Differential calculus (5 cr)
Code: 5031283-3009
General information
- Enrollment
- 12.12.2020 - 10.01.2021
- Registration for the implementation has ended.
- Timing
- 11.01.2021 - 21.03.2021
- Implementation has ended.
- Number of ECTS credits allocated
- 5 cr
- Local portion
- 2 cr
- Virtual portion
- 3 cr
- Mode of delivery
- Blended 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
- Course
- 5031283
Evaluation scale
H-5
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