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Course unit, curriculum year 2023–2024
MATH.APP.111

Introductory Calculus, 5 cr

Tampere University
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.111
Language of instruction
English, Finnish
Academic years
2021–2022, 2022–2023, 2023–2024
Level of study
Basic studies
Grading scale
General scale, 0-5
Persons responsible
Responsible teacher:
Jani Hirvonen, 1. periodi: flippaus
Responsible teacher:
Petteri Laakkonen, 1. periodi: luento-opetus
Responsible teacher:
Markus Klemetti, 2nd period: English implementation
Responsible 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)
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)
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)

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)
Completion option 5
This completion method includes the implementations (in Finnish) whose assessment does not include an exam.

Participation in teaching

No scheduled teaching