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This award-winning text carefully leads the student through the basic topics of Real Analysis. Topics include metric spaces, open and closed sets, convergent sequences, function limits and continuity, compact sets, sequences and series of functions, power series, differentiation and integration, Taylor's theorem, total variation, rectifiable arcs, and sufficient conditions of integrability. Well over 500 exercises (many with extensive hints) assist students through the material. For students who need a review of basic mathematical concepts before beginning "epsilon-delta"-style proofs, the text begins with material on set theory (sets, quantifiers, relations and mappings, countable sets), the real numbers (axioms, natural numbers, induction, consequences of the completeness axiom), and Euclidean and vector spaces; this material is condensed from the author's Basic Concepts of Mathematics, the complete version of which can be used as supplementary background material for the present text.
- Subjects:
- Mathematics and Statistics
- Keywords:
- Mathematical analysis Textbooks
- Resource Type:
- e-book
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e-book
In this expanded new edition of Living with Earthquakes, Robert Yeats, a leading authority on earthquakes in California and the Pacific Northwest, describes the threat posed by the Cascadia Subduction Zone, a great earthquake fault which runs for hundreds of miles offshore from British Columbia to northern California. New research reveals subtle movements on the deepest part of this fault every 14-15 months — building up strain toward the next major earthquake. Combining cutting-edge research with practical safety information, Living with Earthquakes: • introduces new information about the danger from faults beneath major Northwest cities: the Seattle Fault, Tacoma Fault, and Portland Hills Fault• explores such topics as earthquake forecasting, catastrophe insurance, tsunamis, soil liquefaction, and seismic waves in Northwest lakes caused by Alaskan earthquakes• reviews earthquake preparedness and disaster response in the aftermath of the 2001 Nisqually earthquake, the worst natural disaster in Washington's history• suggests actions that citizens can take to protect their families and homesAn essential guide for anyone interested in understanding earthquake science or in preparing for the next earthquake, this book is also a call to action. Vivid descriptions of recent disasters — including the great tsunami that swept down the Northwest coast in 1964, the 1993 Oregon earthquakes, and the 2001 Nisqually earthquake — underscore the urgent need for better earthquake planning and awareness.
- Subjects:
- Risk Assessment and Management and Disaster Control and Management
- Keywords:
- Pacific Northwest Earthquake hazard analysis Textbooks Earthquakes -- Safety measures
- Resource Type:
- e-book
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e-book
This book is an introduction to combinatorial mathematics, also known as combinatorics. The book focuses especially but not exclusively on the part of combinatorics that mathematicians refer to as “counting.” The book consists almost entirely of problems. Some of the problems are designed to lead you to think about a concept, others are designed to help you figure out a concept and state a theorem about it, while still others ask you to prove the theorem. Other problems give you a chance to use a theorem you have proved. From time to time there is a discussion that pulls together some of the things you have learned or introduces a new idea for you to work with. Many of the problems are designed to build up your intuition for how combinatorial mathematics works. There are problems that some people will solve quickly, and there are problems that will take days of thought for everyone. Probably the best way to use this book is to work on a problem until you feel you are not making progress and then go on to the next one. Think about the problem you couldn't get as you do other things. The next chance you get, discuss the problem you are stymied on with other members of the class. Often you will all feel you've hit dead ends, but when you begin comparing notes and listening carefully to each other, you will see more than one approach to the problem and be able to make some progress. In fact, after comparing notes you may realize that there is more than one way to interpret the problem. In this case your first step should be to think together about what the problem is actually asking you to do. You may have learned in school that for every problem you are given, there is a method that has already been taught to you, and you are supposed to figure out which method applies and apply it. That is not the case here. Based on some simplified examples, you will discover the method for yourself. Later on, you may recognize a pattern that suggests you should try to use this method again.
- Subjects:
- Mathematics and Statistics
- Keywords:
- Combinatorial analysis Textbooks
- Resource Type:
- e-book
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e-book
This book was developed at Simon Fraser University for an upper-level physics course. Along with a careful exposition of electricity and magnetism, it devotes a chapter to ferromagnets. According to the course description, the topics covered were “electromagnetics, magnetostatics, waves, transmission lines, wave guides,antennas, and radiating systems.”