Most material will be provided in the form of lecture notes (slideshows) and handouts. Copies of the textbook will be provided for in-class use and for overnight sign-out. Additional resources may be found online at the following sites:

Topics Covered

  1. Geometric and Algebraic Vectors
    1. Unit Outline
    2. Prerequisite Skills
    3. Vector Basics
    4. Adding and Subtracting Vectors
    5. Multiplying Vectors By Scalars
    6. Forces as Vectors
    7. Velocities as Vectors
    8. Resolving Vectors Into Components
    9. Algebraic Vectors In Two- and Three-Space
    10. Magnitudes and Direction Angles
    11. Operations with Algebraic Vectors
    12. Dot Product
    13. Cross Product
    14. Geometric Applications of Dot/Cross Products
    15. Work and Torque
  2. Equations and Intersections of Lines and Planes
    1. Parametric and Vector Equations of Lines in 2-Space | Video Lesson (not mine)
    2. Symmetric and Scalar Equations of Lines in 2-Space | Video Lesson (not mine)
    3. Equations of Lines in 3-Space | Video Lesson (not mine)
    4. Vector and Parametric Equations of Planes | Video Lesson (not mine)
    5. Scalar Equation of a Plane | Video Lesson (not mine)
    6. Sketching Planes
    7. Intersections of Lines in 2-Space
    8. Intersections of Lines in 3-Space | Video Lesson (not mine)
    9. Intersections of Lines and Planes | Video Lesson (not mine)
    10. Solving Linear Systems with 3 Variables
    11. Solving Linear Systems Using Matrices | Video Lesson (not mine)
    12. Intersections of Two Planes | Video Lesson (not mine)
    13. Intersections of Three Planes | Video Lesson (not mine)
    14. Distance From a Point To a Line/Plane | Video Lesson (not mine)
  3. Rates of Change and Limits
    1. Limits of Functions
    2. Algebraic Properties of Limits
    3. Limits In Indeterminate Form
    4. Continuity
    5. Rates of Change
    6. The Derivative of a Function
  4. Derivative Rules
    1. Basic Derivative Rules
    2. Product Rule
    3. Chain Rule | (Proof)
    4. Quotient Rule
    5. Implicit Differentiation
    6. Higher-Order Derivatives
    7. Derivatives of Sinusoidal Functions
    8. Derivatives of Other Trigonometric Functions
    9. Derivative of the Exponential Function, y=ex
    10. Derivative of the Natural Logarithmic Function, y=ln(x)
    11. Derivative of General Exponential and Logarithmic Functions
    12. Logarithmic Differentiation
  5. Curve Sketching and Applications of Derivatives
    1. Increasing/Decreasing Intervals of a Function
    2. Critical Points and Local Extrema
    3. Asymptotes
    4. Concavity and Points of Inflection
    5. Curve Sketching
    6. Absolute Extrema
    7. Optimization (Part 1)
    8. Optimization (Part 2)
    9. Related Rates (Part 1)
    10. Related Rates (Part 2)
    11. L’Hôpital’s Rule