Course unit, curriculum year 2023–2024
MATH.APP.111
Introductory Calculus, 5 cr
Tampere University
- Description
- Completion options
Teaching periods
Active in period 1 (1.8.2023–22.10.2023)
Active in period 2 (23.10.2023–31.12.2023)
Active in period 3 (1.1.2024–3.3.2024)
Active in period 4 (4.3.2024–31.5.2024)
Active in period 5 (1.6.2024–31.7.2024)
Course code
MATH.APP.111Language of instruction
English, FinnishAcademic years
2021–2022, 2022–2023, 2023–2024Level of study
Basic studiesGrading scale
General scale, 0-5Persons responsible
Responsible teacher:
Jani Hirvonen, 1. periodi: flippausResponsible teacher:
Petteri Laakkonen, 1. periodi: luento-opetusResponsible teacher:
Markus Klemetti, 2nd period: English implementationResponsible organisation
Faculty of Information Technology and Communication Sciences 100 %
Coordinating organisation
Computing Sciences Studies 100 %
Core content
- Set union, intersection, difference and complement. Introduction of the logic and proofs needed in mathematical analysis.
- 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'Hopital'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.
- Intermediate value theorem. Continuity of inverse function.
- Derivative of inverse function.
- Applications, for example linear approximations, derivative of a multivariable function, gradient.
Specialist knowledge
- Mean value theorem.
Learning outcomes
Prerequisites
Further information
Learning material
Equivalences
Studies that include this course
Completion option 1
The completion method by lectures (in Finnish) is aimed at all students. Note that for some engineering students this is not the primary completion method of this course, see description of the flipped learning completion method.
Completion of all options is required.
Participation in teaching
No scheduled teaching
Exam
13.10.2023 – 21.10.2023
Active in period 1 (1.8.2023–22.10.2023)
28.08.2023 – 22.10.2023
Active in period 1 (1.8.2023–22.10.2023)
24.11.2023 – 02.12.2023
Active in period 2 (23.10.2023–31.12.2023)
03.11.2023 – 11.11.2023
Active in period 2 (23.10.2023–31.12.2023)
23.10.2023 – 10.12.2023
Active in period 2 (23.10.2023–31.12.2023)
15.12.2023 – 15.12.2023
Active in period 2 (23.10.2023–31.12.2023)
11.12.2023 – 07.01.2024
Active in period 2 (23.10.2023–31.12.2023)
Active in period 3 (1.1.2024–3.3.2024)
08.01.2024 – 03.03.2024
Active in period 3 (1.1.2024–3.3.2024)
08.02.2024 – 08.02.2024
Active in period 3 (1.1.2024–3.3.2024)
06.03.2024 – 06.03.2024
Active in period 4 (4.3.2024–31.5.2024)
16.05.2024 – 31.05.2024
Active in period 4 (4.3.2024–31.5.2024)
04.03.2024 – 15.05.2024
Active in period 4 (4.3.2024–31.5.2024)
01.06.2024 – 16.07.2024
Active in period 5 (1.6.2024–31.7.2024)
17.07.2024 – 23.07.2024
Active in period 5 (1.6.2024–31.7.2024)
24.07.2024 – 31.07.2024
Active in period 5 (1.6.2024–31.7.2024)
Completion option 2
The flipped learning completion method (in Finnish) is aimed at students of the following subjects: Automation engineering, civil engineering, environmental and energy engineering, materials engineering and mechanical engineering.
Completion of all options is required.
Participation in teaching
28.08.2023 – 15.10.2023
Active in period 1 (1.8.2023–22.10.2023)
Exam
13.10.2023 – 21.10.2023
Active in period 1 (1.8.2023–22.10.2023)
28.08.2023 – 22.10.2023
Active in period 1 (1.8.2023–22.10.2023)
24.11.2023 – 02.12.2023
Active in period 2 (23.10.2023–31.12.2023)
03.11.2023 – 11.11.2023
Active in period 2 (23.10.2023–31.12.2023)
23.10.2023 – 10.12.2023
Active in period 2 (23.10.2023–31.12.2023)
15.12.2023 – 15.12.2023
Active in period 2 (23.10.2023–31.12.2023)
11.12.2023 – 07.01.2024
Active in period 2 (23.10.2023–31.12.2023)
Active in period 3 (1.1.2024–3.3.2024)
08.01.2024 – 03.03.2024
Active in period 3 (1.1.2024–3.3.2024)
08.02.2024 – 08.02.2024
Active in period 3 (1.1.2024–3.3.2024)
06.03.2024 – 06.03.2024
Active in period 4 (4.3.2024–31.5.2024)
16.05.2024 – 31.05.2024
Active in period 4 (4.3.2024–31.5.2024)
04.03.2024 – 15.05.2024
Active in period 4 (4.3.2024–31.5.2024)
01.06.2024 – 16.07.2024
Active in period 5 (1.6.2024–31.7.2024)
17.07.2024 – 23.07.2024
Active in period 5 (1.6.2024–31.7.2024)
24.07.2024 – 31.07.2024
Active in period 5 (1.6.2024–31.7.2024)
Completion option 3
The online completion method (in Finnish) is aimed at anyone wanting to participate in mostly distance education. Some of the support measures are also given as proximate learning events when needed.
Completion of all options is required.
Exam
13.10.2023 – 21.10.2023
Active in period 1 (1.8.2023–22.10.2023)
28.08.2023 – 22.10.2023
Active in period 1 (1.8.2023–22.10.2023)
24.11.2023 – 02.12.2023
Active in period 2 (23.10.2023–31.12.2023)
03.11.2023 – 11.11.2023
Active in period 2 (23.10.2023–31.12.2023)
23.10.2023 – 10.12.2023
Active in period 2 (23.10.2023–31.12.2023)
15.12.2023 – 15.12.2023
Active in period 2 (23.10.2023–31.12.2023)
11.12.2023 – 07.01.2024
Active in period 2 (23.10.2023–31.12.2023)
Active in period 3 (1.1.2024–3.3.2024)
08.01.2024 – 03.03.2024
Active in period 3 (1.1.2024–3.3.2024)
08.02.2024 – 08.02.2024
Active in period 3 (1.1.2024–3.3.2024)
06.03.2024 – 06.03.2024
Active in period 4 (4.3.2024–31.5.2024)
16.05.2024 – 31.05.2024
Active in period 4 (4.3.2024–31.5.2024)
04.03.2024 – 15.05.2024
Active in period 4 (4.3.2024–31.5.2024)
01.06.2024 – 16.07.2024
Active in period 5 (1.6.2024–31.7.2024)
17.07.2024 – 23.07.2024
Active in period 5 (1.6.2024–31.7.2024)
24.07.2024 – 31.07.2024
Active in period 5 (1.6.2024–31.7.2024)
Participation in teaching
29.08.2023 – 10.12.2023
Active in period 1 (1.8.2023–22.10.2023)
Active in period 2 (23.10.2023–31.12.2023)
08.01.2024 – 31.05.2024
Active in period 3 (1.1.2024–3.3.2024)
Active in period 4 (4.3.2024–31.5.2024)
14.05.2024 – 31.07.2024
Active in period 4 (4.3.2024–31.5.2024)
Active in period 5 (1.6.2024–31.7.2024)
Completion option 4
The English language completion method is available to all students wanting to take the course in English.
Completion of all options is required.
Participation in teaching
24.10.2023 – 10.12.2023
Active in period 2 (23.10.2023–31.12.2023)
Exam
13.10.2023 – 21.10.2023
Active in period 1 (1.8.2023–22.10.2023)
28.08.2023 – 22.10.2023
Active in period 1 (1.8.2023–22.10.2023)
24.11.2023 – 02.12.2023
Active in period 2 (23.10.2023–31.12.2023)
03.11.2023 – 11.11.2023
Active in period 2 (23.10.2023–31.12.2023)
23.10.2023 – 10.12.2023
Active in period 2 (23.10.2023–31.12.2023)
15.12.2023 – 15.12.2023
Active in period 2 (23.10.2023–31.12.2023)
11.12.2023 – 07.01.2024
Active in period 2 (23.10.2023–31.12.2023)
Active in period 3 (1.1.2024–3.3.2024)
08.01.2024 – 03.03.2024
Active in period 3 (1.1.2024–3.3.2024)
08.02.2024 – 08.02.2024
Active in period 3 (1.1.2024–3.3.2024)
06.03.2024 – 06.03.2024
Active in period 4 (4.3.2024–31.5.2024)
16.05.2024 – 31.05.2024
Active in period 4 (4.3.2024–31.5.2024)
04.03.2024 – 15.05.2024
Active in period 4 (4.3.2024–31.5.2024)
01.06.2024 – 16.07.2024
Active in period 5 (1.6.2024–31.7.2024)
17.07.2024 – 23.07.2024
Active in period 5 (1.6.2024–31.7.2024)
24.07.2024 – 31.07.2024
Active in period 5 (1.6.2024–31.7.2024)
Completion option 5
This completion method includes the implementations (in Finnish) whose assessment does not include an exam.
Participation in teaching
No scheduled teaching