Differential calculus (5 cr)
Code: 5031283-3012
General information
- Enrollment
-
02.12.2021 - 17.01.2022
Registration for the implementation has ended.
- Timing
-
10.01.2022 - 23.03.2022
Implementation has ended.
- Number of ECTS credits allocated
- 5 cr
- Local portion
- 5 cr
- Mode of delivery
- Contact learning
- Unit
- Engineering and Business
- Campus
- Kupittaa Campus
- Teaching languages
- Finnish
- Seats
- 10 - 60
- Degree programmes
- Degree Programme in Construction and Municipal Engineering
- Teachers
- Pekka Saarinen
- Scheduling groups
- Pienryhmä 1 (Size: 5 . Open UAS : 5.)
- Small groups
- Pienryhmä 1
- Course
- 5031283
Evaluation scale
H-5
Content scheduling
Kurssilla käsiteltävät aiheet ja niiden käsittelyjärjestys:
* funktiot ja niiden kuvaajat
* Pythagoraan teoreema ja trigonometriset funktiot
* suora ja kulmakerroin
* eksponentti- ja logaritmifunktiot
* yhdistetty funktio
* funktion raja-arvo ja jatkuvuus
* derivaatan määritelmä
* perusfunktioiden derivaattoja
* derivointisääntöjä
* yhdistetyn funktion derivointi (ketjusääntö)
* tulon ja osamäärän derivointi
* tangentti ja differentiaali
* kriittiset pisteet ja ääriarvot
* ääriarvojen etsintä kriittisten pisteiden tarkastelulla
* usean muuttujan funktiot
* osittaisderivaatat
* differentiaalit ja virhearviot
* kokonaisdifferentiaali
Objective
After completing the course the student:
- operate with mathematical expressions related to technology
- to formulate mathematical model
- understand the concept of a function and recognizes the characteristic properties of different functions
- solve equations involving functions and apply them in practical problems
- use derivatives to analyse graphs
- use differentials to approximate changes and errors
- use matrices and determinants (e.g. for solving linear simultaneous equations),
- use dot and cross products in applications
- give the answer in an expected form
Content
Topics covered in course are (in the order shown):
* functions and graphs
* Pythagoras’ theorem and trigonometric functions
* line and slope
* exponential and logarithmic functions
* function composition
* continuity and limit of a function
* definition of the derivative
* derivatives of basic functions
* derivative rules
* derivative of the composition of functions (chain rule)
* product rule and quotient rule
* tangent and differential
* critical points and extreme values
* finding extreme values by examination of critical points
* functions of several variables
* partial derivatives
* differentials and error estimates
* total differential
Teaching methods
Course consist of lectures and independent calculation exercises, and also of guided calculation exercises as time permitting. There are two long classroom sessions, consisting of lectures and guided calculation exercises. Other lectures are one-hour Teams sessions.
Student workload
Course is worth 5 credits. This means that the estimated workload is 5 * 27 h = 135 h.