Study Guide

Objective

Student is able to use following mathematical tools within engineering framework:
• Handling and simplifying mathematical expressions
• Solving equations, groups of equations and inequalities
• Functions
• Vector algebra and vector models of technical phenomena
• Matrix algebra

Content

• Mathematical expressions, equations, groups of equations and inequalities
• Matrix algebra, inverse matrix and determinant
• Polynomial functions
• Exponential functions
• Logarithmic functions
• Trigonometric functions and radians
• Vector algebra

Evaluation scale

H-5

Objective

Student is able to use following mathematical tools within engineering framework:
• Handling and simplifying mathematical expressions
• Solving equations, groups of equations and inequalities
• Functions
• Vector algebra and vector models of technical phenomena
• Matrix algebra

Content

• Mathematical expressions, equations, groups of equations and inequalities
• Matrix algebra, inverse matrix and determinant
• Polynomial functions
• Exponential functions
• Logarithmic functions
• Trigonometric functions and radians
• Vector algebra

Materials

Electronic and online material, educational videos in the Itslearning learning system and linked there

Teaching methods

learning-by-doing, task-based, independent study, calculation workshops

The course provides the prerequisites for studying the mathematics and physics courses included in engineering education with the help of diverse teaching, guided calculation exercises, electronic Ville exercises, independent practice and group work.

Exam schedules

Midterm exams in weeks 43 and 50
If necessary, 2 repetitions during spring 2024 (exam measuring the content of the entire course)

International connections

learning-by-doing, supporting learning
Learning is largely based on the student's own active participation and performance.
The mathematical skills learned in the course are basic skills needed in working life.
The evaluation is based on completed tasks and demonstration of competence in the exam(s).

Completion alternatives

Independent study and an approved course exam and MATLAB online course

Student workload

5 credits = 135 h of student work, divided on average
- Joint calculation workshops 52 h
- Independent study with the help of calculation handouts and guide videos, about 3 hours/handout = 33 hours
- Independent study at ViLLE 3 hours/week = 20 hours
- Rehearsal for the exam/exams 16 h
- Exam/exams 2-4 h
- MATLAB-Onramp software study 10 h

Content scheduling

The lessons of the course are held in weeks 38-49. Attendance at lessons is compulsory.


Mathematical skills learned in the course are basic skills needed in vocational studies and in working life.
Contents:
- Number representations and number sets
- Basic calculations and order of calculations
- Unit conversions and SI system units
- Powers and powers of ten (also negative and root = fractional powers)
- Processing of polynomials (Simplification of expressions, also fractional expressions)
- Function values and reading the graph of the function
- 1st degree functions and 1st degree function graph
- 1st degree equations and inequalities (also ratios)
- Percentage calculation
- 2nd degree functions and the graph of a 2nd degree function
- 2nd degree equations and inequalities
- Pairs and groups of equations
- Basics of matrix calculation
- Right and oblique triangle trigonometry
- Geometry of other bodies
- Vector calculus
- Angles and angle units
- Trigonometric functions on the unit circle
- Trigonometric equations
- Exponential, logarithmic and trigonometric functions and their graphs
- Exponential, logarithmic and trigonometric equations
- Basic use of MATLAB math software

Further information

The teacher sends the most important announcements of the course by e-mail. Contact the teacher by email (aaro.mustonen@turkuamk.fi). Information related to lessons in Itslearning. Announcements related to the course in Itslearning on the Course Overview page.

Software used: ViLLE, MATLAB, GeoGebra
The student must have at least a function calculator (a graphic or symbolic calculator will also work)

Evaluation scale

H-5

Assessment methods and criteria

The course is evaluated numerically from 0-5.

The evaluation is based on course points, which are collected as follows
- For weekly calculation exercises, max 1p/handout, however a maximum of 12p.
- For independent ViLLE tasks exceeding the required 40%, 1% = 0.1p x 60% = 6p (max)
- Two partial exams (max 50p) or one course exam (max 100p)

Getting course points for weekly calculation exercises requires returning them to Its in electronic form and self-evaluating your own performance by the deadline. You get points in proportion to the number of calculated tasks.

For the approved performance (number 1) is required
- at least 40% of the maximum points of independent ViLLE assignments
- at least 40 course credits in total

Other grades are determined by points on a linear scale.

Assessment criteria, fail (0)

The student lacks one of the required passing conditions:
- The student has not received at least 40% of the maximum points for the ViLLE assignments.
- The student has not achieved at least 40% = 40 course points in total

Assessment criteria, satisfactory (1-2)

- The student has received at least 40% of the maximum points for the ViLLE assignments and course points as follows:
Course points 40-51 = 1
Course points 52-63 = 2

Competence corresponding to level 1-2: The student can solve 1st and 2nd degree polynomial equations and their applications. The student masters right-angled triangle trigonometry and knows how to apply it in vector calculations.

Assessment criteria, good (3-4)

- The student has received at least 40% of the maximum points for the ViLLE assignments and course points as follows:
Course points 64-75 = 3
Course points 76-87 = 4

Competence corresponding to level 3-4: In addition to the competence of level 1-2, the student masters one of the following topics
- Refinement of various powers and expressions
- Graphs of functions and related calculations
- Oblique triangle trigonometry and trigonometric equations
- Vector calculus
- Exponential and logarithmic equations

Assessment criteria, excellent (5)

- The student has received at least 40% of the maximum points for the ViLLE assignments.
- The student has received at least 88 course points in total

Competence corresponding to level 5: In addition to the competence of level 1-2, the student also masters the refinement of various powers and expressions, the examination and calculation related to the graphs of functions, the trigonometry of oblique triangles and trigonometric equations, vector calculations and exponent and logarithmic equations.

Objective

Student is able to use following mathematical tools within engineering framework:
• Handling and simplifying mathematical expressions
• Solving equations, groups of equations and inequalities
• Functions
• Vector algebra and vector models of technical phenomena
• Matrix algebra

Content

• Mathematical expressions, equations, groups of equations and inequalities
• Matrix algebra, inverse matrix and determinant
• Polynomial functions
• Exponential functions
• Logarithmic functions
• Trigonometric functions and radians
• Vector algebra

Evaluation scale

H-5

Objective

Student is able to use following mathematical tools within engineering framework:
• Handling and simplifying mathematical expressions
• Solving equations, groups of equations and inequalities
• Functions
• Vector algebra and vector models of technical phenomena
• Matrix algebra

Content

• Mathematical expressions, equations, groups of equations and inequalities
• Matrix algebra, inverse matrix and determinant
• Polynomial functions
• Exponential functions
• Logarithmic functions
• Trigonometric functions and radians
• Vector algebra

Evaluation scale

H-5

Objective

Student is able to use following mathematical tools within engineering framework:
• Handling and simplifying mathematical expressions
• Solving equations, groups of equations and inequalities
• Functions
• Vector algebra and vector models of technical phenomena
• Matrix algebra

Content

• Mathematical expressions, equations, groups of equations and inequalities
• Matrix algebra, inverse matrix and determinant
• Polynomial functions
• Exponential functions
• Logarithmic functions
• Trigonometric functions and radians
• Vector algebra

Evaluation scale

H-5