Integral calculus and differential equationsLaajuus (3 ECTS)

Objective

The student will be familiar with the concept of integral, will be able to form integral functions, be able to employ the integral function to calculate integral, be able to calculate the approximation of integral by using numerical methods, be able to apply the integral in geometric and physical problems and be able to solve simple differential equations with consideration of boundary conditions.

Content

The concept of integral. Calculating the approximation of integral by using numerical methods. The integral function. Calculating the integral with an integral function. The method of small differentials. The concept of a differential equation. Differential equations of direct integration. Differential equations of separation.

Assessment criteria, satisfactory (1)

The student
- is able to form the expression of the integral approximation of a function and to calculate its value
- is able to form expression of an integral
- knows the meaning of an integral function
- is able to employ simple rules of integration for determining an integral function and an integral
- knows the connection between an integral and the area between a graph and variable axis, and knows how to apply this knowledge to simple problems
- is able to apply boundary conditions to differential equations of direct integration

Assessment criteria, good (3)

In addition to the requirements above, the student
- is able to employ the integral to calculate various areas and volumes
- is able to calculate the mean value of a function
- is familiar with the principle of using the integral to calculate the moment and the second moment of an area, and is able to apply this principle to very simple problems
- is able to solve a simple separable differential equation

Assessment criteria, excellent (5)

In addition to the requirements above, the student
- is able to synthesize the knowledge acquired during the course diversely
- is able to use the integral to calculate the moment and the second moment of an area
- is able to form integrals related to application problems by using the method of small differentials