Calculus (5 op)

Arviointiasteikko

H-5

Sisällön jaksotus

• Limits
• The derivative
• Differentials
• Antiderivatives and the definite integral
• Applications of differentiation and integration
• On differential equations

Tavoitteet

Opintojakson suoritettuaan opiskelija osaa
- käyttää derivaattaa funktion tutkimiseen
- käyttää differentiaalia muutoksen ja virheen arvioinnissa
- laskea integraalin avulla esim. pinta-aloja ja tilavuuksia, keskiarvoja ja neliöllisiä keskiarvoja
- ratkaista integroituvia ja 1. kertaluvun separoituvia differentiaaliyhtälöitä
- käyttää oikein opintojakson sisältöön liittyviä matemaattisia termejä ja merkintöjä

Sisältö

- Raja-arvo
- Derivaatta
- Differentiaali
- Määräämätön ja määrätty integraali
- Differentiaali- ja integraalilaskennan sovelluksia
- Differentiaaliyhtälöistä

Oppimateriaalit

1. Calculus (3rd edition), Fred Safier, SCHAUM’S outlines.
2. Engineering Mathematics (6th edition), K.A. Stroud [MACMILLAN PRESS LTD]
3. Formula book: Technical formulas

Opetusmenetelmät

The course combines a variety of learning methods to support student engagement and understanding. These include:
Teacher-directed classroom activities: Lectures and guided discussions to introduce and explain key concepts.
Group work: Collaborative problem-solving and peer learning through small-group tasks and discussions.
Independent work: Self-paced study and individual assignments to reinforce learning outside the classroom.
Project work: Larger, structured assignments requiring research, planning, implementation, and reporting.
Reports: Written reflections or analyses that document understanding and project outcomes.
Task-based learning (homework): Regular assignments designed to build skills and apply theoretical knowledge.
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Tenttien ajankohdat ja uusintamahdollisuudet

Exam Schedule:
First Exam: 27 October 2025
First Retake: 3 November 2025
Second Exam: 18 December 2025
First Retake: (Date to be confirmed in 2026)
Final Retake for Both Parts: 13 January 2026
Exact times for all exams will be published in the official schedule.

Important:
Homework and exercises must be submitted on time. Late submissions will not be accepted, and there are no opportunities for retakes or make-ups.

Pedagogiset toimintatavat ja kestävä kehitys

The contents of the course give understanding to use the derivatives to analyze functions, use differentials to approximate changes and errors, solve separable and linear first order differential equations, use integrals to calculate e.g. areas and mean values and square mean values of functions and use relevant mathematical denotation correctly, moreover the students can use relevant mathematical denotation correctly.
The students will team up for a project work and writing reports on some current and relevant aspect of math, which gives everyone an opportunity to understand the topic; all students will develop their mathematical proficiency.
Task-based assessment supports learning and is continuous throughout the course. Studying in an international group develops students’ ability to intercultural communication and multicultural collaboration.

Opiskelijan ajankäyttö ja kuormitus

Estimated Student Workload

Classroom Activities:
Participation in lectures, discussions, and in-class exercises – 50 hours

Homework:
Completion of homework sets 1–6 – 30 hours

Project Work:
Research, preparation of presentation materials, and delivery of the presentation – 20 hours

Final Exam Preparation:
Independent study and review for the final exam – 25 hours

Total Estimated Workload: 125 hours

Arviointimenetelmät ja arvioinnin perusteet

Assessment Method

1. Homework Policy
* Completing at least 30% of the homework is mandatory.
* Students can earn homework points only if they complete more than 50% of the total homework assignments.

2. Distribution of Points
- First Exam: 20 points
- Second Exam: 20 points
- Homework: 10 points

Total: 50 points

Hylätty (0)

The student did not pass the final examination and failed to engage with the assigned coursework

Arviointikriteerit, tyydyttävä (1-2)

Scoring between 25 and 35 points in the exams and completing 30% to 50% of the assignments.

Arviointikriteerit, hyvä (3-4)

Scoring between 35 and 45 points in the exams and completing at least 50% to 75% of the assignments.

Arviointikriteerit, kiitettävä (5)

Scoring between 45 and 50 points in the exam and completing at least 75% of the assignments.

Esitietovaatimukset

Insinöörimatematiikan perusteet tai vastaavat taidot

Lisätiedot

All essential practical details related to the course are available on ITS Learning, including:
Timetables: Dates and times for lectures, tutorials, exams, and other scheduled activities.
Project Work: Descriptions of project topics, deadlines, submission guidelines, and evaluation criteria.
Grading Information: Breakdown of how grades are calculated, including the weight of exams, assignments, and project components.
Web Materials: Access to lecture slides, supplementary readings, assignment instructions, and other digital resources.
Announcements: Updates and important notices related to the course.
Please check ITS Learning regularly to stay informed and up to date.