Series

Calculus IA: Limits and Differentiation
Calculus IB: Integration
Advanced Calculus

After successfully completing this course students will

• Be familiar with concepts of infinite sequences and series
• Understand the principles of how a sum of infinite series is formed
• Recognize different types of series
• Understand what is meant by convergence and divergence of a sequence and series
• Master various tests for convergence of series and discern situations in which to apply them
• Represent elementary functions, such as trigonometric functions and logarithms, as series, find domains in which these series converge, and use these series representations to approximate values of functions
• Understand concept of uniform convergence, determine whether a series converges uniformly, and use it to differentiate and integrate a series term by term

All necessary study material can be found in the course area. Most topics are covered in videos created by prof. Mika Seppälä. Some topics are covered in the book "Introduction to Real Analysis" by Trench, available in the course area.

Standard Calculus text books, such as Adams' or Stewart's Calculus books can be used as side material among others.
The parts covering Series in the Finnish “Analyysia reaaliluvuilla” (Harjulehto, Klén, Koskenoja) can be recommended for Finnish speaking students (though language of communication is always English).
NB: sequence of covering topics in these books may vary from that in the course.

Completion methods

Either by final exam or combination of class starters, exercises and final exam.

The course with class starters, exercises and final exam includes compulsory attendance onsite. 

Assessment practices and criteria

Scale 0-5 of grades will be used. Points consist of either final exam 100 % or 30 % exercises, 20 % class starters, 50 % final exam. Passing course with grade 1 will require approximately half of the points of the final exam and for the best grade approximately 5/6 of the exam points are required.

Activities and methods in support of learning

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Target groups

Programme: Bachelor's programme in Science. 

Module: Intermediate studies in Mathematics and Statistics.

The course is optional within the programme but compulsory for the mathematics and statistics study track.

Schedule

The course is offered in the spring every year in Period 4.

Recommended time or stage of studies for completion

Within mathematics and statistics study track, first year of studies.

In other study tracks, according to schedule of track/programme

Study module

Intermediate Studies in Mathematics and Statistics.

Language of instruction

English