MTH198 - Calculus

Outline info
Last revision date 2018-04-10 15:33:06.297
Last review date 2018-04-10 15:33:18.797

Subject Title

Subject Description
This course is designed to extend students' knowledge of functions and their understanding of rates of change. In addition, students will be introduced to the algebra of vectors.

Credit Status

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

1. Investigate rates of change to include the derivatives of polynomial, sinusoidal, exponential, rational, and radical functions

2. Solve problems involving geometric and algebraic representations of vectors and representations of lines and planes in three dimensional space.

3. Apply the skill gained to the application of real world models.

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.

Locate, select, organize, and document information using appropriate technology and information systems.

Analyze, evaluate, and apply relevant information from a variety of sources.

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

Interact with others in groups or teams in ways that contribute to effective working relationships and the achievement of goals.

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 for further information regarding cheating and plagiarism policies and procedures.

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

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.

MTH196 (grade B or higher) or Grade 12U Advanced Functions. 

Topic Outline
1. Advanced Functions Review 

1.1  Polynomial functions: Characteristics of Polynomial Functions; Dividing a Polynomial by a Polynomial; Factoring Polynomials; Solving Polynomial Equations and Inequalities.
1.2  Exponential and Logarithmic Functions: Graphs; Solving Exponential Equations; Laws of Logarithms; Solving Logarithmic Equations.
2. Introduction to Calculus
2.1   Radical Expressions.
2.2   From Secants to Tangents.
2.3   Limits. Limit of a Function. Property of Limits.
2.4   Average and Instantaneous Rates of Change.

3. Derivatives
3.1  The Derivative Function.
3.2   Basic Differentiation Rules.
3.3  The Derivative of Composite Function.
3.4 Implicit Differentiation.
3.5 Derivatives of Exponential and Logarithmic Functions.
3.6 The Derivatives of y = sin x, y = cos x and y = tan x.

4. Derivatives and their Functions

4.1 Velocity and Acceleration.
4.2 Optimization Problems.
4.3 Related Rates.
4.4 Increasing and Decreasing Functions.
4.5 Local Maximum and Minimum Values.
4.6  Curve Sketching.

5.  An Introduction to Vectors

5.1.  Properties of Vectors.
5.2.  Vectors in R2 and R3.
5.3.  Operations with Algebraic Vectors in R2.

6. Applications of Vectors  
             6.1  Vectors and Forces
6.2  Velocity.
6.3 The Dot and Cross Product of Two Vectors.
6.4  Applications of the Dot Product and Cross Product.

7. Equations of Lines and Planes
7.1 Vector and Parametric Equations of a Line in R2.
7.2  Cartesian Equation of a Line
7.3  Vector, Parametric, and Symmetric Equations of a Line in R3.
7.4  Vector and Parametric Equations of a Plane.
7.5  The Cartesian Equation of a Plane
7.6  Sketching Planes in R3.

Mode of Instruction
Your professor will use a variety of appropriate teaching modes and techniques, such as the following:  lecture, question and answer, tutorials, classroom discussion, group work, individual and/or group presentation, computer-aided instruction, consultation, etc.

Prescribed Texts
Calculus And Vectors 12 W/ Online Pdf Files
Publisher: Nelson Education Inc.  Authors: Chris Kirkpatrick, Peter Crippin, Rob Donato & Dave Wright.
ISBN-13: 978-0-17-6678357

Reference Material

Required Supplies

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)
EXC Excellent
SAT Satisfactory
UNSAT Unsatisfactory

For further information, see a copy of the Academic Policy, available online ( or at Seneca's Registrar's Offices.

Modes of Evaluation
To be successful in this course, you must complete all course work as specified and achieve an overall grade of 50% or higher. For further information on evaluation and academic standing, see a copy of the Academic Policy available at Seneca registration offices.

Term Work:

All term work assignments must be completed prior to the time of the examination. Unless students have been granted an extension in advance, late take-home assignments will be penalized one letter grade per day and will not be graded after one week (there is no provision for rewriting late assignments, regardless of the grade).  Students must contact faculty in advance of due date to discuss extensions.
If a student has to miss any in-class quiz/test, he/she must notify the faculty via email or phone messages prior to start time of the quiz/test date.  Valid documentation (such as original stamped doctor's note) must be submitted to the faculty on or before the next scheduled class.  Make-up opportunities may be arranged at the Test Centre.

Grading Scheme:

Test 1 15%
Test 2  15%
Test 3 20%
Assignments (3) 15%

Approved by: Fiona Bain-greenwood