Geometric Measure Theory

Frank Morgan

Academic Press

This book is written by award-winning author, Frank Morgan. It offers a simple and sophisticated point of view, reflecting Morgan's insightful teaching, lecturing, and writing style. Intended for undergraduates studying real analysis, this book builds the theory behind calculus directly from the basic concepts of real numbers, limits, and open and closed sets in $\mathbb{R}^n$. It gives the three characterizations of continuity: via epsilon-delta, sequences, and open sets. It gives the three characterizations of compactness: as "closed and bounded," via sequences, and via open covers. Topics include Fourier series, the Gamma function, metric spaces, and Ascoli's Theorem. This concise text not only provides efficient proofs, but also shows students how to derive them. The excellent exercises are accompanied by select solutions. Ideally suited as an undergraduate textbook, this complete book on real analysis will fit comfortably into one semester. Frank Morgan received the first Haimo Award for distinguished college teaching from the Mathematical Association of America. He has also garnered top teaching awards from Rice University (Houston, TX) and MIT (Cambridge, MA).

Real Analysis

Science & Math

Mathematics

American Mathematical Society

The calculus of variations is a beautiful subject with a rich history and with origins in the minimization problems of calculus. Although it is now at the core of many modern mathematical fields, it does not have a well-defined place in most undergraduate mathematics curricula. This volume should nevertheless give the undergraduate reader a sense of its great character and importance. Interesting functionals, such as area or energy, often give rise to problems for which the most natural solution occurs by differentiating a one-parameter family of variations of some function.The critical points of the functional are related to the solutions of the associated Euler-Lagrange equation. These differential equations are at the heart of the calculus of variations and its applications to other subjects. Some of the topics addressed in this book are Morse theory, wave mechanics, minimal surfaces, soap bubbles, and modeling traffic flow. All are readily accessible to advanced undergraduates. This book is derived from a workshop sponsored by Rice University. It is suitable for advanced undergraduates, graduate students and research mathematicians interested in the calculus of variations and its applications to other subjects.

Six Themes On Variation (Student Mathematical Library, V. 26)

Michael Wolf

FRANK JONES

Robin Forman

Barbara Lee Keyfitz

Amer Mathematical Society

Mathematics can be fun for everyone, and this book shows it. It grew out of the author's popularisation of mathematics via live, call-in TV shows and widely published articles. The questions, comments, and even the answers here come largely from the callers and readers themselves, and so the book covers the kind of mathematical problems that people are interested in, not those that professional mathematicians, writers or even publishers think people should be interested in. The book makes no attempt to fit any mould. Although written by a research mathematician, it goes where the callers and readers have directed it, over a wide range of topics and levels. Everyone paging through it will be captured by something of interest, whether they consider themselves interested in mathematics or not.

The Math Chat Book (Spectrum)

Humor & Entertainment

Puzzles & Games

The Mathematical Association of America

Real Analysis and Applications starts with a streamlined, but complete approach to real analysis. It finishes with a wide variety of applications in Fourier series and the calculus of variations, including minimal surfaces, physics, economics, Riemannian geometry, and general relativity. The basic theory includes all the standard topics: limits of sequences, topology, compactness, the Cantor set and fractals, calculus with the Riemann integral, a chapter on the Lebesgue theory, sequences of functions, infinite series, and the exponential and Gamma functions. The applications conclude with a computation of the relativistic precession of Mercury's orbit, which Einstein called "convincing proof of the correctness of the theory [of General Relativity]." The text not only provides clear, logical proofs, but also shows the student how to come up with them. The excellent exercises come with select solutions in the back. Here is a text which makes it possible to do the full theory and significant applications in one semester. Frank Morgan is the author of six books and over one hundred articles on mathematics. He is an inaugural recipient of the Mathematical Association of America's national Haimo award for excellence in teaching. With this applied version of his Real Analysis text, Morgan brings his famous direct style to the growing numbers of potential mathematics majors who want to see applications right along with the theory.

Real Analysis and Applications

This is a textbook for teaching single-variable calculus. It introduces standard preliminary topics like trigonometry and limits and then actually integrates them into the calculus. The text contains relevant examples and problems to illustrate the general concepts and includes careful explanations and solutions.

Calculus Lite

A.K. Peters

This inspiring book explores the timeless love stories of Ruth and Esther. It shows how these enchanting narratives speak of the elect of all Israel and even reveal our future as Believers. The God of Israel long-ago divided Israel, His bride, into two houses: Ephraim and Judah. The history of both of these houses of Israel, and their divine destiny, is hidden in these fascinating books of Scripture. In breathtaking fashion they reveal the redemption and restoration of all Israel. In his encouraging style, Frank Morgan shares some of the wonderful insights the Father has allowed him to see in the Word (Jeremiah 33:3; Isaiah 48:6). He unveils the deep truths found in these stories of a widow and a maiden, both of whom were used mightily by the God of Israel. Morgan eloquently provides glimpses of the depth of YHVHÌs great love for each of us; he also provides many insights into the FatherÌs great and glorious latter-day plan for a reunited, redeemed, and fully restored people of Israel.

Ruth & Esther: Shadows of Our Future

Parenting & Relationships

Key of David Publishing

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Books by Frank Morgan