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Lecture Notes On Advanced Calculus II written by
Jie Wu
cover the following topics.

Sequences of Real Numbers Sequences, Limits of Sequences, Sequences which tend to ∞, Techniques For Computing Limits, The Least Upper Bounds and the Completeness Property of R, Monotone Sequences, Subsequences, The Limit Superior and Inferior of a Sequence, Cauchy Sequences and the Completeness of R,

Series of Real Numbers Series, Tests for Positive Series, The Dirichlet Test and Alternating Series, Absolute and Conditional Convergence, Remarks on the various tests for convergence/divergence of series

Sequences and Series of Functions Pointwise Convergence, Uniform Convergence, Uniform Convergence of {Fn} and Continuity, Uniform Convergence and Integration, Uniform Convergence and Differentiation, Power Series, Differentiation of Power Series, Taylor Series