Lessons

Unit 0: Introduction

• Course Outline
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Unit 1: Limits [OUTLINE]

• Lesson 1: Review [Note] [Hwk] [Extra Reading/Work]
  • [Videos: Domain/Range, Function Notation, Rationalising the Denominator / Numerator]
• Lesson 2: Slope of a Tangent [Note] [Hwk]
• Lesson 3: Slope of a Tangent Part 2 [Note] [Hwk]
  • [Video]
• Lesson 4: Rate of Change [Note] [Hwk] [Note Answers]
  • [Video: Rate of Change (Line, Curve)]
• Lesson 5: Limits [Note] [Hwk]
• Lesson 6: Mid-Chapter Review
• Lesson 7: Properties of Limits [Note 1] [Note 2]
  • [Videos: Factoring, One Sided Limits (Absolute Values), Change of Variable (Hints, Example), Rationalize the Numerator]
• Lesson 8: Continuity [Note] [Supplementary Handout] [Exit Pass]
• Lesson 9: Limits of Polynomial and Rational Functions [Note]
• Lesson 10: Limits of Functions Involving Rationals [Note]
• Lesson 11: Limits at Infinity [Note]
• Review [Work]

Unit 2: Derivatives [OUTLINE]

• Lesson 1: The Derivative Function [Note - Filled]
• Lesson 2: The Derivative of a Polynomial - Day 1 [Note]
• Lesson 3: The Derivative of a Polynomial - Day 2 [Note]
• Lesson 4: The Product Rule [Note]
• Lesson 5: The Quotient Rule [Note]
• Lesson 6: The Derivative of Composite Functions (Chain Rule) [Note]
• Lesson 7: Leibniz Notation [Note - Filled]
  • Videos: [What is dy/dx?, What is the Difference between d/dx and dy/dx?]
• Implicit Differentiation [Note] (Not Covered)
• Review [In-Class Review] [Quiz Answers]

Unit 3: Curve Sketching [OUTLINE]

• Lesson 1: Prerequisite Skills [Note]
  • Videos: [Solving Inequalities 1, 2, Factor/Remainder Theorem, Synthetic Division]
• Lesson 2: Increasing and Decreasing Functions [Note]
• Lesson 3: Critical Points, Relative Min/Max [Note]
• Lesson 4: Vertical and Horizontal Asymptotes [Note - Filled] [Textbook]
• Lesson 5: Oblique Asymptotes [Note - Filled]
• Lesson 6: Concavity and Points of Inflection [Note]
• Lesson 7: An Algorithm For Graph Sketching [Note]
• Review - TEST HINTS

Unit 4: Applications of Derivatives [OUTLINE]

• Lesson 1: Higher-Order Derivatives, Velocity, and Acceleration [Note]
• Lesson 2: Maximum and Minimum Values Over Intervals [Note]
• Lesson 3: Optimizing Problems - Area/Volume [Note]
• Lesson 4: Optimizing Problems - Pythagorean Distance [Note]
• Lesson 5: Optimization Problems in Economics and Science (Cost Problems) [Note]
• Lesson 6: Related Rates (Area & Distance) [Note]
• Review [Extra Questions and Full Solutions for Word Problems]

Unit 5: Derivatives of Exponents and Trigonometry [OUTLINE]

• Lesson 1: Derivatives of Exponential Functions y=eˣ [Note]
• Lesson 2: Derivatives of Exponential Functions y=bˣ [Note] [Filled]
• Lesson 3: Optimization Problems Involving Exponential Functions [Note] [Homework 1, 2, 3]
• Lesson 4: The Derivative of y=sin(x) and y=cos(x) [Note]
• Lesson 5: The Derivative of y = tan(x) [Note]
• Review

Unit 6: Introduction to Vectors [OUTLINE]

• Lesson 1: Introduction to Vectors [Note] [Filled]
• Lesson 2: Vector Addition [Note] [Filled]
• Lesson 3: Multiplication of a Vector by a Scalar [Note] [Filled]
• Lesson 4: Properties of Vectors [Note] [Filled] [Parallelogram Proofs (pg 299/306)]
• Lesson 5: Vectors in R² and R³ [Note] [Filled]
• Lesson 6: Operations with Vectors in R² [Note] [Filled]
• Lesson 7: Operations with Vectors in R³ [Note] [Filled]
• Lesson 8: Linear Combinations and Spanning Sets [Note] [Filled]
• Review [Extra Work] [Answers to Questions From the Textbook]

Unit 7: Algebraic Vectors and Applications [OUTLINE]

• Lesson 1: Force as a Vector [Note] [Filled]
• Lesson 2: Velocity as a Vector [Note] [Filled]
• Lesson 3: The Dot Product of Two Geometric Vectors [Note] [Filled]
• Lesson 4: The Dot Product of Algebraic Vectors [Note] [Filled]
• Lesson 5: Scalar and Vector Projections [Note] [Filled]
• Lesson 6: The Cross Product of Two Vectors [Note] [Filled]
• Lesson 7: Applications of Dot Product and Cross Product [Note] [Filled]
• Review [Extra Work] [Test Format]

Unit 8: Equations of Lines and Planes [OUTLINE]

• Lesson 1: Vector and Parametric Equations [Note] [Filled]
• Lesson 2: Cartesian Equation of a Line [Note] [Filled]
• Lesson 3: Vector Parametric and Symmetric Equations of a Line in R³ [Note] [Filled]
• Lesson 4: Vector and Parametric Equations of a Plane [Note] [Filled]
• Lesson 5: Cartesian Equation of a Plane [Note] [Filled]
• Lesson 6:
  • Sketching Planes in R³ [Note] [Filled]
  • Intersection of a Line With a Plane and the Intersection of Two Lines [Note] [Filled]
• Lesson 7:
  • Systems of Equations [Note] [Filled] [Alternate Solution to Example 4]
  • Intersection of Two Planes [Note] [Filled]

Review

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