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031010P Calculus I, 5 ECTS cr 
Code 031010P  Validity 01.01.1950 -
Name Calculus I  Abbreviation Calculus I 
Scope5 ECTS cr   
TypeBasic Studies Discipline4338 Engineering Mathematics 
  Grading1 - 5, pass, fail 
Unit Applied Mathematics and Computational Mathematics 

Pauliina Uusitalo 

ECTS Credits 

5 ECTS credits / 135 hours of work

Language of instruction 

Finnish. The course will be lectured also in English.


Fall, period 1

Learning outcomes 

Upon completion of the course, the student

- knows how to solve inequalities and equations with absolute value

- identifies the concepts of vector algebra

- can use vector algebra for solving the problems of analytic geometry

- can explain basic characteristics of elementary functions

- is able to analyse the limit and the continuity of the real valued functions of one variable

- can analyse the local minima and maxima of a function

- knows how to find the derivative for a function given with parametric representation

- is able to evaluate the basic calculation of the complex numbers and can rewrite a complex number in its exponential form

- knows the connection between the integral and area

- knows integral techniques such as integration by parts, a substitution method and a partial fraction composition

- can solve problems associated with the differential and integral calculus of the real valued functions of one variable.


-  Inequalities and absolute value
-   Vector algebra and analytic geometry
-   Concept of the function and elementary functions
-   Monotonicity of the function, the inverse function
-   Limit values
-   Derivative as limit value of the difference quotient. Derivatives of elementary functions
-   The extreme values of a function
-   Parameter presentation of the curve, polar coordinates, complex numbers
-   Integral function and definite integral, applications
-   Integration by parts, substitution method and integration of rational functions

Mode of delivery 

Blended learning, course material is in Moodle learning environment

Learning activities and teaching methods 

Lectures 28 h / Group work 22 h / Self-study 85 h

Target group 

1. year students of technical sciences, mathematics and physics

Prerequisites and co-requisites 


Recommended optional programme components 


Recommended or required reading 

Grossman, S.I.: Calculus of One Variable; Grossman, S.I.: Multivariable Calculus, Linear Algebra, and Differential Equations (partly); Adams, R.A.: A Complete Course Calculus (partly)

Assessment methods and criteria 

The course is completed with mid-term exams or a final exam. When completed with mid-term exams, exercise assignments are part of the continuous assessment. The assessment of the course is based on the learning outcomes of the course. Read more about assessment criteria at the University of Oulu webpage.


The course utilizes a numerical grading scale 0-5. In the numerical scale zero stands for a fail.

Person responsible 

Pauliina Uusitalo

Working life cooperation 

The course does not contain working live cooperation.

Other information 



Current and future instruction
Functions Name Type ECTS cr Teacher Schedule
Registration Calculus I  Course  Pauliina Uusitalo  02.08.21 -25.10.21
Registration Calculus I (in English)  Course  Pauliina Ulkuniemi  31.08.21 -25.10.21

Future examinations
Functions Name Type ECTS cr Teacher Schedule
registration period has not begun Calculus I exam  Exam  Pauliina Uusitalo  03.02.22
registration period has not begun Calculus I exam  Exam  Pauliina Uusitalo  24.03.22