MATH-1610 Reading assignments

Reading is an important component of our learning process. Please read relevant sections before class. You don’t have to fully understand everything, but you should make an honest attempt to understand the key concepts. Below are the sections to be read before each class meeting. Also listed are some “reading questions” you have keep in mind as you read. All the section numbers refer to the textbook by Larson and Edwards. Note that the structure of our lectures does not exactly mirror that of the textbook, so it is possible for one lecture of cover several sections or chapters and vice versa.

• Day 1: Review Precalculus [Chapter 1]
  • What is the slope of a straight line?
  • What does “average rate of change” mean?
  • How do you compute the average speed/velocity of a moving object?
  • What does “instantaneous velocity” mean? Does it even make sense?
  • What make of Zeon’s arrow paradox?
• Day 2: Geometric motivations [Section 3.1]
  • What is a secant line?
  • What is a tangent line?
• Day 3: Instantaneous rate of change and derivative [Section 3.1]
  • What does “instantaneous rate of change” mean?
  • What is the “derivative” of a function at a point?
• Day 4: [Section 3.1]
  • What’s the best way to approximate a curve with a line?
  • What does the word “extrapolation” mean?
• Day 5: Derivatives as limits [Section 2.1, 2.2, 3.1]
  • What does the word “limit” mean in our context?
  • What does it mean for a function be continuous?
• Day 6:
  • What is the mathematical definition of derivative?
  • Why is it defined that way?
• Day 7:
  • What are the basic properties of derivatives?

• Day 8: (Rules)

• Day 9:
  • What is implicit differentiation?
• Day 10:
  • What does “mean value theorem” say?
  • Can you explain it in your own language?
• Day 11:
  • What are “critical points”?
  • What’s the connection between critical points and max/min?
• Day 12:
  • What does “concavity” mean?
  • What does “concave up” and “concave down” mean?
  • What does “inflection point” mean?

• Day 13:

• Day 14:
  • How to find the area of basic shapes? (e.g. triangle, square, rectangle, trapezoid, and circle)
  • What does “integral” mean?
• Day 15:
  • What is a definite integral?
  • What does “Riemann sum” mean?