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800317A Continuity and derivative, 5 ECTS cr 
Code 800317A  Validity 01.01.2017 -
Name Continuity and derivative  Abbreviation Continuity and 
Scope5 ECTS cr   
Type Intermediate Studies Discipline3250 Mathematics 
  Grading1 - 5, pass, fail 
Unit Field of Mathematics 

Esa Järvenpää 

ECTS Credits 

5 ECTS credits / 133 hours of work

Language of instruction 



1st year, 2nd period

Learning outcomes 

Upon completing the course the student is:
- able to define the concept of continuous function and apply this definition in examples and deductions
- able to determine derivatives of functions
- able to apply derivative to study functions
- able to appy the concepts of continuity and derivative in various problems, including deductions


The course concerns continuity and derivative of real-valued functions of one variable. The central topics are the intermediate value theorem, the chain rule, the derivative of inverse functions, the mean value theorem and its applications. Differential calculus is also applied to various problems. The aim of the course is to improve mathematical thinking as well as computational skills.

Mode of delivery 

Face-to-face teaching

Learning activities and teaching methods 

28 h lectures, 14 h exercises, 91 h independent study

Target group 

1st year mathematics and physics students as well as students taking mathematics as a minor subject

Prerequisites and co-requisites 

Functions and limit 800119P, Introduction to mathematical deduction 802151P

Recommended optional programme components 


Recommended or required reading 

In addition to the material hand out in the course, for example the book  P. Harjulehto, R. Klén, M. Koskenoja, Analyysiä reaaliluvuilla.

Assessment methods and criteria 

Final exam, exercises


1-5, fail

Person responsible 

Esa Järvenpää

Working life cooperation 


Other information 

Replaces the course 802163P Derivative.


Current and future instruction
Functions Name Type ECTS cr Teacher Schedule
Registration Continuity and Derivative  Course  Esa Järvenpää  01.11.21 -20.12.21

Future examinations
No examinations in WebOodi