Calculus Express is a concise, easy-to-study test preparation guide to help students improve their Calculus AB Advanced Placement (AP) exam scores. In addition, this resource is useful for non-Advanced Placement introductory calculus students due to the extensive overlap of material. To maximize relevancy, critical content is modeled after the outline of the Calculus AB AP test promulgated by The College Board. Calculus Express is broken down into five parts: Limits Derivatives Applications of Derivatives Integrals Applications of Integrals The primary feature of Calculus Express is that it contains all necessary information in 100+ pages. This enables you to truly cram for the test, memorize key formulas, and walk into the exam site having all the key material in your short-term memory!
An introduction to the philosophy of mathematics grounded in mathematics and motivated by mathematical inquiry and practice. In this book, Joel David Hamkins offers an introduction to the philosophy of mathematics that is grounded in mathematics and motivated by mathematical inquiry and practice. He treats philosophical issues as they arise organically in mathematics, discussing such topics as platonism, realism, logicism, structuralism, formalism, infinity, and intuitionism in mathematical contexts. He organizes the book by mathematical themes--numbers, rigor, geometry, proof, computability, incompleteness, and set theory--that give rise again and again to philosophical considerations.
An authorised reissue of the long out of print classic textbook, Advanced Calculus by the late Dr Lynn Loomis and Dr Shlomo Sternberg both of Harvard University has been a revered but hard to find textbook for the advanced calculus course for decades.This book is based on an honors course in advanced calculus that the authors gave in the 1960's. The foundational material, presented in the unstarred sections of Chapters 1 through 11, was normally covered, but different applications of this basic material were stressed from year to year, and the book therefore contains more material than was covered in any one year. It can accordingly be used (with omissions) as a text for a year's course in advanced calculus, or as a text for a three-semester introduction to analysis.The prerequisites are a good grounding in the calculus of one variable from a mathematically rigorous point of view, together with some acquaintance with linear algebra. The reader should be familiar with limit and continuity type arguments and have a certain amount of mathematical sophistication. As possible introductory texts, we mention Differential and Integral Calculus by R Courant, Calculus by T Apostol, Calculus by M Spivak, and Pure Mathematics by G Hardy. The reader should also have some experience with partial derivatives.In overall plan the book divides roughly into a first half which develops the calculus (principally the differential calculus) in the setting of normed vector spaces, and a second half which deals with the calculus of differentiable manifolds.
Society forges ahead in the process of solving various contradictory problems and it is ceaselessly innovating. It is the desire of mankind to use computers and computing networks to help deal with contradictory problems and to conduct innovative activities. Using formal models to discuss object extension and the possibility of change, as well as the rules and methods for innovation, Extenics is applied to solving contradictory problems and has become the basic theory, method and instrument to achieve this goal. In the 30 years since the foundation of Extenics, researchers have built relatively complete theoretical systems —‘extension theory’, studied formal and modeling innovation methods —‘extension innovation methods’, and launched the applications in various fields such as information, design, automation and management etc. —‘extension engineering’. Extension theory, the extension innovation method and extension engineering jointly constitute the new discipline—Extenics. At the same time, the practical activities of engineering technology and management promote the integration of various innovation methods such as TRIZ and brainstorming etc. This book collects together, from scholars in various fields, the research achievements in Extenics and innovation methods, in order to facilitate and promote the development of Extenics and the various innovation theories and methods, as well as to improve its innovative capacity in academic and business circles.
Easy-to-read writing style. Comprehensive coverage of all database topics. Bullet lists and tables. More detailed examples of database implementations. More SQL, including significant information on planned revisions to the language. Simple and easy explanation to complex topics like relational algebra, relational calculus, query processing and optimization. Covers topics on implementation issues like security, integrity, transaction management, concurrency control, backup and recovery etc. Latest advances in database technology.
"Engineering Mathematics: A Formula Handbook" serves as an invaluable tool for engineers, students, and professionals alike, offering a concise compilation of essential mathematical formulas and concepts relevant to engineering disciplines. Covering a wide array of topics including calculus, linear algebra, differential equations, and complex analysis, this handbook provides quick access to key formulas needed for solving engineering problems. With clear explanations and organized sections, this book is a must-have reference for anyone seeking to apply mathematical principles in engineering practice and academia.
The second of a three-volume work, this is the result of the authors'experience teaching calculus at Berkeley. The book covers techniques and applications of integration, infinite series, and differential equations, the whole time motivating the study of calculus using its applications. The authors include numerous solved problems, as well as extensive exercises at the end of each section. In addition, a separate student guide has been prepared.
This illuminating textbook provides a concise review of the core concepts in mathematics essential to computer scientists. Emphasis is placed on the practical computing applications enabled by seemingly abstract mathematical ideas, presented within their historical context. The text spans a broad selection of key topics, ranging from the use of finite field theory to correct code and the role of number theory in cryptography, to the value of graph theory when modelling networks and the importance of formal methods for safety critical systems. This fully updated new edition has been expanded with a more comprehensive treatment of algorithms, logic, automata theory, model checking, software reliability and dependability, algebra, sequences and series, and mathematical induction. Topics and features: includes numerous pedagogical features, such as chapter-opening key topics, chapter introductions and summaries, review questions, and a glossary; describes the historical contributions of such prominent figures as Leibniz, Babbage, Boole, and von Neumann; introduces the fundamental mathematical concepts of sets, relations and functions, along with the basics of number theory, algebra, algorithms, and matrices; explores arithmetic and geometric sequences and series, mathematical induction and recursion, graph theory, computability and decidability, and automata theory; reviews the core issues of coding theory, language theory, software engineering, and software reliability, as well as formal methods and model checking; covers key topics on logic, from ancient Greek contributions to modern applications in AI, and discusses the nature of mathematical proof and theorem proving; presents a short introduction to probability and statistics, complex numbers and quaternions, and calculus. This engaging and easy-to-understand book will appeal to students of computer science wishing for an overview of the mathematics used in computing, and to mathematicians curious about how their subject is applied in the field of computer science. The book will also capture the interest of the motivated general reader.
A practical hands-on guide to improving the teaching of mathematics. Provides a collection of cases that blend important mathematics content with the real complexities of school and classroom life.
The contents of this second edition have been appropriately enhanced to serve the growing needs of the students pursuing undergraduate engineering courses in Computer Science, Information Technology, as well as postgraduate programmes in Computer Applications (MCA), MSc (IT) and MSc (Computer Science). The book covers the fundamental and theoretical concepts in an elaborate manner using SQL of leading RDBMS—Oracle, MS SQL Server and Sybase. This book is recommended in Guwahati University, Assam. Realizing the importance of RDBMS in all types of architectures and applications, both traditional and modern topics are included for the benefit of IT-savvy readers. A strong understanding of the relational database design is provided in chapters on Entity-Relationship, Relational, Hierarchical and Network Data Models, Normalization, Relational Algebra and Relational Calculus. The architecture of the legacy relational database R system, the hierarchical database IMS of IBM and the network data model DBTG are also given due importance to bring completeness and to show thematic interrelationships among them. Several chapters have been devoted to the latest database features and technologies such as Data Partitioning, Data Mirroring, Replication, High Availability, Security and Auditing. The architecture of Oracle, SQL of Oracle known as PL/SQL, SQL of both Sybase and MS SQL Server known as T-SQL have been covered. KEY FEATURES : Gives wide coverage to topics of network, hierarchical and relational data models of both traditional and generic modern databases. Discusses the concepts and methods of Data Partitioning, Data Mirroring and Replication required to build the centralized architecture of very large databases. Provides several examples, listings, exercises and solutions to selected exercises to stimulate and accelerate the learning process of the readers. Covers the concept of database mirroring and log shipping to demonstrate how to build disaster recovery solution through the use of database technology. Contents: Preface 1. Introduction 2. The Entity-Relationship Model 3. Data Models 4. Storage Structure 5. Relational Data Structure 6. Architecture of System R and Oracle 7. Normalization 8. Structured Query Language 9. T-SQL—Triggers and Dynamic Execution 10. Procedure Language—SQL 11. Cursor Management and Advanced PL/SQL 12. Relational Algebra and Relational Calculus 13. Concurrency Control and Automatic Recovery 14. Distributed Database and Replication 15. High Availability and RAID Technology 16. Security Features Built in RDBMS 17. Queries Optimization 18. Architecture of a Hierarchical DBMS 19. The Architecture of Network based DBTG System 20. Comparison between Different Data Models 21. Performance Improvement and Partitioning 22. Database Mirroring and Log Shipping for Disaster Recovery Bibliography Answers to Selected Exercises Index
