CalculusLaajuus (5 cr)
Code: TE00BX68
Credits
5 op
Objective
Student understands the basic of calculus and is able to
• Apply the derivative to analyze functions
• Apply differentials for error calculations
• Apply the definite integrals, e.g., in calculation of area or average
• Apply differential equations for modeling phenomena within engineering framework
Content
• Limit of a function
• Derivative function
• Differentials
• Integral function
• Definite integral
• Separable differential equations
• Linear differential equations
Enrollment
30.05.2024 - 01.09.2024
Timing
02.09.2024 - 18.12.2024
Number of ECTS credits allocated
5 op
Mode of delivery
Contact teaching
Unit
Engineering and Business
Campus
Kupittaa Campus
Teaching languages
- Finnish
Seats
0 - 50
Degree programmes
- Degree Programme in Energy and Environmental Technology
Teachers
- Tuomas Nurmi
- COS Opettaja
Groups
-
PEYTES23A
Objective
Student understands the basic of calculus and is able to
• Apply the derivative to analyze functions
• Apply differentials for error calculations
• Apply the definite integrals, e.g., in calculation of area or average
• Apply differential equations for modeling phenomena within engineering framework
Content
• Limit of a function
• Derivative function
• Differentials
• Integral function
• Definite integral
• Separable differential equations
• Linear differential equations
Materials
Tuomenlehto, Holmlund et al.: Insinöörin matematiikka. Edita.
Itslearning-sivujen kautta jaettava muu materiaali.
Teaching methods
Sulautuva oppiminen, lähiopetus, tehtäväperustaisuus, itsenäinen opiskelu, tiimityö
Opintojaksolla opiskellaan matemaattisia perustaitoja, jotka ovat insinöörityön perusta. Esimerkit ja tehtävät sisältävät alakohtaisia sovellusesimerkkejä. Opintojaksolla käytetään englanninkielistä lähdemateriaalia ja tutustutaan kansainvälisiin matematiikan merkintätapoihin ja terminologiaan, mikä antaa opiskelijoille valmiuksia ymmärtää kansainvälistä insinöörialan kirjallisuutta, standardeja yms. Tehtävien ratkomisessa opiskelijoita kannustetaan tiimityöskentelyyn. Opintojaksolla käytetään monipuolisesti digitaalista opiskelumateriaalia ja sähköistä oppimisympäristöä.
Exam schedules
-Kaksi osakoetta opintojakson aikana, ajankohdat ilmoitetaan Itslearning-sivuilla.
-Opintojakson päätyttyä kaksi uusintakoetta, joissa voi uusia valinnaisesti kumman tahansa osakokeista.
International connections
Opintojakso toteutetaan lähiopetuksena kampuksella. Kurssi etenee viikkoteemoittan seuraavasti:
1. Opiskelijat tutustuvat itsenäisesti teeman aihepiiriin oppikirjan, opettajan tekemien opetusvideoiden ja erilaisten tukimateriaalien avulla (jaetaan Itslearningissä). Opettajan tekemät opetusvideot toimivat opintojakson luentoina.
2. Opiskelijat harjoittelevat viikkoteeman asioita tekemällä laskuharjoituksia itsenäisesti ja pienryhmissä.
3. Viikoittain, yleensä torstaisin, on laskuharjoitustilaisuus, jossa opettaja ohjaa laskuissa ja neuvoo avoimeksi jääneissä kysymyksissä. Opiskelijat viimeistelevät laskuharjoituksensa tässä tilaisuudessa. Valmiit laskuharjoitukset palautetaan esittelemällä ne laskuharjoitustilaisuudessa opettajalle aikataulun mukaisesti.
4. Opettaja julkaisee malliratkaisut tehtäviin.
Student workload
Kurssin laajuus on 5 op, eli siihen kuuluva työmäärä on noin 135 h.
Kokeisiin ja niihin valmistautumiseen tarvitaan noin 18 h. Täten kurssin 13 viikkoteemaa varten on käytettävissä 117 h eli 9 h viikkoteemaa kohti, mikä jakautuu seuraavasti:
-Itsenäinen työskentely ja ryhmätyöskentely 6 h.
-Opetustilaisuuteen osallistuminen 3 h.
Content scheduling
Aloitusluento 2.9. Lähiopetusta noin kerran viikossa viikkoteemoittain ryhmiteltynä viikoilla 36-51. Tarkempi aikataulu kurssin Itslearning-sivuilla.
Further information
Esitietona tarvitaan opintojakso Insinöörimatematiikan perusteet tai vastaavat tiedot ja taidot.
Evaluation scale
H-5
Assessment methods and criteria
Arviointi perustuu pisteisiin, joita kerätään laskuharjoituksista (max 10 p.) ja osakokeista (max 2*15 p.). Kurssin läpäistääkseen opiskelijan on saatava
-Kummastakin osakokeesta vähintään 4 pistettä ja
-Osakokeista ja laskuharjoituksista yhteensä vähintään 16 pistettä.
LASKUHARJOITUKSISTA SAATAVIEN PISTEIDEN MÄÄRÄYTYMINEN:
--Laskuharjoituksista saatavien hyvityspisteiden määrä = 10*palautettujen tehtävien osuus.
ARVOSANAN MÄÄRÄYTYMINEN:
Arvosana määräytyy pisteiden perusteella (osakokeiden ja laskuharjoitusten yhteispisteet) seuraavan taulukon mukaan:
Arvosana 1 vaatii 16 pistettä
Arvosana 2 vaatii 21 pistettä
Arvosana 3 vaatii 26 pistettä
Arvosana 4 vaatii 31 pistettä
Arvosana 5 vaatii 36 pistettä
Enrollment
01.12.2023 - 05.01.2024
Timing
08.01.2024 - 30.04.2024
Number of ECTS credits allocated
5 op
Mode of delivery
Contact teaching
Unit
Engineering and Business
Teaching languages
- English
Degree programmes
- Degree Programme in Biotechnology and Chemical Engineering
- Degree Programme in Chemical and Materials Engineering
- Degree Programme in Energy and Environmental Technology
Teachers
- Aaro Mustonen
Groups
-
PENERS23Energy and Environmental Engineering, S23
Objective
Student understands the basic of calculus and is able to
• Apply the derivative to analyze functions
• Apply differentials for error calculations
• Apply the definite integrals, e.g., in calculation of area or average
• Apply differential equations for modeling phenomena within engineering framework
Content
• Limit of a function
• Derivative function
• Differentials
• Integral function
• Definite integral
• Separable differential equations
• Linear differential equations
Materials
The course follows the contents of Calculus 1 on the Open Stax website (https://openstax.org/details/books/calculus-volume-1)
In addition, the course uses other material presented online and during contact teaching sessions.
The MATLAB programme is also used during the course, so the student should have access to a personal computer.
The Finnish support book is "Insinöörin matematiikka, Tuomenlehto et.al."
Teaching methods
Methods supporting the construction of the student's own knowledge:
Contact teaching, online learning, collaborative learning, independent work.
The completion of exercises plays a key role in learning, and group work is encouraged in this respect.
Exam schedules
Subtests in weeks 9 and 17.
International connections
Learning methods that support the student's own activity and construction of knowledge
Student workload
- Theoretical areas and calculation exercises approx. 60 h
- Intermediate tests measuring competence 2 x 2 h (or final exam 2 h)
- Independent practical training approximately 70 h (approximately 4 hours/week + practical training for tests/tests)
Content scheduling
The basics of differential and integral calculations and differential equations are discussed in the course. In addition, the pupils familiarise themselves with complex numbers and limit values. The aim is to expand the basis of mathematical thinking needed in engineering studies and tasks as well as the ability to read and use the language of mathematics in professional contexts. In addition, the aim is to familiarise yourself with the use of MATLAB software in modelling and solving mathematical problems. The aim of the course is to use as many examples of engineering work as possible.
More detailed content:
- complex numbers and their applications
- limit values and definition of derivative
- derivation calculation rules
- the concept of differential
- deriving applications
- a specific integral and integral function
- integral calculation rules
- integrated applications
- differential equations and solving them
- differential equation applications
Evaluation scale
H-5
Assessment methods and criteria
In English
The total grade 0-5 for the course is calculated using the course points collected (max 100 points). Course points can be collected
- Two sub-tests (á max 50 p)
- Independent exercises at ViLLE (max. 6 points)
- Weekly calculation exercises (max 12 pts). A precondition for receiving the course points is returning calculation tasks in advance and a self-evaluation based on calculation lesson or model solutions, which has been returned by the normative duration of studies (usually by the end of the week).
The total number of course points collected from the exercises is 18 p, corresponding to approximately 1.5 course numbers.
Students who complete the course with intermediate exams must take both exams. If the completion of the second intermediate exam is exhausted, the course will be renewed with the exam.
Assessment criteria, fail (0)
The student does not achieve at least 40% of the course points = 40p
The student has not participated in both midterm exams.
Assessment criteria, satisfactory (1-2)
Grade 1 requires at least 40% of the course points = 40p
Grade 2 requires at least 52% of the course points = 52p
Assessment criteria, good (3-4)
A grade of 3 requires at least 40% of the course points = 64p
A grade of 4 requires at least 52% of the course points = 76p
Assessment criteria, excellent (5)
Grade 5 requires at least 88% of the course points = 88p
Enrollment
01.12.2023 - 05.01.2024
Timing
08.01.2024 - 10.05.2024
Number of ECTS credits allocated
5 op
Virtual portion
4 op
Mode of delivery
20 % Contact teaching, 80 % Distance learning
Unit
Engineering and Business
Campus
Kupittaa Campus
Teaching languages
- Finnish
Seats
60 - 90
Degree programmes
- Degree Programme in Biotechnology and Chemical Engineering
- Degree Programme in Chemical and Materials Engineering
- Degree Programme in Energy and Environmental Technology
Teachers
- Hannele Kuusisto
Groups
-
PSAHAUS23Electrical and Automation Engineering, Bachelor of Engineering
-
PEYTES23B
Objective
Student understands the basic of calculus and is able to
• Apply the derivative to analyze functions
• Apply differentials for error calculations
• Apply the definite integrals, e.g., in calculation of area or average
• Apply differential equations for modeling phenomena within engineering framework
Content
• Limit of a function
• Derivative function
• Differentials
• Integral function
• Definite integral
• Separable differential equations
• Linear differential equations
Evaluation scale
H-5
Enrollment
01.12.2022 - 16.01.2023
Timing
09.01.2023 - 28.04.2023
Number of ECTS credits allocated
5 op
Virtual portion
3 op
Mode of delivery
40 % Contact teaching, 60 % Distance learning
Unit
Engineering and Business
Campus
Kupittaa Campus
Teaching languages
- Finnish
Seats
0 - 70
Degree programmes
- Degree Programme in Biotechnology and Chemical Engineering
- Degree Programme in Chemical and Materials Engineering
- Degree Programme in Energy and Environmental Technology
Teachers
- Hannele Kuusisto
Groups
-
PEYTES22APEYTES22A
Objective
Student understands the basic of calculus and is able to
• Apply the derivative to analyze functions
• Apply differentials for error calculations
• Apply the definite integrals, e.g., in calculation of area or average
• Apply differential equations for modeling phenomena within engineering framework
Content
• Limit of a function
• Derivative function
• Differentials
• Integral function
• Definite integral
• Separable differential equations
• Linear differential equations
Evaluation scale
H-5
Enrollment
01.12.2022 - 16.01.2023
Timing
09.01.2023 - 28.04.2023
Number of ECTS credits allocated
5 op
Virtual portion
3 op
Mode of delivery
40 % Contact teaching, 60 % Distance learning
Unit
Engineering and Business
Campus
Kupittaa Campus
Teaching languages
- Finnish
Seats
0 - 70
Degree programmes
- Degree Programme in Biotechnology and Chemical Engineering
- Degree Programme in Chemical and Materials Engineering
- Degree Programme in Energy and Environmental Technology
Teachers
- Hannele Kuusisto
Groups
-
PEYTES22BPEYTES22B
Objective
Student understands the basic of calculus and is able to
• Apply the derivative to analyze functions
• Apply differentials for error calculations
• Apply the definite integrals, e.g., in calculation of area or average
• Apply differential equations for modeling phenomena within engineering framework
Content
• Limit of a function
• Derivative function
• Differentials
• Integral function
• Definite integral
• Separable differential equations
• Linear differential equations
Evaluation scale
H-5
Enrollment
01.12.2021 - 18.01.2022
Timing
10.01.2022 - 29.04.2022
Number of ECTS credits allocated
5 op
Virtual portion
3 op
Mode of delivery
40 % Contact teaching, 60 % Distance learning
Unit
Engineering and Business
Campus
Kupittaa Campus
Teaching languages
- Finnish
Seats
40 - 50
Degree programmes
- Degree Programme in Energy and Environmental Technology
Teachers
- Hannele Kuusisto
Groups
-
PEYTES21APEYTES21A
-
PEYTES21
Objective
Student understands the basic of calculus and is able to
• Apply the derivative to analyze functions
• Apply differentials for error calculations
• Apply the definite integrals, e.g., in calculation of area or average
• Apply differential equations for modeling phenomena within engineering framework
Content
• Limit of a function
• Derivative function
• Differentials
• Integral function
• Definite integral
• Separable differential equations
• Linear differential equations
Evaluation scale
H-5
Enrollment
01.12.2021 - 18.01.2022
Timing
10.01.2022 - 29.04.2022
Number of ECTS credits allocated
5 op
Virtual portion
3 op
Mode of delivery
40 % Contact teaching, 60 % Distance learning
Unit
Engineering and Business
Campus
Kupittaa Campus
Teaching languages
- Finnish
Seats
40 - 60
Degree programmes
- Degree Programme in Energy and Environmental Technology
Teachers
- Hannele Kuusisto
Groups
-
PEYTES21BPEYTES21B
-
PEYTES21
Objective
Student understands the basic of calculus and is able to
• Apply the derivative to analyze functions
• Apply differentials for error calculations
• Apply the definite integrals, e.g., in calculation of area or average
• Apply differential equations for modeling phenomena within engineering framework
Content
• Limit of a function
• Derivative function
• Differentials
• Integral function
• Definite integral
• Separable differential equations
• Linear differential equations
Evaluation scale
H-5