Course unit, curriculum year 2024–2025
MATH.APP.111
Introductory Calculus, 5 cr
Tampere University
- Description
- Completion options
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.111Language of instruction
English, FinnishAcademic years
2024–2025, 2025–2026, 2026–2027Level of study
Basic studiesGrading scale
General scale, 0-5Persons responsible
Responsible teacher:
Jani Hirvonen, 1. periodi: flippausResponsible teacher:
Petteri Laakkonen, Verkko-opetusResponsible 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)