Community Projects

PreCalc

1. functions and modelling
   1. function concepts: range, domain, one-to-one, onto, vertical line test
   2. combining functions: sums, products, quotients, compositions
   3. inverse functions
   4. linear functions
   5. intro to polynomial and rational functions
   6. intro to exponential functions
   7. intro to periodic functions
2. modelling with polynomial and rational functions
3. modelling with exponential and logarithmic functions
4. periodic functions and trigonometry
5. systems of equations

DiffCalc

1. introduction
   1. average rate of change over an interval
   2. instantaneous rate of change
      1. at a point
      2. as a function of x
   3. difference quotients
      1. at a point
      2. as a function of x (and h)
   4. marginals (small h approximation to the limit)
2. limits and the definition of the derivative
3. differentiation rules and applications
   1. derivatives of linear combinations
   2. product rule
   3. chain rule
   4. quotient rule
4. techniques
   1. implicit differentiation
   2. related rates
   3. derivatives of inverse functions
5. applications -- theory and practice
   1. intermediate value theorem
   2. optimization