โ Scribed by John B. Conway
No coin nor oath required. For personal study only.
This rigorous textbook is intended for a year-long analysis or advanced calculus course for advanced undergraduate or beginning graduate students. Starting with detailed, slow-paced proofs that allow students to acquire facility in reading and writing proofs, it clearly and concisely explains the basics of differentiation and integration of functions of one and several variables, and covers the theorems of Green, Gauss, and Stokes. Minimal prerequisites are assumed, and relevant linear algebra topics are reviewed right before they are needed, making the material accessible to students from diverse backgrounds. Abstract topics are preceded by concrete examples to facilitate understanding, for example, before introducing differential forms, the text examines low-dimensional examples. The meaning and importance of results are thoroughly discussed, and numerous exercises of varying difficulty give students ample opportunity to test and improve their knowledge of this difficult yet vital subject.
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The real numbers ; Differentiation ; Integration ; Sequences of functions ; Metric and Euclidean spaces ; Differentiation in higher dimensions ; Integration in higher dimensions ; Curves and surfaces ; Differential forms.
The real numbers -- Differentiation -- Integration -- Sequences of functions -- Metric and Euclidean spaces -- Differentiation in higher dimensions -- Integration in higher dimensions -- Curves and surfaces -- Differential forms.;"This rigorous textbook is intended for a year-long analysis or advan
This rigorous textbook is intended for a year-long analysis or advanced calculus course for advanced undergraduate or beginning graduate students. Starting with detailed, slow-paced proofs that allow students to acquire facility in reading and writing proofs, it clearly and concisely explains the ba
This book is an introductory text on real analysis for undergraduate students. The prerequisite for this book is a solid background in freshman calculus in one variable. The intended audience of this book includes undergraduate mathematics majors and students from other disciplines who use real anal
I'm an electrical engineer, with a focus in signal processing. This is the book I learned Fourier analysis from, and once I did, the classes that EEs usually dread were relatively easy for me. This is the only textbook I actually read every chapter of (and we only covered the first half in the Fou