Integral Calculus and Differential EquationsLaajuus (3 ECTS)

Objective

The student will know the concepts of definite and indefinite integral and is able to apply them to different engineering applications. The student is able to solve simple differential equations and to use them to describe different phenomena.

Content

Definite and indefinite integral. Basic rules of integration. Numerical integration. Applications of integration: volume, mass, centre of mass, moment. Differential equations: basic concepts and applications. Finding solutions of differential equations: numerical solutions and simple analytical methods.

Assessment criteria, satisfactory (1)

The student knows the concepts of definite and indefinite integral and is able to use the basic rules of integration. The student knows the principle of how definite integral can be estimated numerically. The student knows the basic concepts relating to differential equations and understands how differential equations can be used to describe simple phenomena.

Assessment criteria, good (3)

In addition to the requirements above, the student can apply definite integral to calculate areas, volumes and mean and quadratic mean of a function, is able to solve simple 1st and 2nd order differential equations, considering the initial conditions when needed. The student also knows the basic principles to find numerical solutions for differential equations.

Assessment criteria, excellent (5)

In addition to the requirements above, the student can apply definite integral to calculate the center of mass and the moment of an area, and is able to write differential equations to describe various phenomena and creatively use different methods to analyze differential equations, their solutions and related phenomena.