Topic 1: Limits (A Numerical and Graphical Approach)

• • Limits – The Main Idea (Lecture, Part 1)
  • Limits at Infinity (Lecture, Part 2)
  • Evaluating a limit using a graphing utility
  • Finding limits from a graph
  • Finding the limit of a function with an absolute value
  • Another limit of a function with an absolute value

Topic 2: Algebraic Limits and Continuity

• • Finding limits of a Rational Function
  • Evaluating Limits Algebraically (Lecture)
  • Continuity (Lecture)
  • Analyzing a Function:  Limits and Continuity (Lecture)
  • Example: Finding k to make a Piecewise Function Continuous
  • Evaluating a limit with 0 divided by 0 example

(MTH 263 only)

• • Finding Delta in a Formal Definition of a Limit
  • Finding Delta Given Epsilon
  • Limits at Infinity – A look at Polynomial and Trig Functions

Topic 3: Average Rates of Change

• • Average Rate of Change (Lecture)
  • How to Graph Open Endpoints Using WA Tools

Topic 4: Differentiation Using Limits of Difference Quotients

• • Using Limits of a Difference Quotient to Find the Slope of a Tangent Line (Lecture, Part 1)
  • Using Limits of a Difference Quotient to Find the Slope of a Tangent Line (Lecture, Part 2)
  • Differentiability (Lecture)
  • Writing a Difference Quotient with a Radical Function
  • Writing a Difference Quotient with a Rational Function
  • Finding m and b so that a Piecewise Function is Differentiable

Topic 5: Rules for Derivatives

• • Rules for Derivatives (Lecture, Power Rule)
  • More Derivatives using the Power Rule (Lecture)

(MTH 263 only)

• • Derivatives with e – The main idea
  • Derivatives of Exponential Functions (lecture)
  • Application Problem:  A Logistic Function

Topic 6: The Product and Quotient Rules

• • The Product and Quotient Rules (Lecture, part 1)
  • The Quotient Rule (2 Examples)
  • The Average Cost, Revenue, Profit Functions
• (MTH 263 only)
• • Using the Quotient Rule with trig functions

Topic 7: The Chain Rule

• • Find the derivative using the Product and Chain Rules (example)
  • The Chain Rule (Lecture, part 1)
  • Find the derivative using the Quotient and Chain Rules (example)
  • Application problems using derivatives

(MTH 263 only)

• • The Chain Rule twice with e and sine – Example

Topic 8: Higher Order Derivatives

• • Higher Order Derivatives (Lecture)
  • Bacteria Growth Application Problem
  • Higher Order Derivatives from a Graph