Hyperreal Calculus

Construction of the hyperreal numbers Intuitive construction Ultrafilters Formal construction Infinitely small and large numbers Enlarging sets Extending functions The transfer principle Stating the transfer principle Using the transfer principle Properties of the hyperreals Terminology and notation Arithmetic of hyperreals Halos Shadows Convergence Convergence in hyperreal calculus Monotone convergence Continuity Continuity in hyperreal calculus Examples Theorems about continuity Uniform continuity Limits and derivatives Limits in hyperreal calculus Differentiation in hyperreal calculus Examples Increments Theorems about derivatives