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Differential calculus (5 cr)

Code: 5031283-3015

General information


Enrollment

02.08.2022 - 15.10.2022

Timing

01.09.2022 - 31.12.2022

Number of ECTS credits allocated

5 op

Mode of delivery

Contact teaching

Unit

Engineering and Business

Campus

Kupittaa Campus

Teaching languages

  • Finnish

Degree programmes

  • Degree Programme in Mechanical Engineering

Teachers

  • Heidi Niskanen
  • Riku Mattila

Teacher in charge

Riku Mattila

Groups

  • PKONTK22A
    PKONTK22A
  • PKONTK22B
    PKONTK22B
  • PKONTK22

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

Evaluation scale

H-5