MCV4UI

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Calculus and Vectors, 12, academic

Fly, baby birds, fly!
- Dr. Gail Walker

1. Derivatives
   • The Derivative (add visuals)
   • Differentiability, Limit Laws
   • Differentiation Rules
   • Equations of Tangents (todo)
2. Related Rates
   • Second Derivatives and Higher Order Derivatives
   • Implicit Differentiation
   • Related Rates
3. Derivatives of Exponential and Logarithmic Functions
   • Definition of e
   • Differentiation Rules for Logarithms and Exponential functions
4. Optimization (examples?)
5. curve sketching (examples?)
   • Increasing and Decreasing Functions
   • First Derivative Test
   • Concavity
   • Second Derivative Test
   • Sketching Polynomial Functions
   • Sketching Rational Functions
6. Vectors ("Geometric vectors")
   • The Vector
7. Vectors ("Algebraic vectors")
   • Dot Product
   • Cross Product
   • Projections, Distances
8. Lines and Planes
   • Vector Equation of a Line
   • Scalar Equation of a Line
   • Distance from a Point to a Line
   • Intersection of Lines
   • Vector Equation of a Plane
   • Scalar Equation of a Plane
   • Distance from a Point to a Plane
   • Intersection of Line and Plane
   • Intersection of Two Planes
   • Intersection of Three Planes
   • Systems of Linear Equations and Matrices