Leif Mejlbro was educated as a mathematician at the University of Copenhagen, where he wrote his thesis on Linear Partial Differential Operators and Distributions. Shortly after he obtained a position at the Technical University of Denmark, where he remained until h
A book with a collection of examples of general, elementary series.
Here follows a collection of examples of general, elementary series. The reader is also referred to Calculus 3b. The main subject is Power series; but first we must consider series in general. We shall in Calculus 3c-3 return to the power series.
Finally, even if I have tried to write as careful as possible, I doubt that all errors have been removed. I hope that the reader will forgive me the unavoidable errors.
1. Partial sums and telescopic series
2. Simple convergence criteria for series
3. The integral criterion
4. Small theoretical examples
5. Conditional convergence and Leibniz’s criterion
6. Series of functions; uniform convergence