7. Differential Calculus

  1. Constructing Tangents
  2. Difference Quotient Functions

     └  

  3. Differentiable Functions
  4. Local Aspects
  5. The Basic Representation Theorem

     └  Example of a locally non-injective, regular function

  6. Calculation Rules for Differentiable Functions
  7. The Derivative
  8. Repeatedly Differentiable Functions
  9. The Mean Value Theorem
  10. Geometric Properties of Differentiable Functions
  11. Extremal Problems
  12. Sequences of Differentiable Functions