Analyze and solve a problem task in the area of mathematical analysis of the function of one variables
(40%)
Define elementary functions of a real variable, analyze their properties and sketch their graphs.
(60%)
The domain of the function. Composition. Bijection. Graph of the function.
Flipped classroom approach
Hankinta
1Repetition of basic concepts
Students receive a pre-prepared video with which they repeat basic concepts of function and graphs of elementary functions.
30 min
Keskustelu
2Disscusion
Students participate in discussions related to the introductory video. They can ask questions that can be answered by other students or a teacher.
15 min
Arviointi
3Quiz (basic concepts)
Students take a short quiz which cover the basic notions from the video.
10 min
1
Hankinta
4Lecture
Professor checks how many students watched the video lesson and what the quiz results were. Based on the results of the quiz, teacher repeats concepts that are less well understood and designs lecture to upgrade and broad the topic. Students have possibility for additional questions.
2h 0min
Käytännön harjoitteet
5Practice
Assistants work with students. During the exercises, students do standard tasks related to the topic. In a group, they solve slightly more complex tasks.
1h 30min
Properties of real functions of a real variable
Hankinta
1Properties of real functions
Students receive a pre-prepared video with which they repeat basic properties of real functions.
30 min
Keskustelu
2Disscusion
Students participate in discussions related to the introductory video. They can ask questions that can be answered by other students or a teacher.
15 min
Arviointi
3Quiz (properties of real function)
Students take a short quiz which cover the basic notions from the video.
10 min
1
Hankinta
4Lecture
Professor checks how many students watched the video lesson and what the quiz results were. Based on the results of the quiz, teacher repeats concepts that are less well understood and designs lecture to upgrade and broad the topic. Students have possibility for additional questions.
2h 0min
Käytännön harjoitteet
5Practice
Assistants work with students. During the exercises, students do standard tasks related to the topic. In a group, they solve slightly more complex tasks.
1h 30min
Käytännön harjoitteet
6Independent practical work
Students work independently using the material in LMS Moodle and textbook.
1h 30min
Arviointi
7Quiz (properties of real function-math problems)
Students take a short quiz which cover the basic math problems.
30 min
2
Examples of functions and their graphs
Hankinta
1Examples (real functions of real variable)
Students receive a pre-prepared video with which they repeat basic properties of real functions.
30 min
Keskustelu
2Disscusion
Students participate in discussions related to the introductory video.
15 min
Arviointi
3Quiz (examples)
Students take a short quiz which cover the basic notions from the video.
10 min
1
Hankinta
4Lecture
Professor checks how many students watched the video lesson and what the quiz results were. Based on the results of the quiz, teacher repeats concepts that are less well understood and designs lecture to upgrade and broad the topic. Students have possibility for additional questions.
2h 0min
Käytännön harjoitteet
5Practice
Assistants work with students. During the exercises, students do standard tasks related to the topic. In a group, they solve slightly more complex tasks.
1h 30min
Käytännön harjoitteet
6Independent practical work
Students work independently using the material in LMS Moodle and textbook.
1h 30min
Sequences of real numbers and their properties
Tutkiminen
1Examples (real functions of real variable)
Students receive a pre-prepared materials with which they repeat basic properties of sequences. Students have to independently investigate and repeat the basic concepts of arithmetic and geometric series.
1h 30min
Hankinta
2Lecture
Teacher repeats basic concepts of sequences (definition, arithmetic and geometric sequences, properties and examples of sequences) and upgrades and broad the topic with limit of sequence.
3h 0min
Arviointi
3Quiz (sequences)
Students take a short quiz which cover the basic notions from lecture.
10 min
1
Käytännön harjoitteet
4Practice
Assistants work with students. During the exercises, students do standard tasks related to the topic. In a group, they solve slightly more complex tasks.
3h 0min
Käytännön harjoitteet
5Independent practical work
Students work independently using the material in LMS Moodle and textbook.
2h 0min
Arviointi
6Quiz (sequences-math problems)
Students take a short quiz which cover basic math problems.
