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Course Description

This course provides an introduction to the calculus of one variable with emphasis on mathematical modelling in the biological sciences. The topics covered include elementary functions, sequences and series, difference equations, differential calculus and integral calculus.

Learning Outcomes

By the end of the course, the learner should be able to:
  1. Determine the domain, range and the inverse of a function and form a composite function;
  2. Describe the differences between sequences and series, and use formulas resulting from finite and infinite series to solve problems involving payments, deposits, dosage of drugs, and population size;
  3. Compute basic limits of functions and discuss the importance of limits to the process of differentiation. Determine where and whether functions are continuous, and identify and classify points of discontinuity;
  4. Explain the derivative in terms of the idea of a tangent line to the graph of a function and how a derivative can be used to describe the rate of change of one quantity with respect to another;
  5. Differentiate a wide class of single-variable functions, including polynomials, trigonometric, exponential, logarithmic, sums, products, quotients, compositions;
  6. Apply the chain rule to find derivatives of different functions including functions raised to a power, exponential, and logarithmic functions;
  7. Compute linear approximations to implicit functions using “implicit differentiation”;
  8. Use derivatives to solve applied problems involving rate-of-change, maximum and minimum values; critical numbers; local extrema and concavity and optimization;
  9. Use integrals to solve problems involving area;
  10. Find a definite integral using the limit of Riemann sums;
  11. Evaluate definite integrals using the Fundamental Theorem of Calculus; and
  12. Find indefinite and definite integral using substitution.

Course Topics

  • Preparing for Calculus
  • Limits and Continuity
  • The Derivative
  • More About Derivatives
  • Applications of the Derivative
  • The Integral

Additional Requirements

Pre-requisite(s): 1 of 4U Advanced Functions, 4U Advanced Functions and Calculus or equivalent

Restriction(s): IPS*1500, MATH*1200

Assessment

Assessment Item Weight Learning Outcomes
Quiz 1 11.4% 1, 2
Quiz 2 11.4% 3
Quiz 3 11.4% 4, 5
Midterm Test 1 20% 1, 2, 3, 4, 5, 6
Quiz 4 11.4% 6, 7
Quiz 5 11.4% 8
Quiz 6 11.4% 9, 10
Quiz 7 11.4% 11, 12
Total 100%  

 

Note:

Additional Technical Requirements

This course will use the following:

  • Zoom as a video communication tool.  A Webcam, a microphone to record video, and headphones/speakers to play back the recording are also needed. 

Please view the Technical Considerations for each.

Technical Requirements

You are responsible for ensuring that your computer system meets the necessary system requirements. Use the browser check tool to ensure your browser settings are compatible and up to date (results will be displayed in a new browser window).

*Course details are subject to change.

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Section Title
Elements of Calculus
Type
Online
Dates
September 09, 2021 to December 03, 2021
Contact Hours
36.0
Delivery Options
Online  
Course Fee(s)
Domestic Tuition Fee (0.5 units) $683.39 Click here to get more information
International Tuition Fee (0.5 units) $2,908.38 Click here to get more information
Available for Credit
0.5 units
Reading List / Textbook

The online platform Achieve includes the textbook and student solutions manual.

Special UofG pricing (ISBN 9781319403515)

Section Notes
If you are in a degree program at the University of Guelph, please DO NOT register using the link above.  You must register through WebAdvisor.
Section Materials
  • e-book (Confirmed) (Mandatory) Calculus: Early Transcendentals by Michael Sullivan and Kathleen Miranda © 2020 MacMillan Learning 2nd edition ISBN Digital:9781319403539,Print/Achieve:9781319406936
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