.
Course competences
EUR-ACE: Knowledge and understanding
You have the knowledge and understanding of mathematics and other basic sciences underlying your engineering specialisation, at a level necessary to achieve the other programme learning outcomes.
Learning outcomes
After completing this course you know the notion of a function, recognise the type of a given function and understand the properties of different kinds of functions.
Content
- The notion of a function and the notation related to functions
- Logarithmic functions and equations
- Exponential functions and equations
- Trigonometric functions: the sine curve
- The use of functions in modelling
- Piecewise defined functions
- Combined functions
- Inverse functions
- Limit of a function
Location and time
One lesson(90min) per week during weeks 2-8 and 11-16.
Oppimateriaali ja suositeltava kirjallisuus
Free openly licensed textbooks will be used. Links will be shared in the learning environment Moodle.
Teaching methods
Weekly lessons and weekly homework exercise, independent studying from theory material (literal and videos), exams.
Exam schedules
Times of the exams will be given in the first lesson of the course.
International connections
approx. 30 h for lessons and exams
approx. 20h independent studying of theory
approx. 30h independent studying of exercises
Evaluation scale
0-5
Arviointikriteerit, tyydyttävä (1-2)
Grade 1
You understand the notion of function and the notation related to functions. You recognise basic elementary functions. You are able to analyze functions with the help of information technology. You can solve basic tasks by using a model.
Grade 2
You understand the notion of function and the notation related to functions. You recognise basic elementary functions. You know basic properties of different types of functions. You are able to independently solve basic tasks. Your use of notation is dubious.
Arviointikriteerit, hyvä (3-4)
Grade 3
You understand the notion of function and the notation related to functions. You can analyze the graph of a function by inspecting the expression of the function and draw the graph without information technology. You are able to solve necessary function-related equations and model simple problems with functions.
Grade 4
You are able to analyze the properties of different types of functions also when the functions expressions contains parameters. Your notation is clear and valid. You solve function-related equations validly. You are able to model phenomena with functions, but you apply your knowledge uncertainly in new situations.
Assessment criteria, excellent (5)
Grade 5
You are able to analyze the properties of different types of functions also when the functions expressions contains parameters. Your notation is precise. You solve function-related equations validly. You are able to model phenomena with functions and apply your knowledge in new situations.
Qualifications
You are able to simplify polynomial and rational expressions. You understand the notion of an equation and common principles to solve equations.
Further information
The course offers good mathematical competencies for studies in other fields than technology. The course is also offered in the open university of applied sciences.
Enrollment
01.11.2021 - 23.01.2022
Timing
10.01.2022 - 25.02.2022
Number of ECTS credits allocated
3 op
Mode of delivery
Face-to-face
Unit
School of Technology
Campus
Main Campus
Teaching languages
- English
Seats
0 - 35
Degree programmes
- Bachelor's Degree Programme in Purchasing and Logistics Engineering
Teachers
- Kalle Niemi
Teacher in charge
Ida Arhosalo
Groups
-
TLP21S1Bachelor's Degree Programme in Purchasing and Logistics Engineering
-
TLP21VSBachelor's Degree Programme in Purchasing and Logistics Engineering (AMK) vaihto-opiskelu/Exchange studies
-
ZJA21STPPLPAvoina amk, tekniikka, Logistics and purchasing, päivä
-
TLP22VKBachelor's Degree Programme in Purchasing and Logistics Engineering (AMK) vaihto-opiskelu/Exchange studies
Objective
Course purpose
During this course you will expand the range of mathematical tools needed in your studies in the field of technology by studying the notion of a function and the use of functions in modelling different phenomena.
Course competences
EUR-ACE: Knowledge and understanding
You have the knowledge and understanding of mathematics and other basic sciences underlying your engineering specialisation, at a level necessary to achieve the other programme learning outcomes.
Learning outcomes
After completing this course you know the notion of a function, recognise the type of a given function and understand the properties of different kinds of functions.
Content
- The notion of a function and the notation related to functions
- Logarithmic functions and equations
- Exponential functions and equations
- Trigonometric functions: the sine curve
- The use of functions in modelling
- Piecewise defined functions
- Combined functions
- Inverse functions
- Limit of a function
Location and time
One lesson(90min) per week during weeks 2-16.
Oppimateriaali ja suositeltava kirjallisuus
Free openly licensed textbooks will be used. Links will be shared in the learning environment Moodle.
Teaching methods
Weekly lessons and weekly homework exercise, independent studying from theory material (literal and videos), exams.
Exam schedules
Times of the exams will be given in the first lesson of the course.
International connections
approx. 30 h for lessons and exams
approx. 20h independent studying of theory
approx. 30h independent studying of exercises
Evaluation scale
0-5
Arviointikriteerit, tyydyttävä (1-2)
Grade 1
You understand the notion of function and the notation related to functions. You recognise basic elementary functions. You are able to analyze functions with the help of information technology. You can solve basic tasks by using a model.
Grade 2
You understand the notion of function and the notation related to functions. You recognise basic elementary functions. You know basic properties of different types of functions. You are able to independently solve basic tasks. Your use of notation is dubious.
Arviointikriteerit, hyvä (3-4)
Grade 3
You understand the notion of function and the notation related to functions. You can analyze the graph of a function by inspecting the expression of the function and draw the graph without information technology. You are able to solve necessary function-related equations and model simple problems with functions.
Grade 4
You are able to analyze the properties of different types of functions also when the functions expressions contains parameters. Your notation is clear and valid. You solve function-related equations validly. You are able to model phenomena with functions, but you apply your knowledge uncertainly in new situations.
Assessment criteria, excellent (5)
Grade 5
You are able to analyze the properties of different types of functions also when the functions expressions contains parameters. Your notation is precise. You solve function-related equations validly. You are able to model phenomena with functions and apply your knowledge in new situations.
Qualifications
You are able to simplify polynomial and rational expressions. You understand the notion of an equation and common principles to solve equations.
Further information
The course offers good mathematical competencies for studies in other fields than technology. The course is also offered in the open university of applied sciences.