Matematiikan peruskurssi B (MATLA0112), 5 op

Basic information

Course name:	Matematiikan peruskurssi B Basic Course in Mathematics B
Course Winha code:	MATLA0112
Kurre acronym:	Mat.B
Credits:	5
Type and level of course:	Basic studies
Year of study, semester or study period:	1.year
Implementation:	3.period, 4.period
Semester:	0607
Language of tuition:	Suomi
Teacher:	Pirkka Peltola
Final assessment:	Grading scale (0-5)

Descriptions

Prerequisites

Basic Course in Mathematics A

Course contents (core content level)

The concept of a function and properties of a function. Outline of the concept of limit values.
Connection between continuity and limit value. Continuity of most common functions.

Derivative and its meaning. Rules to determine the derivative of a given function. Numerical differentiation and the accuracy of the result. Numerical methos to solve equations: interval bisection method and Newtons method. Extremal values and optimization problems solved by using differentiation.

Integral function and definite integral. Connection of these concepts. Integration techniques: basic functions and their linear combinations, integration of a composed function if the inner function is simply multiplication by a constant.

Differential and its use to determine the uncertainty of the result calculated from uncertain values. Differential as a base for definite integral. Applications of integral calculus: areas, volumes, different mean values.

Course contents (additional)

Methods to determine the limit value of a given function. Inverse function. Sketching graphs with the help of the first and second derivative. Integration based on the chain rule for differentiation. Application problems: general principles to form the differential needed in integration.

Core content level learning outcomes (knowledge and understanding)

The student is aware of the meaning of continuity and differentiability in solving equations and finding maximum and minimum values of a function. The student knows that the most common functions are both continuous and differentiable almost everywhere. The student knows how to estimate the accuracy of the results when using numerical methods. The student knows general principles to write down the differential and the definite integral in application problems.

Core content level learning outcomes (skills)

The student is able to differentiate most common functions up to the case where the inner function is of the form kx + b. The student is able to solve an equation numerically using interval bisection method and Newtons method The student can solve optimization problems with the help of the derivative of the function.

The student is able to integrate most common functions up to the case where the inner function is of the form kx + b. The student is able to use definite integrals to determine areas, volumes, and mean values of a given function. The student is able to differentiate and integrate numerically and make an estimation of the accuracy of the result.

Teaching and learning strategies

Lectures and assignments.
Self study.
Laboratory assignments.
Exam.

Teaching methods and student workload

Exam
Lectures and assignments
Laboratory assignments

Assessment weighting and grading

Assessment of computer exercises and exams.

Related competences of the degree programme

International and intercultural skills
Theoretical basis and mathematical and science skills
Information acquisition skills and adaptation of new knowledge