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Course unit, curriculum year 2023–2024
MATH.APP.160

Differential and Integral 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.160
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:
Simo Ali-Löytty
Responsible teacher:
Jani Hirvonen
Responsible teacher:
Jussi Kangas
Responsible teacher:
Samuli Piipponen
Responsible teacher:
Terhi Kaarakka
Responsible organisation
Faculty of Information Technology and Communication Sciences 100 %
Coordinating organisation
Computing Sciences Studies 100 %
Core content
  • Antiderivative and basic integration techniques. Proper and improper integrals.
  • Ordinary linear differential equations of first and second order. Separable first order differential equations.
  • Limit of a sequence, increasing and decreasing sequences.
  • Series (geometric, with positive terms, alternating, Taylor series) and their convergence.
Complementary knowledge
  • Applications of integration in, e.g., determining areas and volumes of geometrical shapes, and computing the length of a curve.
  • Higher order differential equations. Modeling specific real world problems, such as growth of populations, with differential equations.
  • Approximating a function with a polynomial.
  • Using Matlab as a tool in solving the exercise problems.
Specialist knowledge
  • Numerical integration, trapezoid rule and Simpson's formula. Computing the Riemann sums.
  • Existence and uniqueness results, matrix notation for linear systems.
  • Testing convergence. Computing limits and integrals using series. Estimating the error in polynomial approximations of functions.
Learning outcomes
Prerequisites
Recommended prerequisites
Further information
Learning material
Equivalences
Studies that include this course
Completion option 1
Exercises and final exam
Completion of all options is required.

Participation in teaching

28.08.2023 23.10.2023
Active in period 1 (1.8.2023–22.10.2023)
Active in period 2 (23.10.2023–31.12.2023)
09.01.2024 25.02.2024
Active in period 3 (1.1.2024–3.3.2024)
08.01.2024 25.02.2024
Active in period 3 (1.1.2024–3.3.2024)

Exam

13.10.2023 22.10.2023
Active in period 1 (1.8.2023–22.10.2023)
28.08.2023 20.10.2023
Active in period 1 (1.8.2023–22.10.2023)
11.09.2023 30.11.2023
Active in period 1 (1.8.2023–22.10.2023)
Active in period 2 (23.10.2023–31.12.2023)
11.12.2023 15.12.2023
Active in period 2 (23.10.2023–31.12.2023)
10.11.2023 22.11.2023
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)
11.12.2023 22.12.2023
Active in period 2 (23.10.2023–31.12.2023)
29.11.2023 04.12.2023
Active in period 2 (23.10.2023–31.12.2023)
02.01.2024 14.01.2024
Active in period 3 (1.1.2024–3.3.2024)
08.01.2024 25.02.2024
Active in period 3 (1.1.2024–3.3.2024)
22.02.2024 29.02.2024
Active in period 3 (1.1.2024–3.3.2024)
26.02.2024 28.04.2024
Active in period 3 (1.1.2024–3.3.2024)
Active in period 4 (4.3.2024–31.5.2024)
24.02.2024 04.03.2024
Active in period 3 (1.1.2024–3.3.2024)
Active in period 4 (4.3.2024–31.5.2024)
08.04.2024 26.04.2024
Active in period 4 (4.3.2024–31.5.2024)
15.05.2024 15.05.2024
Active in period 4 (4.3.2024–31.5.2024)
11.03.2024 22.03.2024
Active in period 4 (4.3.2024–31.5.2024)
29.04.2024 12.05.2024
Active in period 4 (4.3.2024–31.5.2024)
13.05.2024 07.07.2024
Active in period 4 (4.3.2024–31.5.2024)
Active in period 5 (1.6.2024–31.7.2024)
03.04.2024 03.04.2024
Active in period 4 (4.3.2024–31.5.2024)
11.03.2024 22.03.2024
Active in period 4 (4.3.2024–31.5.2024)
29.04.2024 12.05.2024
Active in period 4 (4.3.2024–31.5.2024)
08.07.2024 31.07.2024
Active in period 5 (1.6.2024–31.7.2024)
Completion option 2
Self-learning, exercises, self and peer assessment, personal timetable plan, participation in prime time sessions, exam. Additional information on the Moodle page.

Participation in teaching

No scheduled teaching
Completion option 3
Web implementation. Additional information on the Moodle page.
Completion of all options is required.

Participation in teaching

31.08.2023 10.12.2023
Active in period 1 (1.8.2023–22.10.2023)
Active in period 2 (23.10.2023–31.12.2023)
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)
13.05.2024 31.07.2024
Active in period 4 (4.3.2024–31.5.2024)
Active in period 5 (1.6.2024–31.7.2024)

Exam

13.10.2023 22.10.2023
Active in period 1 (1.8.2023–22.10.2023)
28.08.2023 20.10.2023
Active in period 1 (1.8.2023–22.10.2023)
11.09.2023 30.11.2023
Active in period 1 (1.8.2023–22.10.2023)
Active in period 2 (23.10.2023–31.12.2023)
11.12.2023 15.12.2023
Active in period 2 (23.10.2023–31.12.2023)
10.11.2023 22.11.2023
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)
11.12.2023 22.12.2023
Active in period 2 (23.10.2023–31.12.2023)
29.11.2023 04.12.2023
Active in period 2 (23.10.2023–31.12.2023)
02.01.2024 14.01.2024
Active in period 3 (1.1.2024–3.3.2024)
08.01.2024 25.02.2024
Active in period 3 (1.1.2024–3.3.2024)
22.02.2024 29.02.2024
Active in period 3 (1.1.2024–3.3.2024)
26.02.2024 28.04.2024
Active in period 3 (1.1.2024–3.3.2024)
Active in period 4 (4.3.2024–31.5.2024)
24.02.2024 04.03.2024
Active in period 3 (1.1.2024–3.3.2024)
Active in period 4 (4.3.2024–31.5.2024)
08.04.2024 26.04.2024
Active in period 4 (4.3.2024–31.5.2024)
15.05.2024 15.05.2024
Active in period 4 (4.3.2024–31.5.2024)
11.03.2024 22.03.2024
Active in period 4 (4.3.2024–31.5.2024)
29.04.2024 12.05.2024
Active in period 4 (4.3.2024–31.5.2024)
13.05.2024 07.07.2024
Active in period 4 (4.3.2024–31.5.2024)
Active in period 5 (1.6.2024–31.7.2024)
03.04.2024 03.04.2024
Active in period 4 (4.3.2024–31.5.2024)
11.03.2024 22.03.2024
Active in period 4 (4.3.2024–31.5.2024)
29.04.2024 12.05.2024
Active in period 4 (4.3.2024–31.5.2024)
08.07.2024 31.07.2024
Active in period 5 (1.6.2024–31.7.2024)