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Opintojakso, lukuvuosi 2020–2021
MATH.APP.110
Fundamentals of Engineering Mathematics, 5 op
Tampereen yliopisto
- Kuvaus
- Suoritustavat
Opetusperiodit
Aktiivinen periodissa 1 (1.8.2020–18.10.2020)
Aktiivinen periodissa 2 (19.10.2020–31.12.2020)
Aktiivinen periodissa 3 (1.1.2021–7.3.2021)
Koodi
MATH.APP.110Opetuskieli
English, FinnishLukuvuosi
2020–2021Opintojakson taso
Basic studiesArvosteluasteikko
General scale, 0-5Vastuuhenkilö
Responsible teacher:
Jani HirvonenResponsible teacher:
Kimmo VattulainenResponsible teacher:
Robert PicheResponsible teacher:
Jussi KangasResponsible organisation
Faculty of Information Technology and Communication Sciences 100 %
Core content
- Set union, intersection, difference and complement. Existence and universal quatifications. Direct and indirect proof, proof by induction.
- Definition of a function. Monotonicity of a function. Inverse function and combined function. Properties of basic functions. Hyperbolic functions and their inverses.
- Complex numbers and their basic properties (sum, difference, product, quotient, conjugate and modulus), presenting and calculating complex numbers both in coordinate form and polar form, complex roots.
- Limit and continuity of a fuction. One-sided and inproper limits, l'Hospital's rule.
- Derivative as limit of difference quotient. Derivating basic functions, products and quotients, chain rule. Studying the values and extrema of a function based on derivatives..
- Basics of integral calculus.
Complementary knowledge
- Preimage, injection, surjection, bijection.
- Roots of real valued polynomials, factorisation.
- Sandwich principle. Intermediate value theorem, continuity of inverse fuction.
- Derivative of inverse function, linear approksimations.
- Applications of integral, like area and volume.
Specialist knowledge
- Mean value theorem.
Osaamistavoitteet
Esitietovaatimukset
Lisätiedot
Oppimateriaalit
Vastaavat opintojaksot
Kokonaisuudet, joihin opintojakso kuuluu
Suoritustapa 1
The English language implementation of this course is aimed at students of Sustainable Urban Development, but any student wanting to take this course in English can participate.
Kaikkien osuuksien suorittaminen on pakollista.
Participation in teaching
24.08.2020 – 08.10.2020
Aktiivinen periodissa 1 (1.8.2020–18.10.2020)
25.08.2020 – 08.10.2020
Aktiivinen periodissa 1 (1.8.2020–18.10.2020)
Exam
13.10.2020 – 13.10.2020
Aktiivinen periodissa 1 (1.8.2020–18.10.2020)
19.11.2020 – 19.11.2020
Aktiivinen periodissa 2 (19.10.2020–31.12.2020)
Suoritustapa 2
This is the flipped learning implementation of this course, and it is only available in Finnish. See completion method 1 for the Lectures and exercises implementation in English.
Participation in teaching
24.08.2020 – 08.10.2020
Aktiivinen periodissa 1 (1.8.2020–18.10.2020)
Suoritustapa 3
This is the online implementation of this course, and it is only available in Finnish. See completion method 1 for the Lectures and exercises implementation in English.
Participation in teaching
24.08.2020 – 09.10.2020
Aktiivinen periodissa 1 (1.8.2020–18.10.2020)
12.01.2021 – 26.02.2021
Aktiivinen periodissa 3 (1.1.2021–7.3.2021)
Suoritustapa 4
Participation in teaching
24.08.2020 – 08.10.2020
Aktiivinen periodissa 1 (1.8.2020–18.10.2020)
25.08.2020 – 08.10.2020
Aktiivinen periodissa 1 (1.8.2020–18.10.2020)