TITLE: Most gentle introduction to undergraduate analysis
QUESTION [7 upvotes]: I will be teaching a course which expects to have the following topics pulled from a now out-of-print book: Fundamental ideas of analysis, by Michael C. Reed, John Wiley&Sons,1998
As we can't use this book, I need something comparable.
The expected topics include (again these are presumably pulled from the book mentioned above, and I'm supposed to teach these):

Set of Natural Numbers
Set of Rational Numbers
Set of Real Numbers
Completeness Axiom
Sequences
Limit Theorems for Sequences
Monotone Sequences and Cauchy Sequences
Series
Alternating Series and Integral Tests
Continuity
Properties of Continuous Functions
Sequences and Series Functions
Uniform Convergence
Differentiation and Integration of Power Series
Mean Value Theorem
L’Hopital Rule
Taylor Theorem
Part one of Integration
Part two of Integration

So can someone tell me the most gentle undergraduate analysis book which would deal with these (as gently as possible)?

REPLY [4 votes]: I adore Spivak's Calculus. I think it covers every topic you mentioned in a completely rigorous fashion, and motivates the definitions (for example, he builds up to the definition of the limit until it seems like the only reasonable thing to do). It's also full of interesting problems.