Community Projects

PreCalc

1. functions and modelling

• function concepts: range, domain, one-to-one, onto, vertical line test
• combining functions: sums, products, quotients, compositions
• inverse functions
• linear functions
• intro to polynomial and rational functions
• intro to exponential functions
• 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

• average rate of change over an interval
• instantaneous rate of change
  • at a point
  • as a function of x
• difference quotients
  • at a point
  • as a function of x (and h)
• marginals (small h approximation to the limit)

2. limits and the definition of the derivative
3. differentiation rules and applications

• derivatives of linear combinations
• product rule
• chain rule
• quotient rule

4. techniques

• implicit differentiation
• related rates
• derivatives of inverse functions

5. applications -- theory and practice

• intermediate value theorem
• optimization