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Course Outline

Course Name: Technical Mathematics 2: Civil Engineering (TMTH 202)

Academic Period: 2023 - 2024

Faculty:


Faculty Availability:

Associate Dean:
Mike Wells
mike.wells@humber.ca

Schedule Type Code:

Land Acknowledgement

Humber College is located within the traditional and treaty lands of the Mississaugas of the Credit. Known as Adoobiigok [A-doe-bee-goke], the “Place of the Alders” in Michi Saagiig [Mi-Chee Saw-Geeg] language, the region is uniquely situated along Humber River Watershed, which historically provided an integral connection for Anishinaabe [Ah-nish-nah-bay], Haudenosaunee [Hoeden-no-shownee], and Wendat [Wine-Dot] peoples between the Ontario Lakeshore and the Lake Simcoe/Georgian Bay regions. Now home to people of numerous nations, Adoobiigok continues to provide a vital source of interconnection for all.

Equity, Diversity and Inclusion Statement

Humber College and the University of Guelph-Humber (Humber) are leaders in providing a learning, working and living environment that recognizes and values equity, diversity and inclusion in all its programs and services. Humber commits to reflect the diversity of the communities the College serves. Students, faculty, support and administrative staff feel a sense of belonging and have opportunities to be their authentic selves.

Faculty or Department Faculty of Liberal Arts & Sciences
Program(s)
Civil Engineering Technology (03351)
Course Name: Technical Mathematics 2: Civil Engineering (TMTH 202)
Pre-Requisites TMTH 105 OR TMTH 102
Co-Requisites none
Pre-Requisites for none
Equates none
Restrictions none
Credit Value 3
Total Course Hours 42
Developed By: Prepared By: Approved by:
Mike Wells

Humber Learning Outcomes (HLOs) in this course.

The HLOs are a cross-institutional learning outcomes strategy aimed at equipping Humber graduates with the employability skills, mindsets, and values they need to succeed in the future of work. To explore all the HLOs, please consult the Humber Learning Outcomes framework.

  • Critical Thinking
  • Communication
  • Strategic Problem-Solving

Course Description

This is a second course in Technical Mathematics designed to provide students with mathematical skills that they will need in their career, including: graphing of trigonometric equations, system of two and three equations in 2 and 3 unknowns, equations of quadratic type, systems of quadratic equations, exponential and logarithmic functions, and plane analytic geometry.

Course Rationale

This is a second course in mathematics designed to provide students with the mathematical skills that they will need in their career, including: • Identifying the premises and assumptions underlying technical problems. • Selecting relevant and useful information within the given data to achieve a solution to the problem. • Organizing and analyzing data using tables, diagrams, and graphs. • Formulating graphical and symbolic models to test hypotheses in applications. • Applying critical and mathematical thinking to solve problems in their fields of expertise. By working through numerous examples and exercises that are drawn from real-world technical application, students will also develop the confidence and versatility in using mathematical tools while appreciating the relevance of these tools in allied technical fields of study.

Program Outcomes Emphasized in this Course

Civil Engineering Technology (03351)

  1. Collect, process, analyze and coordinate technical data to produce written and graphical project-related documents.
  2. Participate in the design and modeling phase of civil engineering projects* by applying engineering concepts, technical mathematics* and principles of science to the review, production and/or modification of project plans.

Course Learning Method(s)

  • Group or Team Work
  • Lecture
  • Inquiry Based Learning

Learning Outcomes

  • Solve Problems that involve manipulation of trigonometric functions.
  • Solve problems involving systems of linear and quadratic equations using substitution, elimination, and/or determinants in two and three equations in two and three unknowns.
  • Solve problems involving quadratic, exponential, logarithmic, and trigonometric equations involving some application problems.
  • Solve problems involving plane analytic geometry including circles, parabola, ellipses, and hyperbola.
  • Create and analyze graphs of exponential, logarithmic, and trigonometric functions.
  • Perform operations on matrices.

Assessment Weighting

Assessment Weight
Instructor-Created Assessments 10%
Final Exam 35%
Midterm Exam 35%
Quiz 20%
Total 100%

Modules of Study

Module Course Learning Outcomes Resources Assessments
Graph of Trigonometric Functions: • The Sine wave • The General Sine Wave, y= a sin (bx+c) • The General Cosine Wave, y= a cos (bx+c)
  • Solve Problems that involve manipulation of trigonometric functions.

17.1 - 5, 6, 7, 11

17.2 - 1, 3, 8, 12, 15, 17

  • Quiz Quizzes
  • Mid-term Midterm Exam
  • Final Exam Final Exam
Systems of Linear Equations of Two and Three Unknowns: • Systems of Two Linear Equations • Other Systems of Equations • Word Problems • Systems of Three Linear Equations
  • Solve problems involving systems of linear and quadratic equations using substitution, elimination, and/or determinants in two and three equations in two and three unknowns.

10.1 - 7, 15, 27, 28, 30

10.2 - 3, 5, 8, 12, 15, 17

10.3 – 1, 6, 8, 19, 20, 24, 25, 26, 30, 31

10. 4 - 3, 7, 11, 13, 16, 17

  • Quiz Quizzes
  • Mid-term Midterm Exam
  • Final Exam Final Exam
Determinants: • Second-Order Determinants • Third-Order Determinants
  • Solve problems involving systems of linear and quadratic equations using substitution, elimination, and/or determinants in two and three equations in two and three unknowns.

11.1 - 3, 5, 10, 12, 19, 29, 31, 36, 40, 41,   43, 44

11.2 - 3, 6, 7, 9, 13, 15, 18, 19, 21, 23, 25

  • Quiz Quizzes
  • Mid-term Midterm Exam
  • Final Exam Final Exam
Matrices: • Matrices Definition • Operation with Matrices • The Inverse of a Matrix ( 2x2) • Solving a System of Linear Equations by Matrix Inversion ( 2x2)
  • Perform operations on matrices.

12.1 - 2, 7, 8, 9, 11, 13, 18

12.2 - 3, 5, 6, 9, 11, 13, 17, 23, 27, 29, 33,

37, 39, 41, 46

12.3 - 1, 2, 3

12.4- 1 (2X2)

12.R- 13

  • Quiz Quizzes
  • Mid-term Midterm Exam
  • Final Exam Final Exam
Quadratic Equations and Systems of Quadratic Equations: • Solving Quadratic by Factoring • Solving Quadratic by Formula • Equations of Quadratic Type • System of Quadratic Equations
  • Solve problems involving systems of linear and quadratic equations using substitution, elimination, and/or determinants in two and three equations in two and three unknowns.
  • Solve problems involving quadratic, exponential, logarithmic, and trigonometric equations involving some application problems.

14.1 - 1, 9, 11, 23, 25, 28, 37, 39

14.3 - 3, 5, 9, 10

14.6 - 1, 2, 4, 5,, 8, 13

14.8 - 1, 3, 7, 10, 11, 12

  • Quiz Quizzes
  • Mid-term Midterm Exam
  • Final Exam Final Exam
Trigonometric Identities and Equations: • Fundamental Identities • Trigonometric Equations
  • Solve Problems that involve manipulation of trigonometric functions.

18.1 - 19, 20, 28, 31, 32, 35, 39, 44, 45

18.5 - 1, 5, 15, 16, 23

  • Quiz Quizzes
  • Final Exam Final Exam
Exponential and Logarithmic Functions: • The Exponential Function • Exponential Growth and Decay • Logarithms • Properties of Logarithms • Exponential Equations • Logarithmic Equations
  • Solve problems involving quadratic, exponential, logarithmic, and trigonometric equations involving some application problems.

20.1 - 3, 4

20.2 - 1, 2, 3, 5, 7, 9, 10, 11, 14, 15

20.3 - 5, 11, 13, 15, 23, 26, 27, 30, 31, 37, 53, 55, 59

20.4 - 3, 7, 9, 11, 17, 19, 21, 25

20.5 - 3, 7, 8, 9, 13, 23, 29, 30, 36, 37

20.6 - 1, 7, 9, 11, 25, 29, 33, 43

  • Quiz Quizzes
  • Final Exam Final Exam
Plane Analytic Geometry: • The Circle • The Parabola (Centre at Origin) • The Ellipse (Centre at Origin) • The Hyperbola (Centre at Origin)
  • Solve problems involving plane analytic geometry including circles, parabola, ellipses, and hyperbola.

22.2 - 1, 5, 7, 11, 19, 21, 22

22.3 - 3, 5, 7, 23, 26

22.4 - 1, 5, 7, 9, 11, 30, 33

22.5 - 1, 5, 7, 9, 10, 27

  • Quiz Quizzes
  • Final Exam Final Exam

Required Resources

Name

Calter, Calter, Wraight & White. (2016). Technical Mathematics with Calculus. (3rd    Cnd ed.). John Wiley & Sons Inc., Canada Ltd. Hardcover Book ISBN: 9781118962145 or E-Text Version ISBN: 9781119272724 (other options available).

Students enrolled in online sections of the course may be required to come to campus to write the tests and exams.

Additional Tools and Equipment

  • Scientific Calculator: CASIO-FX991 ESPLUS2 (Suggested)

Essential Skills

Section Skills Measurement Details
Communication
  • Reading
  • Writing
  • Listening
  • Visual Literacy
Reinforce and measure
  • - Students are taught to extract the useful information from a given set of questions in written or graphical format. - Students are expected to clearly and effectively show their work.
  • - Students' learning will be monitored in class through a variety of formative assessments. - Students' learning is assessed through a variety of summative assessments such as quizzes and exam
Numeracy
  • Understanding and applying mathematical concepts and reasoning
  • Analyzing and using numerical data
Teach and measure
  • _ Students are taught a variety of mathematical concepts and their different applications. - Students are presented with a different possibilities of analyzing and processing a math question to reach a unique final answer.
  • - Students' learning will be monitored in class through a variety of formative assessments. - Students' learning is assessed through a variety of summative assessments such as quizzes and exams.
Critical Thinking and Problem-Solving
  • Analysing
  • Evaluating
Reinforce and measure
  • - Students are taught to break down all the mathematical questions to extract all the useful information. - Students are taught to apply their knowledge and use these information to properly solve each individual problems.
  • - Students' learning will be monitored in class through a variety of formative assessments. - Students' learning is assessed through a variety of summative assessments such as quizzes and exams.
Information Management
  • Gathering and managing information
  • Selecting and using appropriate tools and technology for a task or project
Teach and measure
  • - Students are taught to break down all the mathematical questions to extract all the useful information. - Students are taught to apply their knowledge and their appropriate tools to properly solve each individual problems.
  • - Students' learning will be monitored in class through a variety of formative assessments. - Students' learning is assessed through a variety of small and big summative assessments such as quizzes and exams.
Personal Skills
  • Managing self
  • Managing change and being flexible and adaptable
  • Engaging in reflective practice
  • Demonstrating personal responsibility
Reinforce and measure
  • - by completing their assessments in a timely manner.
  • - Students' learning is assessed through a variety of summative assessments such as quizzes and exams.

Prior Learning Assessment & Recognition (PLAR)

Prior Learning Assessment and Recognition (PLAR) is the formal evaluation and credit-granting process whereby candidates may obtain credits for prior learning. Prior learning includes the knowledge competencies and skills acquired, in both formal and informal ways, outside of post-secondary education. Candidates may have their knowledge, skills and competencies evaluated against the learning outcomes as defined in the course outline. Please review the Assessment Methods Glossary for more information on the Learning Portfolio assessment methods identified below.

The method(s) that are used to assess prior learning for this course may include:

  • Challenge Exam (results recorded as a % grade and added to student’s CGPA)

Please contact the Program Coordinator for more details.

Academic Regulations

It is the student's responsibility to be aware of the College Academic Regulations. The Academic Regulations apply to all applicants to Humber and all current students enrolled in any program or course offered by Humber, in any location. Information about academic appeals is found in the Academic Regulations.  

Anti-Discrimination Statement

At Humber College, all forms of discrimination and harassment are prohibited. Students and employees have the right to study, live and work in an environment that is free from discrimination and harassment. If you need assistance on concerns related to discrimination and harassment, please contact the Centre for Human Rights, Equity and Inclusion or the Office of Student Conduct.

Accessible Learning Services

Humber strives to create a welcoming environment for all students where equity, diversity and inclusion are paramount. Accessible Learning Services facilitates equal access for students with disabilities by coordinating academic accommodations and services.  Staff in Accessible Learning Services are available by appointment to assess specific needs, provide referrals and arrange appropriate accommodations. If you require academic accommodations, contact:

Accessible Learning Services

North Campus: (416) 675-6622 X5090

Lakeshore Campus: (416) 675-6622 X3331 

Academic Integrity

Academic integrity is essentially honesty in all academic endeavors. Academic integrity requires that students avoid all forms of academic misconduct or dishonesty, including plagiarism, cheating on tests or exams or any misrepresentation of academic accomplishment.

Disclaimer

While every effort is made by the professor/faculty to cover all material listed in the outline, the order, content, and/or evaluation may change in the event of special circumstances (e.g. time constraints due to inclement weather, sickness, college closure, technology/equipment problems or changes, etc.). In any such case, students will be given appropriate notification in writing, with approval from the Dean (or designate) of the School.

Copyright

Copyright is the exclusive legal right given to a creator to reproduce, publish, sell or distribute his/her work. All members of the Humber community are required to comply with Canadian copyright law which governs the reproduction, use and distribution of copyrighted materials. This means that the copying, use and distribution of copyright- protected materials, regardless of format, is subject to certain limits and restrictions. For example, photocopying or scanning an entire textbook is not allowed, nor is distributing a scanned book.

See the Humber Libraries website for additional information regarding copyright and for details on allowable limits.


Humber College Institute of Technology and Advanced Learning • 2023/2024.