Worked examples

Sequences and series of functions

One sheet for each type of problem, with several worked examples of increasing difficulty: first the computation, then the explanation in words. Each sheet starts with links to the theory it uses.

• 1Pointwise convergence of sequences of functions
• 2Uniform convergence with the sup criterion
• 3Uniform convergence on subintervals
• 4Pointwise and total convergence of series of functions
• 5Limits of integrals with uniform convergence
• 6Series of functions with total convergence on compact sets
• 7Continuity and differentiability of the sum of a series