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Course unit, curriculum year 2020–2021
MATH.APP.160
Differential and Integral Calculus, 5 cr
Tampere University
- Description
- Completion options
Teaching periods
Active in period 1 (1.8.2020–18.10.2020)
Active in period 2 (19.10.2020–31.12.2020)
Active in period 3 (1.1.2021–7.3.2021)
Active in period 4 (8.3.2021–31.5.2021)
Active in period 5 (1.6.2021–31.7.2021)
Course code
MATH.APP.160Language of instruction
Finnish, EnglishAcademic year
2020–2021Level of study
Basic studiesGrading scale
General scale, 0-5Persons responsible
Responsible teacher:
Jani HirvonenResponsible teacher:
Elina ViroResponsible teacher:
Jussi KangasResponsible teacher:
Kimmo VattulainenResponsible teacher:
Simo Ali-LöyttyResponsible organisation
Faculty of Information Technology and Communication Sciences 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
Compulsory prerequisites
Further information
Learning material
Equivalences
Studies that include this course
Completion option 1
Exercises and final exam
Participation in teaching
11.01.2021 – 26.02.2021
Active in period 3 (1.1.2021–7.3.2021)
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
11.01.2021 – 26.02.2021
Active in period 3 (1.1.2021–7.3.2021)
Completion option 3
Web implementation. Additional information on the Moodle page.
Completion of all options is required.
Independent study
17.05.2021 – 31.07.2021
Active in period 4 (8.3.2021–31.5.2021)
Active in period 5 (1.6.2021–31.7.2021)
17.05.2021 – 31.07.2021
Active in period 4 (8.3.2021–31.5.2021)
Active in period 5 (1.6.2021–31.7.2021)
Exam
27.07.2020 – 16.08.2020
Active in period 1 (1.8.2020–18.10.2020)
04.03.2021 – 04.03.2021
Active in period 3 (1.1.2021–7.3.2021)
17.05.2021 – 31.07.2021
Active in period 4 (8.3.2021–31.5.2021)
Active in period 5 (1.6.2021–31.7.2021)
Completion option 4
Implementation in English.
Participation in teaching
19.10.2020 – 22.12.2020
Active in period 2 (19.10.2020–31.12.2020)
20.10.2020 – 03.12.2020
Active in period 2 (19.10.2020–31.12.2020)
22.10.2020 – 03.12.2020
Active in period 2 (19.10.2020–31.12.2020)
Completion option 5
Verkkototeutus. Tarkemmat ohjeet kurssin Moodle-sivulla.
Independent study
04.01.2021 – 28.02.2021
Active in period 3 (1.1.2021–7.3.2021)