Curricula

Objectives

The object of the course
During this course you will learn the concepts needed to study continuous change and dynamic phenomena. With differential calculus you can study instantaneous rates of change and the slopes of curves. With integral calculus you can study accumulation of quantities and areas bounded by curves. During this course you learn how to use these concepts in applications.

Course competences

EUR-ACE: Knowledge and understanding 
You have the knowledge and understanding of mathematics and other basic sciences underlying your engineering specialisation, at a level necessary to achieve the other programme learning outcomes.

The learning objectives of the course
After completing this course you know the meaning of derivative and integral as tools for modeling dynamic phenomena. You know how to differentiate and integrate. You know how to use the derivative and integral in applications.

Content

The derivative and its different interpretations. Rules of differentiation. Using differentiation in optimization problems and other applications involving the derivative such as estimation of error. The definite integral. Rules of integration. The applications of the integral. Using technology in calculations.

Time and location

Course is implemented between 7.3. - 22.4.2022.

Learning materials and recommended literature

Videos in the learning environment, text files, automatic tests, booklet tasks.

Teaching methods

Lectures face-to-face, guided exercises, booklet tasks, independent work, automatic tests, exam.

Exam dates and retake possibilities

Schedule will be agreed on the first contact lesson of the course.

Alternative completion methods

Web-based course in Summer 2022

Student workload

Lectures, guided exercises and exam 40 h
Independent work and automatic tests 40 h

Further information for students

Avoin AMK 5

Evaluation scale

0-5

Evaluation criteria, satisfactory (1-2)

Sufficient 1
You know the concept of the derivative as the rate of change and as the slope of the tangent. Yo understand how to apply the derivative in optimization problems. You can differentiate and integrate polynomials without technology. You know the concept of the integral as accumulation of quantities and as area under a curve. You know the relation between integral and derivative.

Satisfactory 2
You have achieved the desired goals (look at the criteria of grade 1). You know many of the concepts and methods and how to apply them in familiar situations but your reasoning is sometimes deficient or you make mistakes in calculations.

Evaluation criteria, good (3-4)

Good 3
You have achieved the desired goals(look at the criteria of grade 1). You know most of the concepts and methods and how to apply them in familiar situations showing often the ability to reason completely and calculate flawlessly

Very good 4
You have achieved the desired goals (look at the criteria of grade 1). You know most of the concepts and methods and how to apply them in new situations showing in most cases the ability to reason completely and calculate flawlessly.

Evaluation criteria, excellent (5)

You have achieved the desired goals (look at the criteria of grade 1). You know all the concepts and methods and how to apply them in new situations showing always the ability to combine things, reason completely and calculate flawlessly.

Prerequisites

You know the concept of a limit value. You can work with polynomial, exponential, logarithmic and trigonometric functions.