# Study Guide

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## Differential and integral calculus (5 cr)

Code: 8B00CZ17-3001

### General information

#### Enrollment

19.04.2021 - 09.01.2022

#### Timing

10.01.2022 - 15.05.2022

5 op

• Finnish

#### Degree programmes

• Bachelor of Engineering, Food Processing and Biotechnology

#### Teachers

• Heikki Kokkonen

Jukka Kauppila

• BIELI21
• BIELI21B
• BIELI21A

#### Objective

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.

#### Content

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

#### Materials

The learning material is in the moodle

#### Teaching methods

Lectures and independent work

Lectures 45 h and independent work 90 h

1-5

#### 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.

exam

#### Qualifications

No previous studies are required