MTH255 - Mathematics

Outline info
Semester
School
Last revision date 2017-11-21 10:34:06.52
Last review date 2017-11-21 10:34:12.587


Subject Title
Mathematics

Subject Description
A sequel to Mathematics 155, this subject studies applied trigonometry, radicals, exponents, quadratic equations, factorable equations, quadratic type equations, complex numbers, and analytical trigonometry. In addition, logarithmic and exponential functions with emphasis on electrical/electronic applications are studied. An introduction to statistics and probability is also given.

Credit Status
One subject credit in the Computer Engineering Technology, Electronic Engineering Technology or Electronic Engineering Technician programs.

Learning Outcomes
Upon successful completion of this subject the student will be able to:

1. Identify, analyze and sketch sinusoidal waveforms with emphasis on amplitude, period , and phase shift
2. Simplify algebraic expressions with exponents and radicals
3. Identify the different forms of complex numbers (rectangular, polar, trigonometric and exponential) and perform algebraic operations on each form. Also apply knowledge of complex numbers to ac circuits
4. Recognize and solve quadratic and quadratic type equations by factoring, completing the square , and quadratic formula
5. Prove trigonometric identities, and use trigonometric identities to solve trigonometric equations
6. Apply knowledge of logarithmic and exponential functions to evaluate different electronic applications including charge-discharge of capacitors
7. Organize and display data using x-y graphs, scatter plots, bar and pie charts
8. Predict probability of single event occurring, probability of combining events and mutually exclusive events

Essential Employability Skills
Respond to written, spoken, or visual messages in a manner that ensures effective communication.

Execute mathematical operations accurately.

Apply a systematic approach to solve problems.

Use a variety of thinking skills to anticipate and solve problems.

Show respect for diverse opinions, values, belief systems, and contributions of others.

Manage the use of time and other resources to complete projects.

Take responsibility for one's own actions, decisions, and consequences.

Cheating and Plagiarism
Each student should be aware of the College's policy regarding Cheating and Plagiarism. Seneca's Academic Policy will be strictly enforced.

To support academic honesty at Seneca College, all work submitted by students may be reviewed for authenticity and originality, utilizing software tools and third party services. Please visit the Academic Honesty site on http://library.senecacollege.ca for further information regarding cheating and plagiarism policies and procedures.

Discrimination/Harassment
All students and employees have the right to study and work in an environment that is free from discrimination and/or harassment. Language or activities that defeat this objective violate the College Policy on Discrimination/Harassment and shall not be tolerated. Information and assistance are available from the Student Conduct Office at student.conduct@senecacollege.ca.

Accommodation for Students with Disabilities
The College will provide reasonable accommodation to students with disabilities in order to promote academic success. If you require accommodation, contact the Counselling and Disabilities Services Office at ext. 22900 to initiate the process for documenting, assessing and implementing your individual accommodation needs.

Prerequisite(s)
MTH155 or equivalent

Topic Outline

  1. Applied Trigonometry
  • Radian measure
  • Angles as a function of time
  • Review of sinusoids (amplitude, period and phase shift)
  • Sketch of sinusoids, e.g. V =  Vm (w t+a)
  • Solution of trig. Equations, e.g. Y = Asin(bθ), find  θ
 
  1. Exponents and  Radicals
  • Laws of exponents in general( integral and fractional)
  • Radicals: simplification, operations with radicals
  • Radical equations
 
  1. Complex numbers
  • j operator
  • powers of j
  • complex numbers: rectangular, polar, trigonometric and exponential forms
  • Conversion and operations in all forms
  • Eulers formula and De Moivre’s theorem
  
  1. Quadratic and Other types of Equations
  • Quadratic equations: recognition, solution by factoring, completing the square and quadratic formula
  • Quadratic type equations
  • Simple equations of higher degree, number of roots
  • Non-linear systems of equations
 
  1. Analytical Trigonometry
  • Identities: reciprocal, ratio, Pythagorean, negative angles, compound Angles, double and half angles, factor and product
  • Trig equations: solving for θ, showing applications of solution
  • Graphical solutions of trig. Equations
  • Composite trig. Functions (addition of ordinates)
 
  1. Exponential Functions
  • Definition of exponential function
  • Definition of “e”
  • Evaluation and graphs of  vC = EC(1 - e-t/RC), i = (E/R)e-t/RC        
  • Applied problems: evaluation of above formula; charge-discharge curves
 
  1. Logarithmic Functions
  • Definition of logarithm
  • Graphs of logarithmic functions
  • Laws of logarithms
  • Common logarithms, natural logarithms and converting between logarithmic and exponential forms
 
  1. Introduction to Statistics and Probability
  • Definition and Terminology; sampling, types of variables, data
  • Organizing and Graphing data; x-y graphs, scatter plots, bar and pie charts
  • Empirical curve fitting
  • Graphical summaries; frequency histogram and polygon
  • Numerical description of data; mean, median, mode, range, quartiles, percentiles
  • Probability of a single event occurring
  • Probability of  combining events
  • Mutually exclusive events
 

Mode of Instruction
Lecture hours: 4
Total hours: 4

Prescribed Texts
Title: Technical Mathematics with Calculus, Cdn. 3rd Ed. (2016)
Author:  Paul Calter, Michael Calter, Paul Wraight and Sarah White
Publisher:  Wiley
ISBN: 978-1-119-32572-7 (binder ready version with WileyPlus)

Reference Material
Title:   Technical Mathematics with Calculus, Cdn 2nd Edition
Author:   Paul Calter & Michael Calter
Publisher:  Wiley
ISBN:   978-0-470-67884-8

Required Supplies
Non-programmable calculator

Promotion Policy

Grading Policy
A+ 90%  to  100%
A 80%  to  89%
B+ 75%  to  79%
B 70%  to  74%
C+ 65%  to  69%
C 60%  to  64%
D+ 55%  to  59%
D 50%  to  54%
F 0%    to  49% (Not a Pass)
OR
EXC Excellent
SAT Satisfactory
UNSAT Unsatisfactory

For further information, see a copy of the Academic Policy, available online (http://www.senecacollege.ca/academic-policy) or at Seneca's Registrar's Offices.


Modes of Evaluation
Assignments

  • Assignments are due at the beginning of the class on which they are due.
  • A late penalty of 10% per day is assessed for late assignments, including those not handed in at the beginning of class when due.
  • Material will not be accepted after one week following the due date and/or when the marked material is returned to students, whichever comes first.
  • Assignments are to be prepared by computer.

Absenteeism and Exams
  • Students should be aware that absenteeism almost guarantees an inability to achieve satisfactory grades.
  • Students who are absent for an examination due to an emergency (e.g., motor vehicle accident, hospitalization or death in the family) may provide official documentation within five days of the missed exam and be provided a deferred exam at a later date.  Official documentation includes a death notice or an original doctor’s certificate identifying the date, length of time expected absence and the specific reason for the absence.  Examinations missed without official documentation and approval result in a grade of zero.
  • There are no deferred options for missed tests.  The value of missed tests, at the discretion of the Faculty, will be added to other evaluation components

English Proficiency
  • All written work should demonstrate the following characteristics for clarity and conciseness:
    • writing is consistent with the rules of English grammar
    • spelling and punctuation are correct
    • sentences are structured correctly
    • main ideas are supported with specific, relevant examples and reasons
    • work flows logically through supporting statements/paragraphs
    • work is arranged in correct format (e.g., as a report, essay)
    • up to 10% of the final grade may be deducted on all work if the above English competencies are not met.

Format for Assignments
  • Students must use the standard, APA style for quoting sources.   Help is available at:  http://library.senecacollege.ca

LAB COURSES
Laboratory Attendance

The laboratory component is essential and therefore it is strongly recommended  that you attend all labs.  Any missed labs must be supported with a legal document with three days of the lab.  Any student who fails to attend 2 scheduled laboratory classes for a 7 week subject and more than 3 laboratory classes for a 14 week subject will not pass the subject.   

Laboratory Safety
Students are required to review and understand the safety procedures and guidelines outlined on the first class and sign the sheet to this effect before beginning work in the laboratory.  Students must also wear a lab coat and safety glasses when conducting experiments.
A student who arrives without the proper safety equipment will not be permitted to participant in the lab but will be asked to leave the class.  The student will receive no grade for the lab missed.

3 Term Tests - 60%
Quizzes & Assignments - 10%
Final Examination - 30%

Approved by: Denis Gravelle