Method of Delivery

This course will be delivered using a completely online approach using online course materials in Moodle and live/synchronous sessions in Elluminate Virtual Classroom.

Communication tools used in the course:

• Email
• Moodle Forums
• Skype
• Telephone
• WebWork question feedback options

Course Components:

• Lectures will introduce the key ideas of the course, and will be used to work through introductory examples
• Assignments, along with solutions, will give you the chance to master the skills of the course
• Tutorials will be where tutors can provide additional examples, as well as the opportunity to get further clarification about the assignment problems.
• Tests are written during your tutorial times, 3 times per term. They will be based on the Test Preparation Problems from the Assignments.

Course Objectives

After you complete this course you will be able to:

In Single Variable Differential Calculus:

1. Select a function form or family of functions that have desired graphical and limit properties. (e.g. a function that starts at (0,0), has one peak, and then a horizontal asymptote at y=2)
   1. Have a toolkit of functions for describing relationships in application problems
2. Express (verbally or through calculations or graphs) the meaning of limiting values in application problems.
   1. Calculate value of finite and infinite limits of continuous and discontinuous functions (with or without l'Hopital's rule), given a function
3. Understand the tangent-slope and rate of change meanings of the derivative
   1. Understand the difference between various possible approximations to a function.
4. Construct application models from word problems and use derivatives to investigate properties of the models.
   1. Use derivatives to locate and classify critical points in optimization problems.
   2. Use relationships between modeling variables to construct relationships between their rates of change.
   3. Use relationships between modeling variables to estimate the effects of changes of inputs or outputs

In Single Variable Integral Calculus:

1. Understand the relationship between integration and area under a curve/rate graph
   1. Understand the graphical/area interpretation of integration and average value
2. Construct application models from word problems and use integrals and/or derivatives to investigate properties of the models.
   1. Master core integration techniques.
   2. Understand properties related to the integral - average value, continuous anti-derivatives.
   3. Understand the issues involved with infinite intervals or asymptotic values in evaluating integrals.
3. Construct differential equation models from word problems and use qualitative and algebraic methods to investigate properties of the models.

In Multivariate Differential Calculus:

1. Demonstrate an understanding between graphical presentation and calculus concepts (1st, 2nd part. derivs, gradient, directional deriv) in multivariate functions.
2. Construct application models from word problems involving multivariate functions, and use differential calculus to investigate properties of the model (related rates and optimization)
   1. Vectors
   2. Gradient and directional derivative
   3. Related rates
   4. Concavity
   5. Critical points and optimization
   6. Constrained optimization and Lagrange multipliers

Course Topics