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Course unit, curriculum year 2024–2025
MATH.APP.111

Introductory Calculus, 5 cr

Tampere University
Teaching periods
Active in period 1 (1.8.2024–20.10.2024)
Active in period 2 (21.10.2024–31.12.2024)
Active in period 3 (1.1.2025–2.3.2025)
Active in period 4 (3.3.2025–31.5.2025)
Active in period 5 (1.6.2025–31.7.2025)
Course code
MATH.APP.111
Language of instruction
English, Finnish
Academic years
2024–2025, 2025–2026, 2026–2027
Level of study
Basic studies
Grading scale
General scale, 0-5
Persons responsible
Responsible teacher:
Jani Hirvonen, 1. periodi: flippaus
Responsible teacher:
Petteri Laakkonen, Verkko-opetus
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.
  • Partial derivatives and gradient of a multivariable function.
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.
Specialist knowledge
  • Mean value theorem.
Learning outcomes
Prerequisites
Further information
Learning material
Equivalences
Studies that include this course
Completion option 1
The flipped learning completion method (in Finnish) is aimed at those students who want to participate in contact teaching and all first year students
Completion of all options is required.

Participation in teaching

26.08.2024 13.10.2024
Active in period 1 (1.8.2024–20.10.2024)
22.10.2024 10.12.2024
Active in period 2 (21.10.2024–31.12.2024)

Exam

09.09.2024 20.09.2024
Active in period 1 (1.8.2024–20.10.2024)
11.10.2024 20.10.2024
Active in period 1 (1.8.2024–20.10.2024)
05.12.2024 12.12.2024
Active in period 2 (21.10.2024–31.12.2024)
04.11.2024 15.11.2024
Active in period 2 (21.10.2024–31.12.2024)
12.12.2024 12.12.2024
Active in period 2 (21.10.2024–31.12.2024)
21.02.2025 27.02.2025
Active in period 3 (1.1.2025–2.3.2025)
20.01.2025 31.01.2025
Active in period 3 (1.1.2025–2.3.2025)
05.02.2025 05.02.2025
Active in period 3 (1.1.2025–2.3.2025)
25.04.2025 02.05.2025
Active in period 4 (3.3.2025–31.5.2025)
17.03.2025 28.03.2025
Active in period 4 (3.3.2025–31.5.2025)
12.03.2025 12.03.2025
Active in period 4 (3.3.2025–31.5.2025)
09.06.2025 27.06.2025
Active in period 5 (1.6.2025–31.7.2025)
14.07.2025 31.07.2025
Active in period 5 (1.6.2025–31.7.2025)
Completion option 2
The online completion method 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.

Participation in teaching

26.08.2024 22.12.2024
Active in period 1 (1.8.2024–20.10.2024)
Active in period 2 (21.10.2024–31.12.2024)
07.01.2025 14.05.2025
Active in period 3 (1.1.2025–2.3.2025)
Active in period 4 (3.3.2025–31.5.2025)
15.05.2025 31.07.2025
Active in period 4 (3.3.2025–31.5.2025)
Active in period 5 (1.6.2025–31.7.2025)

Exam

09.09.2024 20.09.2024
Active in period 1 (1.8.2024–20.10.2024)
11.10.2024 20.10.2024
Active in period 1 (1.8.2024–20.10.2024)
05.12.2024 12.12.2024
Active in period 2 (21.10.2024–31.12.2024)
04.11.2024 15.11.2024
Active in period 2 (21.10.2024–31.12.2024)
12.12.2024 12.12.2024
Active in period 2 (21.10.2024–31.12.2024)
21.02.2025 27.02.2025
Active in period 3 (1.1.2025–2.3.2025)
20.01.2025 31.01.2025
Active in period 3 (1.1.2025–2.3.2025)
05.02.2025 05.02.2025
Active in period 3 (1.1.2025–2.3.2025)
25.04.2025 02.05.2025
Active in period 4 (3.3.2025–31.5.2025)
17.03.2025 28.03.2025
Active in period 4 (3.3.2025–31.5.2025)
12.03.2025 12.03.2025
Active in period 4 (3.3.2025–31.5.2025)
09.06.2025 27.06.2025
Active in period 5 (1.6.2025–31.7.2025)
14.07.2025 31.07.2025
Active in period 5 (1.6.2025–31.7.2025)