# Study Guide

Choose language

## Differential and integral calculus (5 cr)

Code: KC03MAT108-3009

### General information

#### Enrollment

19.04.2021 - 29.08.2021

#### Timing

30.08.2021 - 17.12.2021

5 op

• Finnish

#### Degree programmes

• Degree Programme in Food Processing and Biotechnology

#### Teachers

• Heikki Kokkonen

Jukka Kauppila

• MBIELI21

#### 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

Teachers own material in theMoodle

#### Teaching methods

Lectures and excercises

Total work load of the course: 135 h
- of which scheduled studies: 25 h
- of which autonomous studies: 110 h

Grades 1 - 5

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.

#### Assessment methods and criteria

Final exam or midterm exam

#### Qualifications

No previous studies are required