Math3 Derivate and Integral (3 cr)

Evaluation scale

0-5

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

In this course, you will learn to master the tools needed to study phenomena of change, such as the concepts of derivatives and integrals. You will understand the meaning of these concepts and be able to apply them in practice. You will learn to derive and integrate and solve applied problems using these methods. This course will give you a strong foundation in applying mathematical methods to engineering problems.

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

Opintojakso toteutetaan viikoilla 10- 17 (8.3. - 30.4.2021) Lutakon kampuksella kontaktina Dynamolla tai etänä Zoomissa

Materials

Opintojakson pääasiallisena materiaalina toimivat opettajan jakama kirjallinen materiaali sekä videomateriaali verkko-oppimisympäristössä.

Opintojaksoon liittyvä suositeltava kirjallisuus:
- Lehtola, Rantakaulio - Tekninen matematiikka 2

Teaching methods

Kontaktiopetus 3+2 h /viikko, ohjatut laskuharjoitukset, itsenäinen työskentely

Exam schedules

Opintojakson tarkempi aikataulu sovitaan opintojakson aloitustapaamisessa ja julkaistaan verkko-oppimisympäristössä.

Completion alternatives

Mahdollisuus tenttiä kurssikokeella opintojakson alussa.

Student workload

Opintojakson laskennallinen kuormitus on 3op * 27h/op = 81h.
Kontaktiopetus noin 35h
Harjoitukset kontaktituntien ulkopuolella noin 25h
Teoriamateriaalin opiskelu, kokeisiin valmistautuminen ja kokeiden suorittaminen noin 20h

Assessment criteria, satisfactory (1)

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.

Assessment criteria, good (3)

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.

Further information

Opintojaksoon liittyy kotitehtäviä, läpäisytestejä ja koe. Opintojakso on mahdollista suorittaa arvosanalla 1 tekemällä hyväksytysti (80 % oikein) perusasioihin liittyvät läpäisytestit (2 kpl). Korkeampi arvosana edellytttää kokeeseen osallistumista. Jotta kokeeseen voi osallistua, täytyy opintojakson kotitehtävistä olla tehtyinä väh. 30 %.

Avoin AMK 10 paikkaa