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Science & Mathematics - Analysis (1) (Hindustan Book Agency)

Description

Book Synopsis: This is part one of a two-volume introduction to real analysis and is intended for honours undergraduates who have already been exposed to calculus. The emphasis is on rigour and on foundations. The material starts at the very beginning--the construction of the number systems and set theory--then goes on to the basics of analysis (limits, series, continuity, differentiation, Riemann integration), through to power series, several variable calculus and Fourier analysis, and finally to the Lebesgue integral. These are almost entirely set in the concrete setting of the real line and Euclidean spaces, although there is some material on abstract metric and topological spaces. There are also appendices on mathematical logic and the decimal system. The entire text (omitting some less central topics) can be taught in two quarters of twenty-five to thirty lectures each. The course material is deeply intertwined with the exercises, as it is intended that the student actively learn the material (and practice thinking and writing rigorously) by proving several of the key results in the theory. The fourth edition incorporates a large number of additional corrections reported since the release of the third edition, as well as some additional new exercises.

Details

Are you an honours undergraduate looking to expand your knowledge of calculus? Look no further! Hindustan Book Agency's Analysis (1) is the perfect companion for students like you. This two-volume introduction to real analysis focuses on rigour and foundations, ensuring that you develop a solid understanding of the subject. Starting from the very basics, including the construction of number systems and set theory, this book takes you through the essentials of analysis - limits, series, continuity, differentiation, Riemann integration, power series, several variable calculus, Fourier analysis, and even the Lebesgue integral.

What sets Analysis (1) apart is its concrete setting in the real line and Euclidean spaces, making it easy for you to grasp complex mathematical concepts. Additionally, the book covers abstract metric and topological spaces, opening up a world of possibilities for exploration. With appendices on mathematical logic and the decimal system, you'll have a well-rounded understanding of the subject.

Not just a textbook, Analysis (1) encourages active learning through its integrated exercises. By proving key results in the theory, you'll not only gain a deeper understanding of the material but also improve your critical thinking and writing skills. The fourth edition of this book incorporates numerous corrections and additional new exercises, making it even more comprehensive and valuable to your studies.

Don't miss out on the opportunity to enhance your understanding of calculus. Embrace rigour, foundation, and active learning with Analysis (1). Get your copy today and start on the path to mastering real analysis - Buy now!

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