Böcker av Christopher Heil

Developed over years of classroom use, this textbook provides a clear and accessible approach to real analysis. This modern interpretation is based on the author's lecture notes and has been meticulously tailored to motivate students and inspire readers to explore the material, and to continue exploring even after they have finished the book. The definitions, theorems, and proofs contained within are presented with mathematical rigor, but conveyed in an accessible manner and with language and motivation meant for students who have not taken a previous course on this subject.The text covers all of the topics essential for an introductory course, including Lebesgue measure, measurable functions, Lebesgue integrals, differentiation, absolute continuity, Banach and Hilbert spaces, and more. Throughout each chapter, challenging exercises are presented, and the end of each section includes additional problems. Such an inclusive approach creates an abundance of opportunities for readers to develop their understanding, and aids instructors as they plan their coursework. Additional resources are available online, including expanded chapters, enrichment exercises, a detailed course outline, and much more.Introduction to Real Analysis is intended for first-year graduate students taking a first course in real analysis, as well as for instructors seeking detailed lecture material with structure and accessibility in mind. Additionally, its content is appropriate for Ph.D. students in any scientific or engineering discipline who have taken a standard upper-level undergraduate real analysis course.

This text is a self-contained introduction to the three main families that we encounter in analysis - metric spaces, normed spaces, and inner product spaces - and to the operators that transform objects in one into objects in another.

Wish Rings is about a boy named Majunior who learns of his great powers. His powers are brought on by the death of his parents. After Majunior masters his great powers of fire, he stops all sorts of evil that tries to take over earth. Then he uses the great powers of the Mighty Barbarian, which lives within mystical rings, known as the Wish Rings, to undo the damage done to earth by evil. All through Majunior's journey to save earth, he meets new and more powerful people who share their knowledge with him.

This textbook is a self-contained introduction to the abstract theory of bases and redundant frame expansions and their use in both applied and classical harmonic analysis. The four parts of the text take the reader from classical functional analysis and basis theory to modern time-frequency and wavelet theory.