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Numerical Methods for Ordinary Differential Equations is a self-contained introduction to a fundamental field of numerical analysis and scientific computation. Written for undergraduate students with a mathematical background, this book focuses on the analysis of numerical methods without losing sight of the practical nature of the subject. It covers the topics traditionally treated in a first course, but also highlights new and emerging themes. Chapters are broken down into `lecture' sized pieces, motivated and illustrated by numerous theoretical and computational examples. Over 200 exercises are provided and these are starred according to their degree of difficulty. Solutions to all exercises are available to authorized instructors. The book covers key foundation topics: o Taylor series methods o Runge--Kutta methods o Linear multistep methods o Convergence o Stability and a range of modern themes: o Adaptive stepsize selection o Long term dynamics o Modified equations o Geometric integration o Stochastic differential equations The prerequisite of a basic university-level calculus class is assumed, although appropriate background results are also summarized in appendices. A dedicated website for the book containing extra information can be found via www.springer.com

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An Introduction to Programming by the Inventor of C++ Preparation for Programming in the Real World The book assumes that you aim eventually to write non-trivial programs, whether for work in software development or in some other technical field. Focus on Fundamental Concepts and Techniques The book explains fundamental concepts and techniques in greater depth than traditional introductions. This approach will give you a solid foundation for writing useful, correct, maintainable, and efficient code. Programming with Today's C++ (C++11 and C++14) The book is an introduction to programming in general, including object-oriented programming and generic programming. It is also a solid introduction to the C++ programming language, one of the most widely used languages for real-world software. The book presents modern C++ programming techniques from the start, introducing the C++ standard library and C++11 and C++14 features to simplify programming tasks. For Beginners - And Anyone Who Wants to Learn Something New The book is primarily designed for people who have never programmed before, and it has been tested with many thousands of first-year university students. It has also been extensively used for self-study. Also, practitioners and advanced students have gained new insight and guidance by seeing how a master approaches the elements of his art. Provides a Broad View The first half of the book covers a wide range of essential concepts, design and programming techniques, language features, and libraries. Those will enable you to write programs involving input, output, computation, and simple graphics. The second half explores more specialized topics (such as text processing, testing, and the C programming language) and provides abundant reference material. Source code and support supplements are available from the author's website.

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An Introduction to Programming by the Inventor of C++ Preparation for Programming in the Real World The book assumes that you aim eventually to write non-trivial programs, whether for work in software development or in some other technical field. Focus on Fundamental Concepts and Techniques The book explains fundamental concepts and techniques in greater depth than traditional introductions. This approach will give you a solid foundation for writing useful, correct, maintainable, and efficient code. Programming with Today's C++ (C++11 and C++14) The book is an introduction to programming in general, including object-oriented programming and generic programming. It is also a solid introduction to the C++ programming language, one of the most widely used languages for real-world software. The book presents modern C++ programming techniques from the start, introducing the C++ standard library and C++11 and C++14 features to simplify programming tasks. For Beginners-And Anyone Who Wants to Learn Something New The book is primarily designed for people who have never programmed before, and it has been tested with many thousands of first-year university students. It has also been extensively used for self-study. Also, practitioners and advanced students have gained new insight and guidance by seeing how a master approaches the elements of his art. Provides a Broad View The first half of the book covers a wide range of essential concepts, design and programming techniques, language features, and libraries. Those will enable you to write programs involving input, output, computation, and simple graphics. The second half explores more specialized topics (such as text processing, testing, and the C programming language) and provides abundant reference material. Source code and support supplements are available from the author's website.

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Introducing functional programming in the Haskell language, this book is written for students and programmers with little or no experience. It emphasises the process of crafting programmes, problem solving and avoiding common programming pitfalls. Covering basic functional programming, through abstraction to larger scale programming, students are lead step by step through the basics, before being introduced to more advanced topics. Product Description Introducing functional programming in the Haskell language, this book is written for students and programmers with little or no experience. It emphasises the process of crafting programmes, problem solving and avoiding common programming pitfalls. Covering basic functional programming, through abstraction to larger scale programming, students are lead step by step through the basics, before being introduced to more advanced topics. This edition includes new material on testing and domain-specific languages and a variety of new examples and case studies, including simple games. Existing material has been expanded and re-ordered, so that some concepts such as simple data types and input/output are presented at an earlier stage. Features + Benefits Emphasises software engineering principles. Encourages a disciplined approach to building reusable libraries of software components. Case studies are used throughout the book to introduce new ideas, illustrate important concepts, and demonstrate how existing techniques work together. Case studies include: An interactive calculator programme. A coding and decoding system. A small queue simulation package. Companion website contains supporting material (such as visualisation tools and a substantial number of web links) to aid further study. Appendices contain information on Hugs errors. Backcover The third edition of Haskell: The Craft of Functional Programming is essential reading for beginners to functional programming and newcomers to the Haskell programming language. The emphasis is on the process of crafting programs and the text contains many examples and running case studies, as well as advice on program design, testing, problem solving and how to avoid common pitfalls. Revisions to this new edition include new material on testing and domain-specific languages and a variety of new examples and case studies, including simple games. Existing material has been expanded and re-ordered, so that some concepts - such as simple data types and input/output - are presented at an earlier stage. The running example of Pictures is now implemented using web browser graphics as well as lists of strings. The book uses GHCi, the interactive version of the Glasgow Haskell Compiler, as its implementation of choice. It has also been revised to include material about the Haskell Platform, and the Hackage online database of Haskell libraries. In particular, readers are given detailed guidance about how to find their way around what is available in these systems. An accompanying web site supports the book, containing all the program code, further teaching materials and other useful resources. Simon Thompson is Professor of Logic and Computation in the School of Computing at the University of Kent. His research and teaching interests include functional programming and logical aspects of computer science. Simon has written three other books: Erlang Programming (co-authored with Francesco Cesarini), Miranda: The Craft of Functional Programming and Type Theory and Functional Programming. Preface 1 Introducing functional programming 1.1 Computers and modelling 1.2 What is a function? 1.3 Pictures and functions 1.4 Types 1.5 The Haskell programming language 1.6 Expressions and evaluation 1.7 Definitions 1.8 Function definitions 1.9 Types and functional programming 1.10 Calculation and evaluation 1.11 The essence of Haskell programming 1.12 Domain-specific languages 1.13 Two models of Pictures 1.14 Tests, properties and proofs 2 Getting started with Haskell and GHCi 2.1 A first Haskell program 2.2 Using Haskell in practice 2.3 Using GHCi 2.4 The standard prelude and the Haskell libraries 2.5 Modules 2.6 A second example: Pictures 2.7 Errors and error messages 3 Basic types and definitions 3.1 The Booleans: Bool 3.2 The integers: Integer and Int 3.3 Overloading 3.4 Guards 3.5 Characters and strings 3.6 Floating-point numbers: Float 3.7 Syntax 4 Designing and writing programs 4.1 Where do I start? Designing a program in Haskell 4.2 Solving a problem in steps: local definitions 4.3 Defining types for ourselves: enumerated types 4.4 Recursion 4.5 Primitive recursion in practice 4.6 Extended exercise: pictures 4.7 General forms of recursion 4.8 Program testing 5 Data types, tuples and lists 5.1 Introducing tuples and lists 5.2 Tuple types 5.3 Introducing algebraic types 5.4 Our approach to lists 5.5 Lists in Haskell 5.6 List comprehensions 5.7 A library database 6 Programming with lists 6.1 Generic functions: polymorphism 6.2 Haskell list functions in the Prelude 6.3 Finding your way around the Haskell libraries 6.4 The Picture example: implementation 6.5 Extended exercise: alternative implementations of pictures 6.6 Extended exercise: positioned pictures 6.7 Extended exercise: supermarket billing 6.8 Extended exercise: cards and card games 7 Defining functions over lists 7.1 Pattern matching revisited 7.2 Lists and list patterns 7.3 Primitive recursion over lists 7.4 Finding primitive recursive definitions 7.5 General recursions over lists 7.6 Example: text processing 8 Playing the game: I/O in Haskell 8.1 Rock - Paper - Scissors: strategies 8.2 Why is I/O an issue? 8.3 The basics of input/output 8.4 The do notation 8.5 Loops and recursion 8.6 Rock - Paper - Scissors: playing the game 9 Reasoning about programs 9.1 Understanding definitions 9.2 Testing and proof 9.3 Definedness, termination and finiteness 9.4 A little logic 9.6 Further examples of proofs by induction 9.7 Generalizing the proof goal 10 Generalization: patterns of computation 10.1 Patterns of computation over lists 10.2 Higher-order functions: functions as arguments 10.3 Folding and primitive recursion 10.4 Generalizing: splitting up lists 10.5 Case studies revisited 11 Higher-order functions 11.1 Operators: function composition and application 11.2 Expressions for functions: lambda abstractions 11.3 Partial application 11.4 Under the hood: curried functions 11.5 Defining higher-order functions 11.6 Verification and general functions 12 Developing higher-order programs 12.1 Revisiting the Picture example 12.2 Functions as data: strategy combinators 12.3 Functions as data: recognising regular expressions 12.4 Case studies: functions as data 12.5 Example: creating an index 12.6 Development in practice 12.7 Understanding programs 13 Overloading, type classes and type checking 13.1 Why overloading? 13.2 Introducing classes 13.3 Signatures and instances 13.4 A tour of the built-in Haskell classes 13.5 Type checking and type inference: an overview 13.6 Monomorphic type checking 13.7 Polymorphic type checking 13.8 Type checking and classes 14 Algebraic types 14.1 Algebraic type definitions revisited 14.2 Recursive algebraic types 14.3 Polymorphic algebraic types 14.4 Modelling program errors 14.5 Design with algebraic data types 14.6 Algebraic types and type classes 14.7 Reasoning about algebraic types 15 Case study: Huffman codes 15.1 Modules in Haskell 15.2 Modular design 15.3 Coding and decoding 15.4 Implementation I 15.5 Building Huffman trees 15.6 Design 15.7 Implementation II 16 Abstract data types 16.1 Type representations 16.2 The Haskell abstract data type mechanism 16.3 Queues 16.4 Design 16.5 Simulation 16.6 Implementing the simulation 16.7 Search trees 16.8 Sets 16.9 Relations and graphs 16.10 Commentary 17 Lazy programming 17.1 Lazy evaluation 17.2 Calculation rules and lazy evaluation 17.3 List comprehensions revisited 17.4 Data-directed programming 17.5 Case study: parsing expressions 17.6 Infinite lists 17.7 Why infinite lists? 17.8 Case study: simulation 17.9 Proof revisited 18 Programming with monads 18.1 I/O programming 18.2 Further I/O 18.3 The calculator 18.4 The do notation revisited 18.5 Monads: languages for functional programming 18.6 Example: monadic computation over trees 19 Domain-Specific Languages 19.1 Programming languages everywhere 19.2 Why DSLs in Haskell? 19.3 Shallow and deep Embeddings 19.4 A DSL for regular expressions 19.5 Monadic DSLs 19.6 DSLs for computation: generating data in QuickCheck 19.7 Taking it further 20 Time and space behaviour 20.1 Complexity of functions 20.2 The complexity of calculations 20.3 Implementations of sets 20.4 Space behaviour 20.5 Folding revisited 20.6 Avoiding recomputation: memoization 21 Conclusion Appendices A Functional, imperative and 00 programming B Glossary C Haskell operators D Haskell practicalities E GHCi errors F Project ideas BibliographyIntroducing functional programming in the Haskell language, this book is written for students and programmers with little or no experience. It emphasises the process of crafting programmes, problem solving and avoiding common programming pitfalls.

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This book is a result of Master of Philosophy (M.Phil.) research at Jawaharlal Nehru University s Special Centre for Sanskrit Studies during 2006-08. A kridanta Analyzer system is not only essential for a larger Sanskrit NL system, but is also helpful for self-reading and understanding of Sanskrit texts. The book consists of four chapters. The first chapter titled Computational Morphology and Sanskrit discussed Sanskrit and computation, Sanskrit morphology, especially derivational morphology and its importance for the kridanta analysis. The second chapter titled Kridanta in Sanskrit Grammar discusses the Paninian system, major characteristic of krt suffixes and kridanta in Hindi grammar. The third chapter titled Kridanta Recognition and Analysis describes the lexical resources for analysis of krt suffixes in Sanskrit according to Paninian formalism. The fourth chapter titled Kridanta Recognizer and Analyzer for Sanskrit explains the partial implementation of the kridanta analysis system. The Kridanta analyzer system introduced in this book is online on computational linguistics website of Special Centre for Sanskrit Studies, JNU

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