Problems and solutions for undergraduate analysis

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This volume includes all exercises and solutions for Lang's second edition of Undergraduate Analysis. It features a diverse range of problems, from computational to conceptual, covering topics such as real numbers, limits, continuous functions, differentiation, elementary integration, normed vector spaces, compactness, series, improper integrals, convolutions, Fourier series, functions in n-space, derivatives in vector spaces, and ordinary differential equations, among others. The goal is to provide a comprehensive set of completed exercises for those learning and teaching analysis at the undergraduate level. With over 600 exercises, this resource aims to facilitate understanding of the material. The exercises are integral to Lang's text, and readers are encouraged to engage with all of them. Notably, some problems in earlier chapters are foundational for later ones, such as those in Chapter IV, which involve constructing bump functions to address singularities and demonstrate the density of certain function spaces. Problem numbering follows a specific format, e.g., Exercise IX.5.7 refers to Exercise 7 in Chapter IX, §5. Acknowledgments are given to Serge Lang for his invaluable support and guidance throughout this project.