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This is a self-contained book that covers the standard topics in introductory analysis and that in addition, constructs the natural, rational, real and complex numbers, and also handles complex-valued functions, sequences, and series.
The book teaches how to write proofs. Fundamental proof-writing logic is covered in Chapter 1 and is repeated and enhanced in two appendices. Many examples of proofs appear with words in a different font for what should be going on in the proof writer's head.
The book contains many examples and exercises to solidify the understanding. The material is presented rigorously with proofs and with many worked-out examples. Exercises are varied, many involve proofs, and some provide additional learning materials.
Key Features:
o This is an introductory analysis book that covers also complex-valued functions
o Complex numbers allow for a quick overview of trigonometry after covering power series, and the students can forever after derive on their own formulas for sine or cosine of sums of angles
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