Matematiikan peruskurssi B (MATLB0112), 5 op

Basic information

Prerequisites

Preparatory course in mathematics or senior high school (or equivalent) level mathematics

Course contents (core content level)

The limit of a function and graphical inspection of limits. Interpretations of the limit of a function in bio- and food engineering. The derivative, graphical and numerical differentiation. The derivative function and rules for differetiating functions. Applications of the derivative in physics, chemistry and bio- and food-engineering.

The integral function and basic rules for integrating functions. The definitive integral, graphical and numerical integration. Geometrical applications of the integral and applications of the integral in physics, chemistry and bio- and food-engineering.

The concept of a diffential equation. The differential equation y? = ky and its applications.

Functions of several variables and the gradient. Interpretations of the gradient and moving in the direction of the gradient.

Course contents (additional)

Diffrentiation of more complicated equations. Integration of rational functions and using tables of integrals. Alternative methods for numerical integration. Elementary optimization and second degree response surfaces.

Using Excel or mathematical software in problems related to differetation, integration and optimzation.

Core content level learning outcomes (knowledge and understanding)

The student understands the meaning of the derivative and the integral of a function graphically and algebraically. The student is able to apply derivatives and integrals in simple problems of his/hers own field. The student can visualize function of two variables and knows in what kind of problems functions of several variables are needed. The student understands the meaning of a gradient and knows how to apply it in optimization.

Core content level learning outcomes (skills)

The student is able to apply central rules of differentiation and integration into simple function. The student can calculate numerical derivatives and integrals. The student is able to calculate gradients of simple functions and to calculate points along the gradient path

Recommended reading

Launonen, Sorvali, Toivonen: teknisten ammattien matematiikka 3Y
Most books about engineering mathematics
Additional printouts

Teaching and learning strategies

Class room teaching: 56 h
Computer labs: 14 h
Exams: 5h
Student individual workload (workload analysis not carried out): 58 h
Total: 133 h
Follow-up of the student workload analysis performed: -

Teaching methods and student workload

Assessment weighting and grading

Two exams (minimum 40% of the maximum score), approval of the computer labs.

Related competences of the degree programme

Theoretical basis and mathematical and science skills