Nimi Op Opiskelumuoto Aika Paikkakunta Järjestäjä
Calculus IA: Limits and differentiation 5 Cr Examinarium (tenttiakvaario) 17.9.2019 - 21.12.2020
Nimi Op Opiskelumuoto Aika Paikkakunta Järjestäjä
Calculus IA: Limits and differentiation 5 Cr Kurssitentti 21.10.2019 - 21.10.2019
Calculus IA: Limits and differentiation 5 Cr Verkkokurssi 2.9.2019 - 20.10.2019
Calculus IA: Limits and differentiation 5 Cr Tentti 22.10.2018 - 22.10.2018
Calculus IA: Limits and differentiation 5 Cr Verkkokurssi 3.9.2018 - 22.10.2018
Calculus IA: Limits and differentiation 5 Cr Verkkokurssi 4.9.2017 - 22.10.2017


Course is part of bachelor degree program in mathematical sciences and therein basic studies. It is first in a series of online Calculus courses. The collection of the three courses

  • MAT11006: Calculus 1A: Limits and Differentiation
  • MAT11007: Calculus 1B: Integration
  • MAT11008: Advanced Calculus

correspond to the collection of the three Finnish analysis courses

  • MAT11003 Raja-arvot
  • MAT11004 Differentiaalilaskenta
  • MAT11005 Integraalilaskenta

However, no single course in either collection can substitute a course from the other.

Edeltävät opinnot tai edeltävä osaaminen

Mastering precalculus such as in high school mathematics curriculum is necessary. Students are expected already be able to

  • Solve polynomial, rational, trigonometric, exponential equations among others
  • Perform algebraic and trigonometric manipulations and rewritings to mathematical expressions
  • Be familiar with basic functions and their properties
  • Draw graphs of functions, be able to explain where in the graph a function is increasing or decreasing, where does it attain its minimum or maximum values, etc.


After successfully completing this course students will

  • Understand basic concepts of real-valued functions, especially what is meant by limit of a function and continuity.
  • Be familiar with consequences of continuity, especially Bolzano's Theorem, and apply them for example in finding solutions to equations.
  • Be able to find limits of sequences of real numbers and real valued functions with various techniques involving algebraic manipulations or with the squeeze theorem.
  • Understand concept of the derivative from number of perspectives, e.g. as instantaneous rate of change, limit of so called difference quotient, slope of the tangent line to the graph of a continuous function at a point, and through differentiability.
  • Find derivatives of basic functions, derive differentiation rules and apply them.
  • Be familiar with Mean Value Theorem for differentiation, be able to justify why it holds, as well as use it in applications.
  • Use derivative as a tool for studying behavior of functions and in other applications.


This course can be taken as the first mathematics course.

This course is organized in the first period in the fall term.


Course covers the following main topics

  1. Functions
  2. Limits of Functions
  3. Continuity
  4. Derivatives & Differentiation Rules
  5. The Mean Value Theorem
  6. Applications of Derivatives

Oppimista tukevat aktiviteetit ja opetusmenetelmät

Studying in this course follows a weekly cycle. Each week students are expected to:

  1. Watch the prerecorded lectures or read the text allocated for the next workshop at the class Moodle site.
  2. Solve quiz problems. They will help to prepare for the workshops.
  3. Submit solutions to workshop problems by Wednesday evening.
  4. Grade and give feedback to other students’ workshop submissions by Sunday evening.
  5. Also ask questions, hints for solving problems etc. in the discussion forum.


All necessary study material can be found in the course area. Standard Calculus text books, such as Adams' or Stewart's Calculus books can be used as side material among others.

Arviointimenetelmät ja -kriteerit

Continuous formative assessment takes place throughout the course by weekly quizzes and workshops. These will give homework extra credit maximum of 5 points.

Final paper and pencil exam will measure comprehensively the learning goals as specified in section 9.

Scale 1-5 of grades will be used. Passing course with grade 1 will require approximately half of the points of the exam and for the best grade approximately 5/6 of the exam points are required. Homework extra credit points will be added to the exam points.

Suositeltavat valinnaiset opinnot

Online English course MAT21002 Series, or its Finnish equivalent "Sarjat" continues the theme of the calculus courses.


This is an online course. All course material and activities can be found on the online course area. There is a final proctored paper and pencil exam at the end of the course.