Portland Community College | Portland, Oregon CCOG for MT 106 Winter 2022

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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:

1. Introduction to the Powers of Ten
1. Convert numbers from (and to) scientific notation and System International values with prefixes.
2. Present the correct number of significant digits in measurements and calculations
3. Complete basic operations using number expression in scientific notation
2. Fractions, decimals and percentages
1. Perform basic operations on fractions.
2. Convert fractions to decimals.
3. Calculate percentages of numbers written as decimals, in scientific notation and as fractions.
4. Determine variations in measured values as a function of tolerances.
5. Identify the relationship between tolerance and error stacking in system design
3. Units and linear equations
1. Learn the relationship between the base and derived SI units.
2. Convert between SI units and other commonly used units for mechatronic systems
3. Label equations and solutions with units as appropriate.
4. Solve linear equations related to mechatronics applications
4. Graphing
1. Graph linear and non-linear relationships in a rectangular coordinate system
2. Analyze a line for slope, x and y intercepts.
3. Graph non-linear relationships in log-linear and log-log scaling.
4. Identify points on a log-linear and a log-log curve.
5. Estimate data from a graph.
6.  Generate graphs using best practices for axis scaling, axis labels, and font size.
5. Graphical exploration of functions used in mechatronics
1. Explore the relationship between the symbolic and graphical representation of a function
2. Graph polynomial functions in a spreadsheet program.
3. Analyze the relationship between pneumatic design factors, pressure and force in graphical form
6. Geometry
1. Determine the volume of a cylinder using provided dimensions.
2. Determine the cross-sectional area of a cylinder using provided dimensions
3. Apply the Pythagorean theorem to identify the lengths and angles in a right-triangle
7. Complex numbers and trigonometry
1. Perform basic operations using complex numbers.
2. Graph complex numbers in vector format.
3. Convert complex numbers to polar number format.
8. Logarithms, natural logarithms, exponents, decibels
1. Convert between scientific notation and base ten logarithm notation.
2. Perform basic operations on logarithms.
3. Identify the decibel value based upon sound, power, and voltage.
4. Express logarithmic functions using base e.
5. Graph logarithmic relationships.