The Derivative - basic concepts, techniques and rules
11h 10min
FC / instruction-based learning
Explain the concept of the derivative of a real function of one real variable and its geometric interpretation
(90%)
Apply differential calculus to find local extrema of a function with one variable and inflection points of the function.
(30%)
Analyze an elementary function using derivatives and sketch its graph
(20%)
Define elementary functions of a real variable, analyze their properties and sketch their graphs.
(10%)
Concept and definition of the derivative
Flipped classroom approach
Hankinta
1Introduction of problems - motivation FC approach
Video on problems that lead to the derivative: the slope of a tangent, velocity, optimization
30 min
Keskustelu
2Disscusion
Students participate in discussions related to the introductory video.
30 min
0
Hankinta
3Lecture - concept of derivative
Professors work with students in a hybrid format on the development od the concept of the derivative, geometric interpretation and definition.
60 min
Arviointi
4Quiz
Students take a short quiz based on the concept od the derivative.
20 min
1
Käytännön harjoitteet
5Practice
Assistants work with students on derivatives; techniques and rules application.
1h 30min
Käytännön harjoitteet
6Independent practical work.
Students practice different differentiation techniques based on material in LMS and texbooks.
1h 30min
Derivatives of implicit functions, chain rule, higher-order derivatives
Hankinta
1Video lecture - advanced techniques
Students listen to a short video on the introduction advanced techniques of differentiation and then participate in a face to face presentation by the teacher on these techniques.
60 min
Arviointi
2Quiz
Students take a short quiz based on advanced techniques of differentiation.
20 min
2
Käytännön harjoitteet
3Practice
Assistants work with students on examples of derivation of implicit functions and chain rule.
1h 30min
Käytännön harjoitteet
4Independent practical work - advanced techniques.
Students learn and practice higher-order derivatives based on material in LMS and texbooks.
1h 30min
Tutkiminen
5Independent investigation
Students are required to investigate on their own the application areas and history of calculus.
