British Columbia Institute of Technologywww.bcit.ca/study/courses/math1431

# MATH 1431 - Technical Mathematics for Electronics

## Mathematics Part-time Studies Course

### School of Computing and Academic Studies

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# Course Details

This course covers methods for solving systems of linear equations with application to DC networks. Logarithmic and exponential functions and their application to electric transients, decibels and linearization of power and exponential relationships are discussed. Students will learn about trigonometric functions, circular motion, graphing sinusoidal functions and addition of sinusoids. In addition, students will carry out the representation and arithmetic of complex numbers with application to AC circuit analysis.

## Credits

6.0

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# Learning Outcomes

Upon successful completion of this course, the student will be able to:

• Solve (iii) a system of linear equations involving two or three variables with substitution, unstructured/structured elimination and determinants. [1]
• Use (iii) loop analysis and nodal analysis to set up a system of linear equations for a DC network comprised of resistors and independent voltage and current sources. [1, 2]
• Solve (iii) logarithmic and exponential equations, primarily involving base ‘e’ and base ‘10’. [1]
• Calculate (iii) the power gain (in dB) and power ratio for single and multi-stage power amplifier arrangements. [1, 2]
• Prepare (iii) generalized exponential decay equations (in terms of initial value, final value and time constant) for voltage and current transients in RL and RC circuits subjected to DC (or “step-type”) input voltages. [1, 2]
• Use (iii) plotting on ordinary, semi-logarithmic and full-logarithmic graph paper as a means of verifying simple linear, exponential and power law relationships and determining the constants in the appropriate relationship. [1, 2]
• Apply (iii) trigonometric functions in situations involving right-angled and oblique-angled triangles. [1]
• Identify (iii) the amplitude, period, frequency, DC offset and time-displacement of a sinusoidal waveform from either an equation or a graph of the waveform. [1]
• Prepare (iii) voltage and impedance triangles for simple AC circuits (i.e. series RLC). [1]
• Represent (iii) a complex number in its various forms (rectangular, polar, exponential and trigonometric). [1]
• Perform (iii) addition, subtraction, multiplication and division of complex numbers both manually and with a recommended calculator. [1]
• Apply (iii) the concepts of phasors, complex impedance and complex admittance to single-source AC circuits. [1, 2]
• Calculate (iii) the simplest equivalent circuits (both series and parallel) for a given AC network and operating frequency. [1, 2]

## Learning Outcome Taxonomy

Based on the BCIT Learning and Teaching Centre publication “Writing Learning Outcomes”, the ECET department has defined four levels describing the depth of learning for each outcome. These are:

(i) Knowledge – Topics are mentioned, but not covered much beyond introduction or awareness.

(ii) Comprehension - Students are expected to explain and understand a topic.

(iii) Application - Students are expected to apply the information in new, but similar, situations.

(iv) Analysis, Evaluation, Synthesis - A thorough covering of a topic such that students can analyze and design new solutions.

## Engineering Accreditation

The Canadian Engineering Accreditation Board (CEAB) oversees the accreditation of engineering programs across Canada. To measure the effectiveness of an engineering program the CEAB has identified twelve specific attributes that the graduate is expected to possess and use as the foundation to developing and advancing an engineering career. To ensure that the overall curriculum of the Bachelor of Engineering in Electrical program covers these attributes sufficiently, the learning outcomes for each course have been mapped to applicable CEAB graduate attributes.

1. A knowledge base for engineering: Demonstrated competence in university level mathematics, natural sciences, engineering fundamentals, and specialized engineering knowledge appropriate to the program.

2. Problem analysis: An ability to use appropriate knowledge and skills to identify, formulate, analyze, and solve complex engineering problems in order to reach substantiated conclusions.

3. Investigation: An ability to conduct investigations of complex problems by methods that include appropriate experiments, analysis and interpretation of data, and synthesis of information in order to reach valid conclusions.

4. Design: An ability to design solutions for complex, open-ended engineering problems and to design systems, components or processes that meet specified needs with appropriate attention to health and safety risks, applicable standards, and economic, environmental, cultural and societal considerations.

5. Use of engineering tools: An ability to create, select, apply, adapt, and extend appropriate techniques, resources, and modern engineering tools to a range of engineering activities, from simple to complex, with an understanding of the associated limitations.

6. Individual and team work: An ability to work effectively as a member and leader in teams, preferably in a multi-disciplinary setting.

7. Communication skills: An ability to communicate complex engineering concepts within the profession and with society at large. Such ability includes reading, writing, speaking and listening, and the ability to comprehend and write effective reports and design documentation, and to give and effectively respond to clear instructions.

8. Professionalism: An understanding of the roles and responsibilities of the professional engineer in society, especially the primary role of protection of the public and the public interest.

9. Impact of engineering on society and the environment: An ability to analyze social and environmental aspects of engineering activities. Such ability includes an understanding of the interactions that engineering has with the economic, social, health, safety, legal, and cultural aspects of society, the uncertainties in the prediction of such interactions; and the concepts of sustainable design and development and environmental stewardship.

10. Ethics and equity: An ability to apply professional ethics, accountability, and equity.

11. Economics and project management: An ability to appropriately incorporate economics and business practices including project, risk, and change management into the practice of engineering and to understand their limitations.

12. Life-long learning: An ability to identify and to address their own educational needs in a changing world in ways sufficient to maintain their competence and to allow them to contribute to the advancement of knowledge.

Effective as of Fall 2018

# Related Programs

MATH 1431 is offered as a part of the following programs:

## School of Energy

1. Electrical Engineering
Full-time   Bachelor of Engineering
2. Electrical and Computer Engineering Technology (Automation and Instrumentation Option)
Full-time/Cooperative Education   Diploma
3. Electrical and Computer Engineering Technology (Electrical Power and Industrial Control Option)
Full-time/Cooperative Education   Diploma
4. Electrical and Computer Engineering Technology (Telecommunications and Networks Option)
Full-time/Cooperative Education   Diploma

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