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This text is intended for an honors calculus course or for an introduction to analysis. Involving rigorous analysis, computational dexterity, and a breadth of applications, it is ideal for undergraduate majors. This third edition includes corrections as well as some additional material. Some features of the text: The text is completely self-contained and starts with the real number axioms; There is a heavy emphasis on computational problems; There are applications from many parts of analysis, e.g., convexity, the Cantor set, continued fractions, the AGM, the theta and zeta functions, and many more; Traditionally transcendentally presented material, such as infinite products, the Bernoulli series, and the zeta functional equation, is developed over the reals; There are 385 problems with all the solutions at the back of the text.

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1 The Set of Real Numbers.- 1.1 Sets and Mappings.- 1.2 The Set R.- 1.3 The Subset N and the Principle of Induction.- 1.4 The Completeness Property.- 1.5 Sequences and Limits.- 1.6 Nonnegative Series and Decimal Expansions.- 1.7 Signed Series and Cauchy Sequences.- 2 Continuity.- 2.1 Compactness.- 2.2 Continuous Limits.- 2.3 Continuous Functions.- 3 Differentiation.- 3.1 Derivatives.- 3.2 Mapping Properties.- 3.3 Graphing Techniques.- 3.4 Power Series.- 3.5 Trigonometry.- 3.6 Primitives.- 4 Integration.- 4.1 The Cantor Set.- 4.2 Area.- 4.3 The Integral.- 4.4 The Fundamental Theorem of Calculus.- 4.5 The Method of Exhaustion.- 5 Applications.- 5.1 Euler´s Gamma Function.- 5.2 The Number pi.- 5.3 Gauss´ Arithmetic-Geometric Mean (AGM).- 5.4 The Gaussian Integral.- 5.5 Stirling´s Approximation of n!.- 5.6 Infinite Products.- 5.7 Jacobi´s Theta Functions.- 5.8 Riemann´s Zeta Function.- 5.9 The Euler-Maclaurin Formula.- A Solutions.- A.1 Solutions to chapter 1 .- A.2 Solutions to chapter 2.- A.3 Solutions to chapter 3.- A.4 Solutions to chapter 4.- A.5 Solutions to chapter 5.- References.- Index

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