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Mat3 Derivaatta ja integraaliLaajuus (3 op)

Tunnus: TZLM3300

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
Käytyäsi tämän opintojakson hallitset muutosilmiöiden tarkastelussa tarvittavia työkaluja. Muutoksen matemaattinen tarkastelu edellyttää derivaatan ja integraalin käsitteitä. Tällä opintojaksolla opit nämä käsitteet sekä niiden soveltamista.

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 derivaatan ja integraalin käsitteet. Osaat derivoida ja integroida. Osaat ratkaista soveltavia tehtäviä derivaattaa ja integraalia hyödyntäen.

Sisältö

Derivaatta ja sen tulkinnat. Derivointisäännöt. Derivaatan soveltaminen optimointitehtävissä sekä muissa derivaattaa hyödyntävissä sovelluksissa kuten virhearvioinnissa. Integraali ja integrointisäännöt sekä integraalin erilaiset sovelluskohteet. Teknisten apuvälineiden käyttö.

Esitietovaatimukset

Tunnet raja-arvon käsitteen. Osaat laskea polynomi-, eksponentti-, logaritmi- ja trigonometrisilla funktioilla.

Arviointikriteerit, tyydyttävä (1)

1: Tunnet derivaatan merkityksen muutosnopeutena ja tangentin kulmakertoimena. Ymmärrät, kuinka derivaattaa voi käyttää yksinkertaisissa ääriarvotehtävien sovelluksissa. Osaat derivoida polynomin ilman laskinta. Tunnet integraalin pinta-alatulkinnan sekä kertymätulkinnan. Tunnet integraalin ja derivaatan yhteyden. Osaat integroida polynomin ilman laskinta.

2: Olet saavuttanut tavoitellut osaamiset (ks arvosanan 1 kriteerit). Tunnet useita käsitteitä ja menetelmiä ja osaat soveltaa niitä itsellesi tutuissa tilanteissa, mutta joskus päättelysi on puutteellista tai laskelmasi virheellisiä.

Arviointikriteerit, hyvä (3)

3: Olet saavuttanut tavoitellut osaamiset (ks arvosanan 1 kriteerit). Tunnet lähes kaikki käsitteet ja menetelmät ja osaat soveltaa niitä itsellesi tutuissa tilanteissa usein täydellisesti päätellen ja virheettömästi laskien.

4: Olet saavuttanut tavoitellut osaamiset (ks arvosanan 1 kriteerit). Tunnet lähes kaikki käsitteet ja menetelmät ja osaat soveltaa niitä myös itsellesi uusissa tilanteissa lähes aina täydellisesti päätellen ja virheettömästi laskien.

Arviointikriteerit, kiitettävä (5)

5: Olet saavuttanut tavoitellut osaamiset (ks arvosanan 1 kriteerit). Tunnet kaikki käsitteet ja menetelmät ja osaat soveltaa niitä itsellesi uusissa tilanteissa asioita yhdistellen, täydellisesti päätellen ja virheettömästi laskien.

Enrollment

01.08.2024 - 22.08.2024

Timing

02.09.2024 - 08.12.2024

Number of ECTS credits allocated

3 op

Mode of delivery

Face-to-face

Unit

School of Technology

Campus

Main Campus

Teaching languages
  • English
Seats

20 - 44

Degree programmes
  • Bachelor's Degree Programme in Purchasing and Logistics Engineering
Teachers
  • Kalle Niemi
Groups
  • TLP24VS
    Bachelor's Degree Programme in Purchasing and Logistics Engineering (AMK) vaihto-opiskelu/Exchange studies
  • TLP23S1
    Bachelor's Degree Programme in Purchasing and Logistics Engineering

Objective

The object of the course
During this course you will learn the concepts needed to study continuous change and dynamic phenomena. With differential calculus you can study instantaneous rates of change and the slopes of curves. With integral calculus you can study accumulation of quantities and areas bounded by curves. During this course you learn how to use these concepts in applications.

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.

The learning objectives of the course
After completing this course you know the meaning of derivative and integral as tools for modeling dynamic phenomena. You know how to differentiate and integrate. You know how to use the derivative and integral in applications.

Content

The derivative and its different interpretations. Rules of differentiation. Using differentiation in optimization problems and other applications involving the derivative such as estimation of error. The definite integral. Rules of integration. The applications of the integral. Using technology in calculations.

Location and time

Course is implemented between 2.9. - 8.12.

Oppimateriaali ja suositeltava kirjallisuus

Videos in the learning environment, text files, automatic tests, booklet tasks.

Teaching methods

Lectures face-to-face, guided exercises, booklet tasks, independent work, automatic tests, exam.

Exam schedules

Läpäisykoe Examissa viikolta 48 lähtien, arvosanakoe viikolla 17, uusintakoe 1 viikolla 19 ja uusintakoe 2 viikolla 21.

Student workload

Lectures, guided exercises and exam 30 h
Independent work and automatic tests 51 h

Further information

Jatkuva palaute: automaattitestit ja palautettavat tehtävät
Läpäisykoe
Arvosanakoe
Bonustehtävä

Avoin AMK 5

Evaluation scale

0-5

Arviointikriteerit, tyydyttävä (1-2)

Sufficient 1
You know the concept of the derivative as the rate of change and as the slope of the tangent. Yo understand how to apply the derivative in optimization problems. You can differentiate and integrate polynomials without technology. You know the concept of the integral as accumulation of quantities and as area under a curve. You know the relation between integral and derivative.

Satisfactory 2
You have achieved the desired goals (look at the criteria of grade 1). You know many of the concepts and methods and how to apply them in familiar situations but your reasoning is sometimes deficient or you make mistakes in calculations.

Arviointikriteerit, hyvä (3-4)

Good 3
You have achieved the desired goals(look at the criteria of grade 1). You know most of the concepts and methods and how to apply them in familiar situations showing often the ability to reason completely and calculate flawlessly

Very good 4
You have achieved the desired goals (look at the criteria of grade 1). You know most of the concepts and methods and how to apply them in new situations showing in most cases the ability to reason completely and calculate flawlessly.

Assessment criteria, excellent (5)

You have achieved the desired goals (look at the criteria of grade 1). You know all the concepts and methods and how to apply them in new situations showing always the ability to combine things, reason completely and calculate flawlessly.

Qualifications

You know the concept of a limit value. You can work with polynomial, exponential, logarithmic and trigonometric functions.

Enrollment

01.08.2023 - 24.08.2023

Timing

28.08.2023 - 19.12.2023

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
  • TLP22S1
    Bachelor's Degree Programme in Purchasing and Logistics Engineering
  • TLP23VS
    Bachelor's Degree Programme in Purchasing and Logistics Engineering (AMK) vaihto-opiskelu/Exchange studies

Objective

The object of the course
During this course you will learn the concepts needed to study continuous change and dynamic phenomena. With differential calculus you can study instantaneous rates of change and the slopes of curves. With integral calculus you can study accumulation of quantities and areas bounded by curves. During this course you learn how to use these concepts in applications.

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.

The learning objectives of the course
After completing this course you know the meaning of derivative and integral as tools for modeling dynamic phenomena. You know how to differentiate and integrate. You know how to use the derivative and integral in applications.

Content

The derivative and its different interpretations. Rules of differentiation. Using differentiation in optimization problems and other applications involving the derivative such as estimation of error. The definite integral. Rules of integration. The applications of the integral. Using technology in calculations.

Location and time

Course is implemented between 30.10. - 17.12.2023.

Oppimateriaali ja suositeltava kirjallisuus

Videos in the learning environment, text files, automatic tests, booklet tasks.

Teaching methods

Lectures face-to-face, guided exercises, booklet tasks, independent work, automatic tests, exam.

Exam schedules

Läpäisykoe Examissa viikolta 48 lähtien, arvosanakoe viikolla 17, uusintakoe 1 viikolla 19 ja uusintakoe 2 viikolla 21.

Student workload

Lectures, guided exercises and exam 30 h
Independent work and automatic tests 51 h

Further information

Jatkuva palaute: automaattitestit ja palautettavat tehtävät
Läpäisykoe
Arvosanakoe
Bonustehtävä

Avoin AMK 5

Evaluation scale

0-5

Arviointikriteerit, tyydyttävä (1-2)

Sufficient 1
You know the concept of the derivative as the rate of change and as the slope of the tangent. Yo understand how to apply the derivative in optimization problems. You can differentiate and integrate polynomials without technology. You know the concept of the integral as accumulation of quantities and as area under a curve. You know the relation between integral and derivative.

Satisfactory 2
You have achieved the desired goals (look at the criteria of grade 1). You know many of the concepts and methods and how to apply them in familiar situations but your reasoning is sometimes deficient or you make mistakes in calculations.

Arviointikriteerit, hyvä (3-4)

Good 3
You have achieved the desired goals(look at the criteria of grade 1). You know most of the concepts and methods and how to apply them in familiar situations showing often the ability to reason completely and calculate flawlessly

Very good 4
You have achieved the desired goals (look at the criteria of grade 1). You know most of the concepts and methods and how to apply them in new situations showing in most cases the ability to reason completely and calculate flawlessly.

Assessment criteria, excellent (5)

You have achieved the desired goals (look at the criteria of grade 1). You know all the concepts and methods and how to apply them in new situations showing always the ability to combine things, reason completely and calculate flawlessly.

Qualifications

You know the concept of a limit value. You can work with polynomial, exponential, logarithmic and trigonometric functions.

Enrollment

01.08.2022 - 25.08.2022

Timing

29.08.2022 - 31.10.2022

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 - 30

Degree programmes
  • Bachelor's Degree Programme in Purchasing and Logistics Engineering
Teachers
  • Ida Arhosalo
Teacher in charge

Ida Arhosalo

Groups
  • TLP22VS
    Bachelor's Degree Programme in Purchasing and Logistics Engineering (AMK) vaihto-opiskelu/Exchange studies
  • TLP21S1
    Bachelor's Degree Programme in Purchasing and Logistics Engineering

Objective

The object of the course
During this course you will learn the concepts needed to study continuous change and dynamic phenomena. With differential calculus you can study instantaneous rates of change and the slopes of curves. With integral calculus you can study accumulation of quantities and areas bounded by curves. During this course you learn how to use these concepts in applications.

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.

The learning objectives of the course
After completing this course you know the meaning of derivative and integral as tools for modeling dynamic phenomena. You know how to differentiate and integrate. You know how to use the derivative and integral in applications.

Content

The derivative and its different interpretations. Rules of differentiation. Using differentiation in optimization problems and other applications involving the derivative such as estimation of error. The definite integral. Rules of integration. The applications of the integral. Using technology in calculations.

Location and time

Two lessons (90min) per week during weeks 35-40, exam on week 41.

Oppimateriaali ja suositeltava kirjallisuus

Free openly licensed textbooks will be used. Links will be shared in the learning environment Moodle.

Teaching methods

Weekly face-to-face lessons and weekly homework exercise, independent studying from theory material (literal and videos), exams.

Employer connections

approx. 30 h for lessons and exams
approx. 50 h for independent studying.

Vaihtoehtoiset suoritustavat

Times of the exams will be given in the first lesson of the course.

Evaluation scale

0-5

Arviointikriteerit, tyydyttävä (1-2)

Sufficient 1
You know the concept of the derivative as the rate of change and as the slope of the tangent. Yo understand how to apply the derivative in optimization problems. You can differentiate and integrate polynomials without technology. You know the concept of the integral as accumulation of quantities and as area under a curve. You know the relation between integral and derivative.

Satisfactory 2
You have achieved the desired goals (look at the criteria of grade 1). You know many of the concepts and methods and how to apply them in familiar situations but your reasoning is sometimes deficient or you make mistakes in calculations.

Arviointikriteerit, hyvä (3-4)

Good 3
You have achieved the desired goals(look at the criteria of grade 1). You know most of the concepts and methods and how to apply them in familiar situations showing often the ability to reason completely and calculate flawlessly

Very good 4
You have achieved the desired goals (look at the criteria of grade 1). You know most of the concepts and methods and how to apply them in new situations showing in most cases the ability to reason completely and calculate flawlessly.

Assessment criteria, excellent (5)

You have achieved the desired goals (look at the criteria of grade 1). You know all the concepts and methods and how to apply them in new situations showing always the ability to combine things, reason completely and calculate flawlessly.

Qualifications

You know the concept of a limit value. You can work with polynomial, exponential, logarithmic and trigonometric functions.