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Differential and integral calculus (5 cr)

Code: 8B00CZ17-3001

General information


19.04.2021 - 09.01.2022


10.01.2022 - 15.05.2022


5 op

Teaching languages

  • Finnish

Degree programmes

  • Bachelor of Engineering, Food Processing and Biotechnology


  • Heikki Kokkonen

Responsible person

Jukka Kauppila

Student groups

  • BIELI21
  • BIELI21B
  • BIELI21A


Professional part (5 ects):
Upon completion of the course, students will be able to define the derivative and integral for one-variable functions. They will be competent in derivating and integrating the more common mathematical functions and calculating definite integrals and applying their knowledge to common applications. Students will also be capable of calculation tools to solve problems in one-variable differential and integral calculus and be able to solve simple differential equations. They will also apply this knowledge in their Professional Studies and working world.


Professional part (5 ects):
- Definition of one-variable derivative and integral
- Polynomials: derivation and integration
- Composite functions: derivation and integration
- Tangent of a curve
- Extreme values
- Definite integral
- Area and volume
- Small differentials
- Concept of a differential equation
- separate differential equation
- first and second order linear differential equation
- Applications in engineering


The learning material is in the moodle

Teaching methods

Lectures and independent work

Student workload

Lectures 45 h and independent work 90 h

Evaluation scale


Assessment criteria, satisfactory (1)

Students are able to form the polynomial function of the first and second degree in practical situations. The student is able to derive the polynomial and determine the largest and lowest value of the function with a closed interval. Students are able to integrate the polynomial and calculate the specified integral and apply them to the simplest practical situations.

Assessment criteria, good (3)

In addition to the above criteria, the student is able to derive the combined function and apply this to instantaneous growth rates. The student mastered simple differential equations and uses them for kinematics problems.

Assessment criteria, excellent (5)

In addition to the above criteria, the student is able to apply the derivate, integral and differential equations to practical problems such as solving extreme value problems, general determination of volume, and solving problems that require kinematics.

Assessment methods and criteria



No previous studies are required