AP Calculus BC
Calc III Intro (Calculus by Stewart)
Advanced Mathematical Thinking (Mathematical Proofs by Chartrand)

Week of May 18
Monday, May 18 - Final Presentations
  • Final Presentations

Tuesday, May 19 - Final Presentations
  • Final Presentations

Wednesday, May 20 - Three Dimensional Coordinate Systems and Vectors
  • What does the coordinate plane in 3 dimensions look like?
  • What is R3?
  • How would you graph a plane in R3?
  • Plot (2, 3, -1) in R3.

Thursday, May 21 - The Dot Product
  • What is a scalar quantity?
  • What are the properties of vector addition?
  • Explain i, j, and k in the context of vectors in R3.
  • How do you find the length of a vector in R3?
  • What is the dot product? How is it useful?
  • Define "orthogonal." What does it mean in the context of the dot product?

Friday, May 22 - The Cross Product
  • Given two vectors a and b, how does one find the cross product?
  • How do matrices and the determinant help to find cross products?
  • What do you get if cross vector a with itself? In other words, a x a.
  • How can you use the cross product to find the angle between two vectors?
  • What is the geometric representation of the cross product?
  • What do you get if you find the cross product between two parallel vectors?
Week of May 25
Monday, May 25 - No School
  • Memorial Day

Tuesday, May 26 - Quadric Surfaces (12.6) and Functions of Several Variables (14.1)
  • Examine the six types of quadric surfaces. Make sense of them based on what you know about their counterparts in R2.
  • What is a function of two variables? How is it expressed?
  • What are level curves? How are they used?
  • Be able to identify a graph in R3 based on its equation.

Wednesday, May 27 - Guest Presenter
  • Mathematical Career Pathway: Actuary

Thursday, May 28 - Quadric Surfaces (12.6) and Functions of Several Variables (14.1)
  • Same as Tuesday

Friday, May 29 - Limits and Continuity (14.2) and Partial Derivatives (14.3)
  • What is the method for determining the limit of a function in two variables?
  • How can we determine continuity of a function in two variables?
  • How can one find a partial derivative? Why is it called a "partial derivative"?
  • What is the graphical interpretation of a partial derivative? What about a second partial derivative?

Extra: Tangent Planes (14.4) and Max/Min Values (14.7)
  • Why do we talk about tangent planes (instead of tangent lines) in R3?
  • How does one determine the equation for a tangent plane in R3?
  • What is the process for determining where a function has a minimum/maximum value in R3?
  • What is a saddle point? How does one determine the existence of a saddle point?
Week of June 1
Monday, June 1 - Set Theory (Ch 1)
  • Dual Enrollment Presentation by Mr. Carlin
  • Sets, Subsets, and Set Operations (#3, 4, 5, 8, 12, 13, 14, 21, 22, 26, 46, 48, 50)

Tuesday, June 2 - Logic (Ch 2)
  • Implications and Truth Tables (#2, 3, 4, 11, 12, 13, 15, 16, 19, 20, 22, 24, 27, 29)

Wednesday, June 3 - Logic (Ch 2)

Thursday, June 4 - Proofs (Ch 3)
  • Direct Proof (#9, 10, 11, 17, 20)
  • Proof by Contrapositive

Friday, June 5 - Proofs (Ch 3)
  • Proof by Cases (#27, 28, 29)
Week of June 8
Monday, June 8 - Proofs (Ch 4)
  • Proofs Involving Divisibility of Integers
  • Proofs Involving Congruence of Integers (modulo)

Tuesday, June 9 - Proofs (Ch 5/6)
  • Proof by Contradiction
  • Mathematical Induction

Wednesday, June 10 - Exams
  • 1st and 2nd Hour - Proofs Exercises

Thursday, June 11 - Exams
  • 3rd and 4th Hour

Friday, June 12 - Exams
  • 5th and 6th Hour