Study Guide

Objective

After completing the course the student can
- use derivatives to analyze functions
- use differentials to approximate changes and errors
- use integrals to calculate e.g. areas and volumes, mean values and square mean values
- solve integrable and 1. order separable differential equations
- use relevant mathematical denotation correctly

Content

- Limits
- The derivative
- Differentials
- Antiderivatives and the definite integral
- Applications of differentiation and integration
- On differential equations

Materials

1. Calculus (3rd edition), Fred Safier, SCHAUM’S outlines.
2. Engineering Mathematics (6th edition), K.A. Stroud [MACMILLAN PRESS LTD]
3. Formula book: Technical formulas

Teaching methods

Teacher-directed classroom activities, group work and independent work; project work, reports, task-based (homework)

International connections

The contents of the course give understanding to use the derivatives to analyze functions, use differentials to approximate changes and errors, solve separable and linear first order differential equations, use integrals to calculate e.g. areas and mean values and square mean values of functions and use relevant mathematical denotation correctly, moreover the students can use relevant mathematical denotation correctly.
The students will team up for a project work and writing reports on some current and relevant aspect of math, which gives everyone an opportunity to understand the topic; all students will develop their mathematical proficiency.
Task-based assessment supports learning and is continuous throughout the course. Studying in an international group develops students’ ability to intercultural communication and multicultural collaboration.

Student workload

Classroom activities: Classroom activities participation: 50 h
Homework: Working on homework sets 1-6: 30 h
Project work: Research, presentation material, presentation: 20h
Final exam: Preparing for the final exam : 25 h

Content scheduling

• Limits
• The derivative
• Differentials
• Antiderivatives and the definite integral
• Applications of differentiation and integration
• On differential equations

Further information

All practical information on timetables, project work, grading etc., as well as links to web materials are provided in ITS Learning

Evaluation scale

H-5

Assessment methods and criteria

Assessment Method
1. 30% of the homework is MANDATORY and students can get points if they do more than 50%.

2. Points distributed as follow:
i. First Exam = 20 points
ii. Second Exam = 20 points
iii. Homework =10 points
Total = 50 points

Assessment criteria, fail (0)

Fail in the final exam and not doing the assignments.
collect (0--20) points

Assessment criteria, satisfactory (1-2)

Collect (20--32) points in the exams and doing more 50% of the assignments.

Assessment criteria, good (3-4)

Collect (32--44) points in the exams and doing at least 75% of the assignments

Assessment criteria, excellent (5)

Collect (44--50) points in the exam and doing at least 85% of the assignments

Qualifications

Precalculus course or equivalent skills

Objective

After completing the course the student can
- use derivatives to analyze functions
- use differentials to approximate changes and errors
- use integrals to calculate e.g. areas and volumes, mean values and square mean values
- solve integrable and 1. order separable differential equations
- use relevant mathematical denotation correctly

Content

- Limits
- The derivative
- Differentials
- Antiderivatives and the definite integral
- Applications of differentiation and integration
- On differential equations

Materials

ITSL-alustalta löytyvä luento- ja tehtävämateriaali.

Teaching methods

Lähiopetus-luennot.
Tehtävien tekeminen yksin ja ryhmässä.
Kokeet

Exam schedules

Kaksi osakoetta.
OSAKOE1 on puolessa välissä kurssia oppituntien 1-12 jälkeen. Yksi uusinta.
OSAKOE2 on kurssin lopussa oppituntien 13-22 jälkeen. Yksi uusinta.
Kurssin päätyttyä kummankin osakokeen voi uusia vielä yhden kerran.

Student workload

Luennot 22*2h
Laskuharjoitukset 22*1h
Kokeet 2*2h
loppu opiskelijan itsenäistä opiskelua

Content scheduling

Differentiaalilaskenta:
1 Muutosnopeus
2 Raja-arvo
3 Derivaatan määritelmä
4 Polynomin derivointi
5 Funktion kulkukaavio
6 Derivaattafunktion kuvaaja
7 Derivointikaavoja
8 Yhdistetyn funktion derivointi
9 Potenssin derivointi
10 Eksponentin ja logaritmin derivointi
11 Derivointimenetelmiä
12 Differentiaali

Integraalilaskenta:
13 Integraalifunktio
14 Integrointikaavoja
15 Yhdistetyn funktion integrointi
16 Määrätty integraali
17 Määrätyn integraalin ominaisuuksia
18 Pinta-ala
19 Tilavuus
20 Funktion keskiarvot
21 Integroituva differentiaaliyhtälö
22 Separoituva differentiaaliyhtälö

Further information

Sähköposti.

Evaluation scale

H-5

Assessment methods and criteria

Arvosana määräytyy osakokeista saadun yhteispistemäärän (max. 20+20=40) ja kotitehtävistä saadun pistemäärän (max. 10) perusteella seuraavan taulukon mukaisesti (osakokeista täytyy saada yhteensä vähintään 16 pistettä päästäkseen läpi kurssista):

Yhteispistemäärä Arvosana
0-15: 0
16-22: 1
23-29: 2
30-35: 3
36-42: 4
43-50: 5

Assessment criteria, fail (0)

Arvosanataulukon mukaan.

Assessment criteria, satisfactory (1-2)

Arvosanataulukon mukaan.

Assessment criteria, good (3-4)

Arvosanataulukon mukaan.

Assessment criteria, excellent (5)

Arvosanataulukon mukaan.

Qualifications

Precalculus course or equivalent skills

Objective

After completing the course the student can
- use derivatives to analyze functions
- use differentials to approximate changes and errors
- use integrals to calculate e.g. areas and volumes, mean values and square mean values
- solve integrable and 1. order separable differential equations
- use relevant mathematical denotation correctly

Content

- Limits
- The derivative
- Differentials
- Antiderivatives and the definite integral
- Applications of differentiation and integration
- On differential equations

Materials

Kirja: Tuomenlehto, Holmlund et al.: Insinöörin matematiikka. Edita 2018.
Itslearningin kautta jaettava muu materiaali.

Teaching methods

lähiopetus, tehtäväperustaisuus, itsenäinen opiskelu

Exam schedules

Osakokeet 1-3 oppitunneilla, ajankohdat ilmoitetaan kurssin aikana Itslearningissä. Tarvittaessa järjestetään uusintatentti.

International connections

Opintojaksolla opiskellaan matemaattisia perustaitoja, jotka ovat insinöörityön perusta.

Completion alternatives

Kotitehtävät ja osakokeet (tai kurssin jälkeinen uusintatentti)

Student workload

Lähiopetusta n. 90 h.
Itsenäistä työskentelyä (opiskelumateriaali, tehtävät, osakokeisiin valmistautuminen) 45 h.
Yhteensä 135 h.

Content scheduling

- Raja-arvo
- Derivaatta
- Differentiaali
- Määräämätön ja määrätty integraali
- Differentiaali- ja integraalilaskennan sovelluksia
- Differentiaaliyhtälöistä

2x2h luento + 2h laskuharjoitus viikottain, 15 viikkoa

Further information

Edeltävyysehdot: Insinöörimatematiikan perusteet tai vastaavat tiedot ja taidot

Evaluation scale

H-5

Assessment methods and criteria

Arvosana perustuu osakokeiden pistemääriin. Osakokeiden pistemäärää voi lisätä tekemällä kotitehtäviä. Itslearning alustalla julkaistaan taulukko, jonka perusteella suoritukset muutetaan kurssiarvosanaksi.

Qualifications

Precalculus course or equivalent skills

Objective

After completing the course the student can
- use derivatives to analyze functions
- use differentials to approximate changes and errors
- use integrals to calculate e.g. areas and volumes, mean values and square mean values
- solve integrable and 1. order separable differential equations
- use relevant mathematical denotation correctly

Content

- Limits
- The derivative
- Differentials
- Antiderivatives and the definite integral
- Applications of differentiation and integration
- On differential equations

Materials

1. Calculus (3rd edition), Fred Safier, SCHAUM’S outlines.
2. Engineering Mathematics (6th edition), K.A. Stroud [MACMILLAN PRESS LTD]
3. Formula book: Technical formulas

Teaching methods

Teacher-directed classroom activities, group work and independent work; project work, reports, task-based (homework

International connections

The contents of the course give understanding to use the derivatives to analyze functions, use differentials to approximate changes and errors, solve separable and linear first order differential equations, use integrals to calculate e.g. areas and mean values and square mean values of functions
and use relevant mathematical denotation correctly, moreover the students can use relevant mathematical denotation correctly.
The students will team up for a project work and writing reports on some current and relevant aspect of math, which gives everyone an opportunity to understand the topic; all students will develop their mathematical proficiency.
Task-based assessment supports learning and is continuous throughout the course. Studying in an international group develops students’ ability to intercultural communication and multicultural collaboration.

Student workload

Classroom activities: Classroom activities participation: 50 h
Homework: Working on homework sets 1-6: 30 h
Project work: Research, presentation material, presentation: 20h
Final exam: Preparing for the final exam : 25 h

Content scheduling

• Limits
• The derivative
• Differentials
• Antiderivatives and the definite integral
• Applications of differentiation and integration
• On differential equations

Further information

All practical information on timetables, project work, grading etc., as well as links to web materials are provided in Optim

Evaluation scale

H-5

Assessment methods and criteria

Homework sets 1-6: 30 %: Total of thirty homework exercises based on reading material and classroom notes: diagnostic/formative self / teacher evaluation
in connection with each homework set return session.
Project work, reports, presentations: 40 % : Each outcome of the project work is assessed independently (assessment criteria is specified in Optima): peer feedback summative teacher feedback at the end of the course.
Final exam: 30 %: A written exam (1,5 hrs) on specified material: Summative teacher evaluation at the end of the course

Assessment criteria, fail (0)

Fail in the final exam and not doing the assignments.

Assessment criteria, satisfactory (1-2)

Collect (50--60) points in the exam and doing 50% of the assignments.

Assessment criteria, good (3-4)

Collect (70--80) points in the exam and doing at least 75% of the assignments

Assessment criteria, excellent (5)

Collect (90--100) points in the exam and doing at least 90% of the assignments

Qualifications

Precalculus course or equivalent skills

Objective

After completing the course the student can
- use derivatives to analyze functions
- use differentials to approximate changes and errors
- use integrals to calculate e.g. areas and volumes, mean values and square mean values
- solve integrable and 1. order separable differential equations
- use relevant mathematical denotation correctly

Content

- Limits
- The derivative
- Differentials
- Antiderivatives and the definite integral
- Applications of differentiation and integration
- On differential equations

Evaluation scale

H-5

Qualifications

Precalculus course or equivalent skills

Objective

After completing the course the student can
- use derivatives to analyze functions
- use differentials to approximate changes and errors
- use integrals to calculate e.g. areas and volumes, mean values and square mean values
- solve integrable and 1. order separable differential equations
- use relevant mathematical denotation correctly

Content

- Limits
- The derivative
- Differentials
- Antiderivatives and the definite integral
- Applications of differentiation and integration
- On differential equations

Materials

1. Calculus (3rd edition), Fred Safier, SCHAUM’S outlines.
2. Engineering Mathematics (6th edition), K.A. Stroud [MACMILLAN PRESS LTD]
3. Formula book: Technical formulas

Teaching methods

Teacher-directed classroom activities, group work and independent work; project work, reports, task-based (homework

International connections

The contents of the course give understanding to use the derivatives to analyze functions, use differentials to approximate changes and errors, solve separable and linear first order differential equations, use integrals to calculate e.g. areas and mean values and square mean values of functions
and use relevant mathematical denotation correctly, moreover the students can use relevant mathematical denotation correctly.
The students will team up for a project work and writing reports on some current and relevant aspect of math, which gives everyone an opportunity to understand the topic; all students will develop their mathematical proficiency.
Task-based assessment supports learning and is continuous throughout the course. Studying in an international group develops students’ ability to intercultural communication and multicultural collaboration.

Student workload

Classroom activities: Classroom activities participation: 50 h
Homework: Working on homework sets 1-6: 30 h
Project work: Research, presentation material, presentation: 20h
Final exam: Preparing for the final exam : 25 h

Content scheduling

• Limits
• The derivative
• Differentials
• Antiderivatives and the definite integral
• Applications of differentiation and integration
• On differential equations

Further information

All practical information on timetables, project work, grading etc., as well as links to web materials are provided in Optim

Evaluation scale

H-5

Assessment methods and criteria

Homework sets 1-6: 30 %: Total of thirty homework exercises based on reading material and classroom notes: diagnostic/formative self / teacher evaluation
in connection with each homework set return session.
Project work, reports, presentations: 40 % : Each outcome of the project work is assessed independently (assessment criteria is specified in Optima): peer feedback summative teacher feedback at the end of the course.
Final exam: 30 %: A written exam (1,5 hrs) on specified material: Summative teacher evaluation at the end of the course

Assessment criteria, fail (0)

Fail in the final exam and not doing the assignments.

Assessment criteria, satisfactory (1-2)

Collect (50--60) points in the exam and doing 50% of the assignments.

Assessment criteria, good (3-4)

Collect (70--80) points in the exam and doing at least 75% of the assignments

Assessment criteria, excellent (5)

Collect (90--100) points in the exam and doing at least 90% of the assignments

Qualifications

Precalculus course or equivalent skills