Daniel W. Cunningham – författare

Typically, undergraduates see real analysis as one of the most difficult courses that a mathematics major is required to take. The main reason for this perception is twofold: Students must comprehend new abstract concepts and learn to deal with these concepts on a level of rigor and proof not previously encountered. A key challenge for an instructor of real analysis is to find a way to bridge the gap between a student’s preparation and the mathematical skills that are required to be successful in such a course. Real Analysis: With Proof Strategies provides a resolution to the "bridging-the-gap problem." The book not only presents the fundamental theorems of real analysis, but also shows the reader how to compose and produce the proofs of these theorems. The detail, rigor, and proof strategies offered in this textbook will be appreciated by all readers. Features Explicitly shows the reader how to produce and compose the proofs of the basic theorems in real analysis Suitable for junior or senior undergraduates majoring in mathematics.

Typically, undergraduates see real analysis as one of the most difficult courses that a mathematics major is required to take. The main reason for this perception is twofold: Students must comprehend new abstract concepts and learn to deal with these concepts on a level of rigor and proof not previously encountered. A key challenge for an instructor of real analysis is to find a way to bridge the gap between a student’s preparation and the mathematical skills that are required to be successful in such a course. Real Analysis: With Proof Strategies provides a resolution to the "bridging-the-gap problem." The book not only presents the fundamental theorems of real analysis, but also shows the reader how to compose and produce the proofs of these theorems. The detail, rigor, and proof strategies offered in this textbook will be appreciated by all readers. Features Explicitly shows the reader how to produce and compose the proofs of the basic theorems in real analysis Suitable for junior or senior undergraduates majoring in mathematics.

Typically, undergraduates see real analysis as one of the most difficult courses that a mathematics major is required to take. The main reason for this perception is twofold: Students must comprehend new abstract concepts and learn to deal with these concepts on a level of rigor and proof not previously encountered. A key challenge for an instructor of real analysis is to find a way to bridge the gap between a student’s preparation and the mathematical skills that are required to be successful in such a course.

Real Analysis: With Proof Strategies provides a resolution to the "bridging-the-gap problem." The book not only presents the fundamental theorems of real analysis, but also shows the reader how to compose and produce the proofs of these theorems. The detail, rigor, and proof strategies offered in this textbook will be appreciated by all readers.

Features

Explicitly shows the reader how to produce and compose the proofs of the basic theorems in real analysis

Suitable for junior or senior undergraduates majoring in mathematics.

Typically, undergraduates see real analysis as one of the most difficult courses that a mathematics major is required to take. The main reason for this perception is twofold: Students must comprehend new abstract concepts and learn to deal with these concepts on a level of rigor and proof not previously encountered. A key challenge for an instructor of real analysis is to find a way to bridge the gap between a student’s preparation and the mathematical skills that are required to be successful in such a course.

Real Analysis: With Proof Strategies provides a resolution to the "bridging-the-gap problem." The book not only presents the fundamental theorems of real analysis, but also shows the reader how to compose and produce the proofs of these theorems. The detail, rigor, and proof strategies offered in this textbook will be appreciated by all readers.

Features

Explicitly shows the reader how to produce and compose the proofs of the basic theorems in real analysis

Suitable for junior or senior undergraduates majoring in mathematics.

This undergraduate textbook carefully introduces the fundamentals of axiomatic set theory; a rich and beautiful subject whose fundamental concepts permeate virtually every branch of mathematics. One can thus say that set theory is a foundation for mathematics. The proofs are rigorous, clear, and complete, while remaining accessible to undergraduates who are new to upper-level mathematics. Topics covered include relations, functions, the natural numbers, order, cardinality, transfinite recursion, the axiom of choice, ordinal numbers, and cardinal numbers. Exercises are given at the end of each section in a chapter. The second edition includes a new chapter on set-theoretic constructions of the integers, the rational numbers, and the real numbers; a new chapter on models of set theory. There are also new sections on the hyperreals and applications of stationary sets, club sets, and Fodor's Theorem, as well as additional explanation, examples, and figures. A solutions manual is available for instructors.

Set theory is a rich and beautiful subject whose fundamental concepts permeate virtually every branch of mathematics. One could say that set theory is a unifying theory for mathematics, since nearly all mathematical concepts and results can be formalized within set theory. This textbook is meant for an upper undergraduate course in set theory. In this text, the fundamentals of abstract sets, including relations, functions, the natural numbers, order, cardinality, transfinite recursion, the axiom of choice, ordinal numbers, and cardinal numbers, are developed within the framework of axiomatic set theory. The reader will need to be comfortable reading and writing mathematical proofs. The proofs in this textbook are rigorous, clear, and complete, while remaining accessible to undergraduates who are new to upper-level mathematics. Exercises are included at the end of each section in a chapter, with useful suggestions for the more challenging exercises.

Set theory is a rich and beautiful subject whose fundamental concepts permeate virtually every branch of mathematics. One could say that set theory is a unifying theory for mathematics, since nearly all mathematical concepts and results can be formalized within set theory. This textbook is meant for an upper undergraduate course in set theory. In this text, the fundamentals of abstract sets, including relations, functions, the natural numbers, order, cardinality, transfinite recursion, the axiom of choice, ordinal numbers, and cardinal numbers, are developed within the framework of axiomatic set theory. The reader will need to be comfortable reading and writing mathematical proofs. The proofs in this textbook are rigorous, clear, and complete, while remaining accessible to undergraduates who are new to upper-level mathematics. Exercises are included at the end of each section in a chapter, with useful suggestions for the more challenging exercises.

Set theory is a rich and beautiful subject whose fundamental concepts permeate virtually every branch of mathematics. One could say that set theory is a unifying theory for mathematics, since nearly all mathematical concepts and results can be formalized within set theory. This textbook is meant for an upper undergraduate course in set theory. In this text, the fundamentals of abstract sets, including relations, functions, the natural numbers, order, cardinality, transfinite recursion, the axiom of choice, ordinal numbers, and cardinal numbers, are developed within the framework of axiomatic set theory. The reader will need to be comfortable reading and writing mathematical proofs. The proofs in this textbook are rigorous, clear, and complete, while remaining accessible to undergraduates who are new to upper-level mathematics. Exercises are included at the end of each section in a chapter, with useful suggestions for the more challenging exercises.

The book is intended for students who want to learn how to prove theorems and be better prepared for the rigors required in more advance mathematics. One of the key components in this textbook is the development of a methodology to lay bare the structure underpinning the construction of a proof, much as diagramming a sentence lays bare its grammatical structure. Diagramming a proof is a way of presenting the relationships between the various parts of a proof. A proof diagram provides a tool for showing students how to write correct mathematical proofs.

The book is intended for students who want to learn how to prove theorems and be better prepared for the rigors required in more advance mathematics. One of the key components in this textbook is the development of a methodology to lay bare the structure underpinning the construction of a proof, much as diagramming a sentence lays bare its grammatical structure. Diagramming a proof is a way of presenting the relationships between the various parts of a proof. A proof diagram provides a tool for showing students how to write correct mathematical proofs.

The book is intended for students who want to learn how to prove theorems and be better prepared for the rigors required in more advance mathematics. One of the key components in this textbook is the development of a methodology to lay bare the structure underpinning the construction of a proof, much as diagramming a sentence lays bare its grammatical structure. Diagramming a proof is a way of presenting the relationships between the various parts of a proof. A proof diagram provides a tool for showing students how to write correct mathematical proofs.

The lack of effective DC fault protection technology remains a major barrier for the DC paradigm shift. In addressing the key challenges, Direct Current Fault Protection: Basic Concepts and Technology Advances starts with an introduction to the advantages of DC power systems before moving on to an in-depth review of DC fault protection technologies, including mechanical circuit breaker (MCB), solid-state circuit breaker (SSCB), hybrid circuit breaker (HCB), converter based (breakerless) protection, and fault current limiter (FCL). Coverage includes a comprehensive comparison of various DC fault interruption technologies and their suitable applications, state-of-the-art DC fault protection concepts and advances in research, identification of fundamental challenges and future directions in the field, and commercialization aspects. This book will be a valuable reference for practicing engineers, researchers, and graduate students in the field of power electronics andDC power systems.

The lack of effective DC fault protection technology remains a major barrier for the DC paradigm shift. In addressing the key challenges, Direct Current Fault Protection: Basic Concepts and Technology Advances starts with an introduction to the advantages of DC power systems before moving on to an in-depth review of DC fault protection technologies, including mechanical circuit breaker (MCB), solid-state circuit breaker (SSCB), hybrid circuit breaker (HCB), converter based (breakerless) protection, and fault current limiter (FCL). Coverage includes a comprehensive comparison of various DC fault interruption technologies and their suitable applications, state-of-the-art DC fault protection concepts and advances in research, identification of fundamental challenges and future directions in the field, and commercialization aspects. This book will be a valuable reference for practicing engineers, researchers, and graduate students in the field of power electronics andDC power systems.

The lack of effective DC fault protection technology remains a major barrier for the DC paradigm shift. In addressing the key challenges, Direct Current Fault Protection: Basic Concepts and Technology Advances starts with an introduction to the advantages of DC power systems before moving on to an in-depth review of DC fault protection technologies, including mechanical circuit breaker (MCB), solid-state circuit breaker (SSCB), hybrid circuit breaker (HCB), converter based (breakerless) protection, and fault current limiter (FCL). Coverage includes a comprehensive comparison of various DC fault interruption technologies and their suitable applications, state-of-the-art DC fault protection concepts and advances in research, identification of fundamental challenges and future directions in the field, and commercialization aspects. This book will be a valuable reference for practicing engineers, researchers, and graduate students in the field of power electronics andDC power systems.

This book presents the transformational progress in next-generation advanced converter circuit topologies based on the unique electrical properties of wide-bandgap semiconductors, including silicon carbide (SiC) and gallium nitride (GaN). It addresses the opportunities for significant advances in power electronics circuit performance opened by the availability of wide-bandgap power devices and the challenges associated with using these devices that must be overcome when applying them. The authors tackle specific grand challenges in application areas covering a broad range of power electronics circuits and systems disciplines, including electric motor-driven systems, automotive applications, air/rail/ship propulsion, electric vehicle chargers, high-performance computing and data centers, power supplies, solar inverters, wind-electric systems, high/medium voltage transmission/distribution equipment and power electronics interacting with the grid, power conversion for grid storage, monolithic power processing, and solid-state circuit breakers. Wide Bandgap Power Electronics: Emerging Converter Technologies and Applications introduces readers to the unique characteristics of wide-bandgap power semiconductor devices and the revolutionary impact that they are capable of having on the performance of power converters in future power electronics applications and will be an invaluable resource for practicing engineers, researchers, and graduate students in the field of power electronics, applications, and systems.