Study Guide

Objective

After completing the course the student can:
- operate with mathematical expressions related to technology
- to formulate the simple mathematical model
- solve equations
- understand the concept of a function and recognizes the characteristic properties of different basic functions
- solve equations involving basic functions and apply them in practical problems
- recognize graphs of basic functions
- understand basic terminology of geometry
- calculate areas and volumes of two- and three-dimensional objects
- apply vectors to technical problems

Content

- Mathematical expressions
- Basic Functions and terminology
- Basic of Vectors and Trigonometric

Materials

Edita; Insinöörin matematiikka; Ari Tuomenlehto & co.
Itslearning-site and material linked there.

Teaching methods

The teaching is based on contact teaching, exercises and ViLLE-excercices.
Course has 8 mandatory teaching sessions which focus on excericices.

Exam schedules

The first mid exam on week 9.
The second mid exam on week 16.

There is a possibility of taking a full exam in May and August. A mid exam cannot be redone.

International connections

Teaching sessions consist of theory and examples. The focus on learning is placed on the activity of the student in participation and working on exercises.

Completion alternatives

Finishing the final exam.

Student workload

5 credits = 134 hours of work by the student

36 * 2 h = 72 h contact teaching
2 * 2 h = 4 h exams
58 h personal studying (approximately 5 hours a week) including working on exercises and preparing for exams.

Content scheduling

Compentence objectives

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 vector for modeling and solving technical problems.
- Understands the basics concepts of geometry and trigonometry, and can apply the in modeling and problem solving
- Understands the concept of function and knows basic properties of functions.
- Can apply functions for modeling and solving technical problems.
- Understands the basic concepts of matrix algebra
- Can apply groups of equations for modeling and solving technical problems
- Can apply correct mathematical notations within the engineering framework.
- Content of the study unit
- Representation of numbers
- Integers, rationals and Reals
- Basic mathematical operations and the order of operations
- Rational expressions, Powers and Polynomials
- Polynomial functions and polynomial equations of first or second degree
- Simultaneous equations
- Roots and root equations
- Exponential functions and exponential equations
- Logarithmic functions and logarithmic equations
- Unit circle and radians
- Trigonometric functions and trigonometric equations
- The sine and cosine rules and solving common triangles
- Basic concepts of vector algebra and modeling with vectors
- Scalar product and cross product of vectors
- Basics of matrix algebra, determinant, inverse matrix
- Field-specific content.

Further information

Informing is done during contact teaching, by email or in the ITS-learning site. If you want to contact the teacher, please do it via email.

Evaluation scale

H-5

Assessment methods and criteria

Course points (max 42 p) consist of:

Exercises 0-6 p.
ViLLE exercises 0-4 p.

and EITHER

Mid exam 1: 0-16 p
Mid exam 2: 0-16 p

OR

Final exam 0-32p

A passed grade requires 10 points in total from mid exams or 10 points from the final exam. After this the grade is given by the following table:

Grade 1: 16 course ponts
Grade 2: 21 course points
Grade 3: 26 course points
Grade 4: 31 course points
Grade 5: 36 course points

Assessment criteria, fail (0)

The student has under 16 course points OR has not attended the mandatory sessions OR has not acquired 40 % of all possible points from ViLLE exercises..

Assessment criteria, satisfactory (1-2)

The student has attended the mandatory sessions AND gathered 16-25 course points.

Assessment criteria, good (3-4)

The student has attended the mandatory sessions AND gathered 26-35 course points.

Assessment criteria, excellent (5)

The student has attended the mandatory sessions AND gathered at least 36 course points.

Objective

After completing the course the student can:
- operate with mathematical expressions related to technology
- to formulate the simple mathematical model
- solve equations
- understand the concept of a function and recognizes the characteristic properties of different basic functions
- solve equations involving basic functions and apply them in practical problems
- recognize graphs of basic functions
- understand basic terminology of geometry
- calculate areas and volumes of two- and three-dimensional objects
- apply vectors to technical problems

Content

- Mathematical expressions
- Basic Functions and terminology
- Basic of Vectors and Trigonometric

Evaluation scale

H-5

Objective

After completing the course the student can:
- operate with mathematical expressions related to technology
- to formulate the simple mathematical model
- solve equations
- understand the concept of a function and recognizes the characteristic properties of different basic functions
- solve equations involving basic functions and apply them in practical problems
- recognize graphs of basic functions
- understand basic terminology of geometry
- calculate areas and volumes of two- and three-dimensional objects
- apply vectors to technical problems

Content

- Mathematical expressions
- Basic Functions and terminology
- Basic of Vectors and Trigonometric

Evaluation scale

H-5

Objective

After completing the course the student can:
- operate with mathematical expressions related to technology
- to formulate the simple mathematical model
- solve equations
- understand the concept of a function and recognizes the characteristic properties of different basic functions
- solve equations involving basic functions and apply them in practical problems
- recognize graphs of basic functions
- understand basic terminology of geometry
- calculate areas and volumes of two- and three-dimensional objects
- apply vectors to technical problems

Content

- Mathematical expressions
- Basic Functions and terminology
- Basic of Vectors and Trigonometric

Evaluation scale

H-5

Objective

After completing the course the student can:
- operate with mathematical expressions related to technology
- to formulate the simple mathematical model
- solve equations
- understand the concept of a function and recognizes the characteristic properties of different basic functions
- solve equations involving basic functions and apply them in practical problems
- recognize graphs of basic functions
- understand basic terminology of geometry
- calculate areas and volumes of two- and three-dimensional objects
- apply vectors to technical problems

Content

- Mathematical expressions
- Basic Functions and terminology
- Basic of Vectors and Trigonometric

Materials

Edita; Insinöörin matematiikka; Ari Tuomenlehto & co.
Itslearning-site and material linked there.

Teaching methods

The teaching is based on contact teaching, exercises and ViLLE-excercises.
One of the teaching sessions emphasizes in weekly exercises.

Exam schedules

The first mid exam on week 43.
The second mid exam on week 50.

There is a possibility of taking a full exam in January and February. A mid exam cannot be redone.

International connections

Teaching sessions consist of theory and examples. The focus on learning is placed on the activity of the student in participation and working on exercises.

Completion alternatives

Finishing the final exam.

Student workload

5 credits = 134 hours of work by the student

35 * 2 h = 70 h contact teaching
2 * 2 h = 4 h exams
60 h personal studying (approximately 5 hours a week) including working on exercises and preparing for exams.

Content scheduling

Compentence objectives

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 vector for modeling and solving technical problems.
- Understands the basics concepts of geometry and trigonometry, and can apply the in modeling and problem solving
- Understands the concept of function and knows basic properties of functions.
- Can apply functions for modeling and solving technical problems.
- Understands the basic concepts of matrix algebra
- Can apply groups of equations for modeling and solving technical problems
- Can apply correct mathematical notations within the engineering framework.
- Content of the study unit
- Representation of numbers
- Integers, rationals and Reals
- Basic mathematical operations and the order of operations
- Rational expressions, Powers and Polynomials
- Polynomial functions and polynomial equations of first or second degree
- Simultaneous equations
- Roots and root equations
- Exponential functions and exponential equations
- Logarithmic functions and logarithmic equations
- Unit circle and radians
- Trigonometric functions and trigonometric equations
- The sine and cosine rules and solving common triangles
- Basic concepts of vector algebra and modeling with vectors
- Scalar product and cross product of vectors
- Basics of matrix algebra, determinant, inverse matrix
- Field-specific content.

Further information

Informing is done during contact teaching, by email or in the ITS-learning site. If you want to contact the teacher, please do it via email.

Evaluation scale

H-5

Assessment methods and criteria

Course points (max 42 p) consist of:

Exercises 0-7 p.
ViLLE exercises 0-3 p.

and EITHER

Mid exam 1: 0-16 p
Mid exam 2: 0-16 p

OR

Final exam 0-32p

A passed grade requires 10 points in total from mid exams or 10 points from the final exam. After this the grade is given by the following table:

Grade 1: 16 course ponts
Grade 2: 21 course points
Grade 3: 26 course points
Grade 4: 31 course points
Grade 5: 36 course points

Objective

After completing the course the student can:
- operate with mathematical expressions related to technology
- to formulate the simple mathematical model
- solve equations
- understand the concept of a function and recognizes the characteristic properties of different basic functions
- solve equations involving basic functions and apply them in practical problems
- recognize graphs of basic functions
- understand basic terminology of geometry
- calculate areas and volumes of two- and three-dimensional objects
- apply vectors to technical problems

Content

- Mathematical expressions
- Basic Functions and terminology
- Basic of Vectors and Trigonometric

Evaluation scale

H-5

Objective

After completing the course the student can:
- operate with mathematical expressions related to technology
- to formulate the simple mathematical model
- solve equations
- understand the concept of a function and recognizes the characteristic properties of different basic functions
- solve equations involving basic functions and apply them in practical problems
- recognize graphs of basic functions
- understand basic terminology of geometry
- calculate areas and volumes of two- and three-dimensional objects
- apply vectors to technical problems

Content

- Mathematical expressions
- Basic Functions and terminology
- Basic of Vectors and Trigonometric

Evaluation scale

H-5

Objective

After completing the course the student can:
- operate with mathematical expressions related to technology
- to formulate the simple mathematical model
- solve equations
- understand the concept of a function and recognizes the characteristic properties of different basic functions
- solve equations involving basic functions and apply them in practical problems
- recognize graphs of basic functions
- understand basic terminology of geometry
- calculate areas and volumes of two- and three-dimensional objects
- apply vectors to technical problems

Content

- Mathematical expressions
- Basic Functions and terminology
- Basic of Vectors and Trigonometric

Evaluation scale

H-5

Objective

After completing the course the student can:
- operate with mathematical expressions related to technology
- to formulate the simple mathematical model
- solve equations
- understand the concept of a function and recognizes the characteristic properties of different basic functions
- solve equations involving basic functions and apply them in practical problems
- recognize graphs of basic functions
- understand basic terminology of geometry
- calculate areas and volumes of two- and three-dimensional objects
- apply vectors to technical problems

Content

- Mathematical expressions
- Basic Functions and terminology
- Basic of Vectors and Trigonometric

Evaluation scale

H-5

Objective

After completing the course the student can:
- operate with mathematical expressions related to technology
- to formulate the simple mathematical model
- solve equations
- understand the concept of a function and recognizes the characteristic properties of different basic functions
- solve equations involving basic functions and apply them in practical problems
- recognize graphs of basic functions
- understand basic terminology of geometry
- calculate areas and volumes of two- and three-dimensional objects
- apply vectors to technical problems

Content

- Mathematical expressions
- Basic Functions and terminology
- Basic of Vectors and Trigonometric

Evaluation scale

H-5

Objective

After completing the course the student can:
- operate with mathematical expressions related to technology
- to formulate the simple mathematical model
- solve equations
- understand the concept of a function and recognizes the characteristic properties of different basic functions
- solve equations involving basic functions and apply them in practical problems
- recognize graphs of basic functions
- understand basic terminology of geometry
- calculate areas and volumes of two- and three-dimensional objects
- apply vectors to technical problems

Content

- Mathematical expressions
- Basic Functions and terminology
- Basic of Vectors and Trigonometric

Evaluation scale

H-5