Insinöörimatematiikan perusteet (5 op)

Arviointiasteikko

H-5

Sisällön jaksotus

- Sets of numbers and number systems
- Real functions
- Polynomials equations and inequalities, exponential and logarithmic equations;
- Trigonometry for right triangles
- Complex numbers
- Vectors and matrices

Tavoitteet

Opintojakson suoritettuaan opiskelija
• osaa käsitellä tekniikan aloilla esiintyviä matemaattisia lausekkeita.
• ymmärtää yhtälönratkaisun periaatteet ja osaa ratkaista tekniikan aloille tyypillisiä yhtälöitä.
• ymmärtää vektorilaskennan periaatteet ja osaa soveltaa vektoreita tekniikan alan ongelmien mallintamiseen ja ratkaisemiseen.
• ymmärtää geometrian ja trigonometrian peruskäsitteet ja osaa soveltaa niitä ongelmaratkaisussa.
• ymmärtää funktion käsitteen ja tietää funktioiden perusominaisuuksia.
• osaa soveltaa funktioita tekniikan ongelmien mallintamiseen ja ratkaisemiseen.
• ymmärtää matriisilaskennan periaatteet
• osaa soveltaa yhtälöryhmiä tekniikan alan ongelmien ratkaisussa.
• tuntee matematiikan merkintätapoja ja osaa soveltaa niitä tekniikan aloilla.

Sisältö

• Lukujen esitystavat ja lukujoukot
• Peruslaskutoimitukset ja laskujärjestys
• Murtolausekkeet, potenssit, polynomilausekkeet ja rationaalilausekkeet
• Polynomifunktiot sekä I ja II asteen polynomiyhtälöt ja -epäyhtälöt
• Yhtälöryhmät
• Juuret ja juuriyhtälöt
• Eksponenttifunktiot ja -yhtälöt
• Logaritmifunktiot ja -yhtälöt
• Kulmat ja kulmayksiköt
• Suorakulmaisen kolmion trigonometria
• Trigonometriset funktiot yksikköympyrässä
• Trigonometriset yhtälöt
• Sinilause, kosinilause ja yleisen kolmion ratkaiseminen
• Vektorilaskennan peruskäsitteet ja tekniikan ongelmien mallintaminen vektorien avulla
• Vektorien pistetulo ja ristitulo
• Matriisilaskennan peruskäsitteet, determinantti ja käänteismatriisi
• Koulutuskohtaisia sisältöjä

Oppimateriaalit

1. Precalculus (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: 29 October 2025
First Retake: 5 November 2025
Second Exam: 17 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 of the basic mathematics and help students to solve equations, including radical, exponential and logarithmic equations and use determinants and matrices (e.g. for solving linear simultaneous equations), apply dot and cross products (e.g. in games, physics and electrical engineering applications), 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 basic 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

Exam Schedule:
First Exam: 29 October 2025
First Retake: 5 November 2025
Second Exam: 17 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.

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

Opintojakso "Matemaattisen aineiden perustaidot" tai vastaavat tiedot ja 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.