### CCOG for MT 106 Winter 2022

- Course Number:
- MT 106
- Course Title:
- Math for Mechatronics
- Credit Hours:
- 3
- Lecture Hours:
- 30
- Lecture/Lab Hours:
- 0
- Lab Hours:
- 0

#### Course Description

Provides a framework for applying mathematical concepts and principles to mechatronics situations and problems through collaborative learning. Involves development, articulation, and documentation of individual problem-solving strategies. Explores mechatronics problem topics including dimensional analysis, metrology, the metric system, pneumatics and hydraulics. Graphing technology and use of a spreadsheet program is required. Prerequisites: (MTH 58 or MTH 60), (WR 115 and RD 115) or IRW 115 or equivalent placement. Audit available.

#### Intended Outcomes for the course

Upon completion of the course student should be able to:

- Solve problems related to mechatronics systems using appropriate techniques involving algebra, geometry, and trigonometry correctly.
- Apply dimensional analysis both to convert between different systems of units and to evaluate relationships between the form and function of a mechatronics system.
- ?Communicate mathematical mechatronics information in written and oral form.

#### Aspirational Goals

Confidence in implementation of mathematics to support empirical design and troubleshooting of Mechatronics systems.

#### Course Activities and Design

The course will include 3 hours of lecture per week. Campus and/or distance training may be employed.

#### Outcome Assessment Strategies

The instructor may use attendance, quizzes, exams, homework, group projects, or individual projects to assess student progress.

#### Course Content (Themes, Concepts, Issues and Skills)

Themes, Concepts, and Issues:

- Accuracy in performing calculations and analysis across different systems of units
- Problem solving using mathematical concepts in support of empirical troubleshooting
- Interpretation of graphs
- Communication of mathematical concepts related to mechatronics in written and oral form

Skills:

- Introduction to the Powers of Ten
- Convert numbers from (and to) scientific notation and System International values with prefixes.
- Present the correct number of significant digits in measurements and calculations
- Complete basic operations using number expression in scientific notation

- Fractions, decimals and percentages
- Perform basic operations on fractions.
- Convert fractions to decimals.
- Calculate percentages of numbers written as decimals, in scientific notation and as fractions.
- Determine variations in measured values as a function of tolerances.
- Identify the relationship between tolerance and error stacking in system design

- Units and linear equations
- Learn the relationship between the base and derived SI units.
- Convert between SI units and other commonly used units for mechatronic systems
- Label equations and solutions with units as appropriate.
- Solve linear equations related to mechatronics applications

- Graphing
- Graph linear and non-linear relationships in a rectangular coordinate system
- Analyze a line for slope, x and y intercepts.
- Graph non-linear relationships in log-linear and log-log scaling.
- Identify points on a log-linear and a log-log curve.
- Estimate data from a graph.
- Generate graphs using best practices for axis scaling, axis labels, and font size.

- Graphical exploration of functions used in mechatronics
- Explore the relationship between the symbolic and graphical representation of a function
- Graph polynomial functions in a spreadsheet program.
- Analyze the relationship between pneumatic design factors, pressure and force in graphical form

- Geometry
- Determine the volume of a cylinder using provided dimensions.
- Determine the cross-sectional area of a cylinder using provided dimensions
- Apply the Pythagorean theorem to identify the lengths and angles in a right-triangle

- Complex numbers and trigonometry
- Perform basic operations using complex numbers.
- Graph complex numbers in vector format.
- Convert complex numbers to polar number format.

- Logarithms, natural logarithms, exponents, decibels
- Convert between scientific notation and base ten logarithm notation.
- Perform basic operations on logarithms.
- Identify the decibel value based upon sound, power, and voltage.
- Express logarithmic functions using base e.
- Graph logarithmic relationships.