Mathematics for Engineers 1 (5cr)

Objectives (course unit)

After completing this course student is able to
- operate with mathematical expressions related to technology and to formulate the mathematical model and solve the equations
- understand basic terminology of geometry
- solve a scalene triangle, calculate areas and volumes of two- and three-dimensional objects
- determine the center of mass of a plane region
- perform basic vector calculations, apply vectors to technical problems

Content (course unit)

Mathematical Notations, Unit Conversations. Mathematical Expressions. Solving Linear, Quadratic and Pair of equations. Percentages. Solving Right Triangle. Terminology of Geometry, Solving a Scalene Triangle, Areas and Volumes, Center of Mass of a Plane Region, Similarity, Scale, Vectors and Applications, Complex Numbers

Assessment criteria, satisfactory (1-2) (course unit)

Can handle basic mathematical expressions and solve simple linear equations. Limited ability in formulating mathematical models. Shows rudimentary understanding of geometry terms and basic ability in calculating areas, volumes, and solving scalene triangles. Understands basic concepts of the center of mass, vector calculations, and can perform simple calculations with complex numbers.

Assessment criteria, good (3-4) (course unit)

Effectively uses mathematical expressions and solves a range of equations, including quadratic. Good understanding of mathematical model formulation. Demonstrates a solid grasp of geometry, efficiently solving problems involving scalene triangles, and accurately calculating areas and volumes of more complex shapes. Capable of determining the center of mass for varied plane regions and performing intermediate vector calculations, applying these to technical problems.

Assessment criteria, excellent (5) (course unit)

Exhibits mastery in operating with complex mathematical expressions and solving diverse and challenging equations. Shows exceptional skill in formulating and solving mathematical models. Advanced understanding of geometry, solving complex problems involving scalene triangles, calculating areas and volumes of intricate three-dimensional objects. Accurately determines the center of mass for complex plane regions, excels in vector calculations, and innovatively applies complex numbers in various technical contexts.

Location and time

Dates and times are shown in TuniMoodle.

Exam schedules

Part 1: Geometry, Vectors and Matrices
The exam will be held on Thursday, 23th of October at 15.15-18.00 in the classroom B3-28.

Part 2: Functions
The exam will be held on Friday, 5th of December at 15.15-18.00 in the festival hall D1-04.

Two re-sit exams, the first one will be held in January and the second in February. (More information later.)

Assessment methods and criteria

The final grade is based on two exams (45 +45 points) and the homework (6 points).

A minimum of 20% of the maximum score must be achieved in each exam i.e., at least 9 points per exam. The total score from the exams and the homework must be at least 21 points."

A homework package is given weekly (approximately 12 packages). Half point is given for every submitted homework package in Moodle by deadline. Homework packages are not accepted by email. The maximum points for the part 1 (Geometry and Vectors) is 45 points and part 2 (Functions and Matrices) is 45 points. The homework and the exams together give the maximum of 45+45+6=96 points. The grade is based on the following table

21 points -> grade 1
37 points -> grade 2
53 points -> grade 3
69 points -> grade 4
85 points -> grade 5

Students are expected to study regularly, and receiving a grade requires at least 80 % attendance.

Assessment scale

0-5

Teaching methods

Contact lessons, exercises, self-study, videos, homework, exam.
A student solves exercises and saves them in TuniMoodle by given dead-lines.

Learning materials

All material, theory and exercises, can be found in TuniMoodle. If necessary, a student can use math books he/she has used before and the Internet to search more information about the topics. A student can borrow books in TAMK library. The solutions for the some homework will be published in TuniMoodle after every deadline.

Student workload

A student is expected to study 27 hours / credit unit (135 hours / 5 credit units).

Content scheduling

Topics are shown in TuniMoodle.

Completion alternatives

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Practical training and working life cooperation

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International connections

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Further information

A student is expected to have a scientific calculator and a formula book. (Formula book Technical Formulas published by Tammertekniikka is recommended.)