Differential and Integral CalculusLaajuus (6 ECTS)

Objective

After completing this course, the student will be familiar with the notion of limit of a function, the student will be able to calculate some simple limits, and he or she will understand what is meant by the continuity of a function. The student will understand the derivative as the limit of the difference quotient and he or she will be able to calculate the derivative for the most common real functions, as well as expressions composed of them. The student will be able to study the monotonicity and extrema of a function with the aid of a derivative. The student will be able to distinguish between the limit of a function and the limit of a sequence of real numbers. The student will understand the sum of an infinite series as the limit of the sequence of partial sums. The student will be able to determine the sum of a geometric series and some other series. The student will understand what is meant by the series expansion of a function. After completing this course, the student will be able to construct and solve mathematical models associated with variable quantities and the rate of change. The student will also be able to interpret the solutions given by a model.

After completing this course the student will be familiar with the notion of an integral, its variations and basic applications. The student will be able to construct and solve mathematical models associated with cumulative quantities and interpret the solutions given by the models. On demand the student will be able to transform an analytical model into a numerical one and produce an approximate solution.

Content

1) Limit and continuity
2) Derivative and applications
3) Infinite sequences and series
4) Definite and indefinite integral
5) Applications
6) Numerical integration

Qualifications

Alternatively the course “Functions, Vectors and Matrices“, or a course with similar content.

Assessment criteria, satisfactory (1)

Students have achieved the course objectives fairly. Students will be able to identify, define and use the course subject area’s concepts and models. The student understands the criteria and principles of the expertise development.

Assessment criteria, good (3)

Students have achieved the course objectives well, even though the knowledge and skills need improvement on some areas. Students are able to define the course concepts and models and are able to justify the analysis. The student is able to apply their knowledge in study and work situations. The student understands the importance of expertise in the field of information technology and is able to analyze his/her own expertise.

Assessment criteria, excellent (5)

Students have achieved the objectives of the course with excellent marks. Students master commendably the course subject area’s concepts and models. Students are able to make justified and fluent analysis and to present concrete development measures. The students are well prepared to apply their knowledge in study and work situations. Students are able to analyze the information technology sector expertise and the evolvement of their own expertise.

Assessment criteria, approved/failed

All exercises have been completed and approved.