Calculus (5 cr)

Evaluation scale

H-5

Content scheduling

The basics of differential and integral calculations and differential equations are discussed in the course. In addition, the pupils familiarise themselves with complex numbers and limit values. The aim is to expand the basis of mathematical thinking needed in engineering studies and tasks as well as the ability to read and use the language of mathematics in professional contexts. In addition, the aim is to familiarise yourself with the use of MATLAB software in modelling and solving mathematical problems. The aim of the course is to use as many examples of engineering work as possible.

More detailed content:
- complex numbers and their applications
- limit values and definition of derivative
- derivation calculation rules
- the concept of differential
- deriving applications
- a specific integral and integral function
- integral calculation rules
- integrated applications
- differential equations and solving them
- differential equation applications

Objective

Student understands the basic of calculus and is able to
• Apply the derivative to analyze functions
• Apply differentials for error calculations
• Apply the definite integrals, e.g., in calculation of area or average
• Apply differential equations for modeling phenomena within engineering framework

Content

• Limit of a function
• Derivative function
• Differentials
• Integral function
• Definite integral
• Separable differential equations
• Linear differential equations

Materials

The course follows the contents of Calculus 1 on the Open Stax website (https://openstax.org/details/books/calculus-volume-1)
In addition, the course uses other material presented online and during contact teaching sessions.
The MATLAB programme is also used during the course, so the student should have access to a personal computer.
The Finnish support book is "Insinöörin matematiikka, Tuomenlehto et.al."

Teaching methods

Methods supporting the construction of the student's own knowledge:
Contact teaching, online learning, collaborative learning, independent work.
The completion of exercises plays a key role in learning, and group work is encouraged in this respect.

Exam schedules

Exams at around weeks 40 and 48.

Pedagogic approaches and sustainable development

Learning methods that support the student's own activity and construction of knowledge. Lesson examples and exercises related to optimization and wise use of resources.

Completion alternatives

No substitute methods of performance.

Student workload

- Theoretical areas and calculation exercises approx. 60 h
- Intermediate tests measuring competence 2 x 2 h (or final exam 2 h)
- Independent practical training approximately 70 h (approximately 4 hours/week + practical training for tests/tests)

Evaluation methods and criteria

(The preliminary plan will be further refined by September 2025)
The total grade 0-5 for the course is calculated using the course points collected (max 100 points). Course points can be collected
- Two sub-tests (á max 50 p)
- Independent exercises at ViLLE (max. 6 points)
- Weekly calculation exercises (max 12 pts). A precondition for receiving the course points is returning calculation tasks in advance and a self-evaluation based on calculation lesson or model solutions, which has been returned by the normative duration of studies (usually by the end of the week).

The total number of course points collected from the exercises is 18 p, corresponding to approximately 1.5 course numbers.

Students who complete the course with intermediate exams must take both exams. If the completion of the second intermediate exam is exhausted, the course will be renewed with the exam.

Failed (0)

The student does not achieve at least 40% of the course points = 40p
The student has not participated in both midterm exams.

Assessment criteria, satisfactory (1-2)

Grade 1 requires at least 40% of the course points = 40p
Grade 2 requires at least 52% of the course points = 52p

Assessment criteria, good (3-4)

A grade of 3 requires at least 40% of the course points = 64p
A grade of 4 requires at least 52% of the course points = 76p

Assessment criteria, excellent (5)

Grade 5 requires at least 88% of the course points = 88p

Further information

The teacher sends the most important messages about the course by email, and daily announcements are posted on the discussion board on the itsleaning main page.