PREP 7107 - UWindsor Prep Calculus

Course Description

UWindsor Prep Calculus is a non-credit online course that reviews and supplements Grade 12 concepts and problem solving techniques to help students prepare for calculus at the University of Windsor.

This online course extends students’ experience with calculus. Students will review limits, derivative rules, and their applications to polynomial, rational, exponential, logarithmic and trigonometric functions. These skills will then be applied to produce graphs of combinations of functions and to solve optimization problems. These skills with then be extended to include implicit differentiation and related rate problems. The course will be structured to allow for a combination of direct instruction, independent work, and small group learning. Emphasis will be placed on making connections between previous learning and new learning, and on deepening students’ understanding of foundational skills necessary for further studies in calculus.

Take this refresher if you are registered in the following UWindsor academic courses:

• MATH-1720.Differential Calculus
• MATH-1760. Functions and Differential Calculus
• MATH-1780 Access to Differential Calculus
• PHYS-1400. Introductory Physics I

Course Outline

To successfully complete this course participants must attend online classes and complete a series of online quizzes and assignments. Upon completion students will be awarded a grade of complete or incomplete.

Learner Outcomes

Limits and Derivatives

By the end of this course, students will be able to:

• Define the limit of a function and apply properties of limits to simplify and determine the behaviour of graphs for a variety of types of functions
• Determine derivatives of functions from first principles and graph the derivative function for polynomial, exponential, and sinusoidal functions
• Prove derivative rules from first principles, including the chain rule
• Apply derivative rules to polynomial, rational, exponential, logarithmic, radical, and sinusoidal functions and combinations of these functions

Applications of Derivatives

By the end of this course, students will be able to:

• Calculate higher order derivatives for polynomial, rational, exponential, logarithmic, radical, and sinusoidal functions, as well as for combinations of these functions
• Make connections between the first and second derivatives of a function and the properties of the graph of that function and apply this understanding to sketch the curve for the function
• Solve problems (including optimization problems) that require the use of derivatives and their properties

Implicit Differentiation and Applications

By the end of this course students will be able to:

• Differentiate an implicit function by using the chain rule and isolating the desired derivative
• Apply the process of implicit differentiation to solve related rate problems
• Apply the process of implicit differentiation to determine the derivative of the natural logarithmic function, f(x) = ln x, and to differentiate functions that include the natural logarithm

Notes

Brightspace Requirements

This class is offered online through Brightspace. A link will be provided through email and you will have access the first day of class.

Please activate your UWin ID. Your UWin ID and password are needed to access Brightspace. If you have any issues, please contact continue@uwindsor.ca.

Review the full Brightspace system requirements.

Microsoft Teams

Instructional time will be held on Microsoft Teams. As a student of this course, the University of Windsor will provide you with access to Microsoft Teams.

Once you register you will be prompted to activate your UWin ID. Your UWin ID and password are needed to access Microsoft Teams. If you have any issues, please contact continue@uwindsor.ca.

Microsoft Teams is available in three versions including desktop, web and mobile app. The Microsoft Teams desktop app is available for both Windows 7 and 10 and macOS 10.10 or later. On Windows, Teams requires .NET framework 4.5 or later; the Teams installer will offer to install it for you if you don't have it. If you are unable to install Desktop App, you can use web version of Teams. In addition, Microsoft Teams mobile app is available for iOS and Android devices. You can download it from your respective app store on the device. Full instructions will be provided before the course start.