Study Guide

Objective

After completing the course, the student
• can handle mathematical expressions and formulas within the engineering framework.
• understands the principles of solving equations and can solve equations encountered within technical applications.
• understands the basics of vector algebra and can apply vectors for modelling and solving technical problems.
• understands the basics concepts of geometry and trigonometry, and can apply them in modelling and problem solving.
• understands the concept of function and knows basic properties of functions.
• can apply functions for modelling and solving technical problems.
• understands the basic concepts of matrix algebra.
• can apply simultaneous equations for modelling and solving technical problems.
• can apply correct mathematical notations within the engineering framework.

Content

• Real numbers
• Basic arithmetic operations and the order of operations
• Algebraic expressions
• First and second order of polynomial equations and inequalities
• Simultaneous linear equations
• Radical functions and equations
• Exponential and logarithmic functions and equations
• Angles and angular units
• Right triangle and trigonometry
• Trigonometric functions and the unit circle
• Trigonometric equations
• The sine and cosine rules
• Basic concepts of vector algebra and modelling with vectors
• Scalar product and cross product of two vectors
• Basics of matrix algebra, determinant, inverse of a square matrix
• Field-specific content

Materials

Textbook: College Algebra 2e https://openstax.org/details/books/college-algebra-2e
The table book/Formula will be distributed during the course.
Calculator: Casio FX-82CW ClassWiz Function Calculator (recommended) or Function Calculator TI-30XA (adequate basic calculator). A graphic/symbolic calculator will also work.
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

In the course, the theory is reviewed under the guidance of the teacher, but before the class, students are offered instructional videos and pre-tasks to familiarize themselves with the topic. The lessons support the calculation of the weekly calculation exercises, and the main focus of the lesson is on the issues about which the students have questions based on the teaching videos and preliminary assignments.

Exam schedules

Midterm exams during the week ** OR course exam during the week **. To be completed at the start of the course
If necessary, 2 retakes during spring 2025 (you can repeat either midterm exam 2 or the exam that measures the content of the entire course)

International connections

Learning-by-doing and theory lectures.
Learning is largely based on the student's own active participation and performance.
Students are given both review tasks and material to support their performance on the studied subjects.
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 a course exam measuring the content of the course at a time agreed with the teacher.

Student workload

5 credits = 134 t of student work, divided into meetings and independent tasks.
- Classroom meetings 56 h
- Independent study (calculation exercises and studying for exams) 71-74 h = about 5 hours of independent study per week!
- Competence tests that measure competence (performance is taken into account in the case of a grade limit) 2 h
- 2 midterm exams OR one course exam (part of the course credits) 2-5 h

Content scheduling

The start meeting of the course is in week 3.

Attending classes is mandatory and the teacher must be informed in advance of absences.

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
- Trigonometry of right and oblique triangles
- 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 mathematics software to support tasks

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

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:
- Calculation practice handouts max 1 p/handout * 12 handouts, however a maximum of 11 p.
- For independent ViLLE tasks exceeding the required 30%, 1% = 0.1p, total max 7p
- Two partial exams (max 50p) or one course exam (max 100p)

To get course points from the calculations, it is necessary to return them to Its in electronic form and to self-evaluate 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 30% of the maximum points of independent ViLLE tasks
- at least 40 course credits in total

Other grades are determined by points on a linear scale.

A good performance in intermediate tests that measure competence is taken into account in the case of a grade limit.

Assessment criteria, fail (0)

The student lacks one of the required passing conditions:
- The student has not received at least 30% 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 30% of the maximum points of 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 30% of the maximum points of 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 30% 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, trigonometry and trigonometric equations of diagonal triangles, vector calculations and exponent and logarithmic equations.

Qualifications

Introduction to mathematical sciences or corresponding skills.