First Semester

This concise text, first published in 2003, is for a one-semester course for upper-level undergraduates and beginning graduate students in engineering, science, and mathematics, and can also serve as a quick reference for professionals. The major topics in ordinary differential equations, initial value problems, boundary value problems, and delay differential equations, are usually taught in three separate semester-long courses. This single book provides a sound treatment of all three in fewer than 300 pages. Each chapter begins with a discussion of the 'facts of life' for the problem, mainly by means of examples. Numerical methods for the problem are then developed, but only those methods most widely used. The treatment of each method is brief and technical issues are minimized, but all the issues important in practice and for understanding the codes are discussed. The last part of each chapter is a tutorial that shows how to solve problems by means of small, but realistic, examples.

This book provides a broad introduction to the subject of dynamical systems, suitable for a one- or two-semester graduate course. In the first chapter, the authors introduce over a dozen examples, and then use these examples throughout the book to motivate and clarify the development of the theory. Topics include topological dynamics, symbolic dynamics, ergodic theory, hyperbolic dynamics, one-dimensional dynamics, complex dynamics, and measure-theoretic entropy. The authors top off the presentation with some beautiful and remarkable applications of dynamical systems to such areas as number theory, data storage, and Internet search engines. This book grew out of lecture notes from the graduate dynamical systems course at the University of Maryland, College Park, and reflects not only the tastes of the authors, but also to some extent the collective opinion of the Dynamics Group at the University of Maryland, which includes experts in virtually every major area of dynamical systems.

This is an introduction to algebraic K-theory with no prerequisite beyond a first semester of algebra (including Galois theory and modules over a principal ideal domain). The presentation is almost entirely self-contained, and is divided into short sections with exercises to reinforce the ideas and suggest further lines of inquiry. No experience with analysis, geometry, number theory or topology is assumed. Within the context of linear algebra, K-theory organises and clarifies the relations among ideal class groups, group representations, quadratic forms, dimensions of a ring, determinants, quadratic reciprocity and Brauer groups of fields. By including introductions to standard algebra topics (tensor products, localisation, Jacobson radical, chain conditions, Dedekind domains, semi-simple rings, exterior algebras), the author makes algebraic K-theory accessible to first-year graduate students and other mathematically sophisticated readers. Even if your algebra is rusty, you can read

This book, first published in 2000, addresses problems in financial mathematics of pricing and hedging derivative securities in an environment of uncertain and changing market volatility. These problems are important to investors from large trading institutions to pension funds. It presents mathematical and statistical tools that exploit the bursty nature of market volatility. The mathematics is introduced through examples and illustrated with simulations and the modeling approach that is described is validated and tested on market data. The material is suitable for a one semester course for graduate students who have had exposure to methods of stochastic modeling and arbitrage pricing theory in finance. It is easily accessible to derivatives practitioners in the financial engineering industry.

From the author of the highly-acclaimed "A First Course in Real Analysis" comes a volume designed specifically for a short one-semester course in real analysis. Many students of mathematics and the ph

In the fall of 1990, I taught Math 581 at New Mexico State University for the first time. This course on field theory is the first semester of the year-long graduate algebra course here at NMSU. In th

The aim of this text is to present some of the key results in the representation theory of finite groups. In order to keep the account reasonably elementary, so that it can be used for graduate-level courses, Professor Alperin has concentrated on local representation theory, emphasising module theory throughout. In this way many deep results can be obtained rather quickly. After two introductory chapters, the basic results of Green are proved, which in turn lead in due course to Brauer's First Main Theorem. A proof of the module form of Brauer's Second Main Theorem is then presented, followed by a discussion of Feit's work connecting maps and the Green correspondence. The work concludes with a treatment, new in part, of the Brauer-Dade theory. As a text, this book contains ample material for a one semester course. Exercises are provided at the end of most sections; the results of some are used later in the text. Representation theory is applied in number theory, combinatorics and in ma

When eighteen-year-old Mark returned home from his first semester at college, his family thought he was on drugs. In fact, he was suffering from manic depression, a devastating mental illness that a

These lecture notes comprise a three-semester graduate course in quantum mechanics at the University of Illinois. There are a number of texts which present the basic topics very well; but since a fair quantity of the material discussed in my course was not available to the students in elementary quantum mechanics books, I was asked to prepare written notes. In retrospect these lecture notes seemed sufficiently interesting to warrant their publication in this format. The notes, presented here in slightly revised form, consitutute a self-contained course in quantum mechanics from first principles to elementary and relativistic one-particle mechanics. Prerequisite to reading these notes is some familiarity with elementary quantum mechanics, at least at the undergraduate level. Preferably the reader should already have met the uncertainty principle and the concept of a wave function. Prerequisites also include sufficient acquaintance with complex cariables to be able to do simple contour i

Ideal for the single-variable, one-semester calculus course, Calculus I, 8/e, contains the first 6 chapters of Calculus, 8/e. The text continues to offer instructors and students new and innovative te

A Concise and Easy Study Guide to Ace General Chemistry I Learn the important concepts covered in the first semester of a college general chemistry course in this concise but comprehensive study guide

Riana: I wasn’t expecting to meet anyone when I arrived at Shaw University. After my last stint at love, the only thing I wanted to focus on is getting through my first semester of college without any

Book #2 in the adventures of a precocious and endearing heroine full of can-do spirit, good-heartedness, and zest for life. Alice-Miranda Highton-Smith-Kennington-Jones has survived her first semester

After staking out, obtaining, and then being forced to give up her first boyfriend, Josh, all Cammie Morgan wants is a peaceful semester. But that's easier said than done when you're a CIA legacy and

This book tells the story of Justin, a 15-year-old boy with autism who is starting his first semester in a mainstream school, and Brad, the school track star, all-around "cool guy," and Justin's assig

This is an introductory textbook covering the mathematics of interest rates, life contingencies and loss models. It can be adopted as (1) the main text of a one-semester first course in the mathematic

Newly widowed Harriet MacIver has just taken on her first travel writing assignment–rating an adventure cruise in the Caribbean. Add a gaggle of college students on a mini semester-at-sea voyage, a ru

Ideal for the single-variable, one-semester calculus course, Calculus I, 8/e, contains the first 6 chapters of Calculus, 8/e. The text continues to offer instructors and students new and innovative te

Ideal for the single-variable, one-semester calculus course, Calculus I, 8/e, contains the first 6 chapters of Calculus, 8/e. The text continues to offer instructors and students new and innovative te

Elements of Quantum Mechanics provides a solid grounding in the fundamentals of quantum theory and is designed for a first semester graduate or advanced undergraduate course in quantum mechanics for c

Suitable for a one-semester course covering the applications of calculus to business, economics and social science, this edition includes the same material as the first eight chapters of the two-semes

The Integrated Chinese Volume 3 Textbook is designed to cover the first semester of study at the college level. Learners develop real-life communicative skills as they discuss topics related to everyday life and learn useful grammatical structures presented alongside clear, jargon-free explanations. Two review lessons are included for cumulative practice. In Volume 3, both simplified and traditional characters are shown side-by-side.The Volume 3 Textbook is also available as a fully integrated, multimedia-rich digital course on Cheng & Tsui’s FluencyLink platformNew to the 4th Edition:Full-color, contemporary layoutContent updated to reflect latest ACTFL 21st Century World-Readiness StandardsGrammar section now includes exercises to consolidate newly learned structuresNew recurring language learning devices in every lessonRedesigned Cultural Literacy section promotes students’ cross-cultural awareness through new Compare & Contrast activitiesNew Lesson Wrap-Up section includes