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91 results in Engineering mathematics and programming

Page 1 of 5

Elementary Cartesian Tensors

Verification, Validation, and Uncertainty Quantification in Scientific Computing
  • 2nd edition
  • William L. Oberkampf, Christopher J. Roy
  • Published online:
    22 March 2025
    Print publication:
    03 April 2025
  • Can you trust results from modeling and simulation? This text provides a framework for assessing the reliability of and uncertainty included in the results used by decision makers and policy makers in industry and government. The emphasis is on models described by PDEs and their numerical solution. Procedures and results from all aspects of verification and validation are integrated with modern methods in uncertainty quantification and stochastic simulation. Methods for combining numerical approximation errors, uncertainty in model input parameters, and model form uncertainty are presented in order to estimate the uncertain response of a system in the presence of stochastic inputs and lack of knowledge uncertainty. This new edition has been extensively updated, including a fresh look at model accuracy assessment and the responsibilities of management for modeling and simulation activities. Extra homework problems and worked examples have been added to each chapter, suitable for course use or self-study.

Numerical Methods
  • Theory and Engineering Applications
  • Amiya K. Jana
  • Published online:
    31 December 2024
    Print publication:
    24 October 2024
  • Numerical methods are a cornerstone of modern engineering. This lucid textbook strikes a balance between theory and analysis of numerical methods and their practical applications in engineering. Each chapter starts with the formulation and graphical representation of the numerical method. This is followed by the algorithms required to create computer assisted solutions and simulations, which are then applied on real-world examples and case studies to show how exactly they are used. Finally, the strengths and weaknesses of the numerical method under discussion is explained, thus helping the reader choose the best method for a specific problem at hand. Using extensive mathematical problems, illustrative examples and industrially relevant case studies, the book gives the readers physical insights into the ground realities of engineering applications, particularly in areas like heat transfer, fluid mechanics, mass transfer, transport phenomena, and thermodynamics.

Mathematical Methods for Physics
  • An Introduction to Group Theory, Topology and Geometry
  • Esko Keski-Vakkuri, Claus Montonen, Marco Panero
  • Published online:
    08 December 2022
    Print publication:
    22 December 2022
  • This detailed yet accessible text provides an essential introduction to the advanced mathematical methods at the core of theoretical physics. The book steadily develops the key concepts required for an understanding of symmetry principles and topological structures, such as group theory, differentiable manifolds, Riemannian geometry, and Lie algebras. Based on a course for senior undergraduate students of physics, it is written in a clear, pedagogical style and would also be valuable to students in other areas of science and engineering. The material has been subject to more than twenty years of feedback from students, ensuring that explanations and examples are lucid and considered, and numerous worked examples and exercises reinforce key concepts and further strengthen readers' understanding. This text unites a wide variety of important topics that are often scattered across different books, and provides a solid platform for more specialized study or research.

Introduction to Parallel Programming
  • Subodh Kumar
  • Published online:
    27 October 2022
    Print publication:
    05 January 2023
  • In modern computer science, there exists no truly sequential computing system; and most advanced programming is parallel programming. This is particularly evident in modern application domains like scientific computation, data science, machine intelligence, etc. This lucid introductory textbook will be invaluable to students of computer science and technology, acting as a self-contained primer to parallel programming. It takes the reader from introduction to expertise, addressing a broad gamut of issues. It covers different parallel programming styles, describes parallel architecture, includes parallel programming frameworks and techniques, presents algorithmic and analysis techniques and discusses parallel design and performance issues. With its broad coverage, the book can be useful in a wide range of courses; and can also prove useful as a ready reckoner for professionals in the field.

Classical Numerical Analysis
  • A Comprehensive Course
  • Abner J. Salgado, Steven M. Wise
  • Published online:
    29 September 2022
    Print publication:
    20 October 2022
  • Numerical Analysis is a broad field, and coming to grips with all of it may seem like a daunting task. This text provides a thorough and comprehensive exposition of all the topics contained in a classical graduate sequence in numerical analysis. With an emphasis on theory and connections with linear algebra and analysis, the book shows all the rigor of numerical analysis. Its high level and exhaustive coverage will prepare students for research in the field and become a valuable reference as they continue their career. Students will appreciate the simple notation, clear assumptions and arguments, as well as the many examples and classroom-tested exercises ranging from simple verification to qualifying exam-level problems. In addition to the many examples with hand calculations, readers will also be able to translate theory into practical computational codes by running sample MATLAB codes as they try out new concepts.

Introduction to Finite Elements in Engineering
  • 5th edition
  • Tirupathi Chandrupatla, Ashok Belegundu
  • Published online:
    08 November 2021
    Print publication:
    21 October 2021
  • Thoroughly updated with improved pedagogy, the fifth edition of this classic textbook continues to provide students with a clear and comprehensive introduction the fundamentals of the finite element method. New features include enhanced coverage of introductory topics in the context of simple 1D problems, providing students with a solid base from which to advance to 2D and 3D problems; expanded coverage of more advanced concepts, to reinforce students' understanding; over 30 additional solved problems; and downloadable MATLAB, Python, C, Javascript, Fortran and Excel VBA code packages, providing students with hands-on experience, and preparing them for commercial software. Accompanied by online solutions for instructors, this is the definitive text for senior undergraduate and graduate students studying a first course in the finite element method and finite element analysis, and for professional engineers keen to shore up their understanding of finite element fundamentals.

Introduction to Complex Variables and Applications
  • Mark J. Ablowitz, Athanassios S. Fokas
  • Published online:
    18 August 2021
    Print publication:
    25 March 2021
  • The study of complex variables is beautiful from a purely mathematical point of view, and very useful for solving a wide array of problems arising in applications. This introduction to complex variables, suitable as a text for a one-semester course, has been written for undergraduate students in applied mathematics, science, and engineering. Based on the authors' extensive teaching experience, it covers topics of keen interest to these students, including ordinary differential equations, as well as Fourier and Laplace transform methods for solving partial differential equations arising in physical applications. Many worked examples, applications, and exercises are included. With this foundation, students can progress beyond the standard course and explore a range of additional topics, including generalized Cauchy theorem, Painlevé equations, computational methods, and conformal mapping with circular arcs. Advanced topics are labeled with an asterisk and can be included in the syllabus or form the basis for challenging student projects.

Finite Element Method for Solids and Structures
  • A Concise Approach
  • Sung W. Lee, Peter W. Chung
  • Published online:
    08 July 2021
    Print publication:
    17 June 2021
  • This innovative approach to teaching the finite element method blends theoretical, textbook-based learning with practical application using online and video resources. This hybrid teaching package features computational software such as MATLAB®, and tutorials presenting software applications such as PTC Creo Parametric, ANSYS APDL, ANSYS Workbench and SolidWorks, complete with detailed annotations and instructions so students can confidently develop hands-on experience. Suitable for senior undergraduate and graduate level classes, students will transition seamlessly between mathematical models and practical commercial software problems, empowering them to advance from basic differential equations to industry-standard modelling and analysis. Complete with over 120 end-of chapter problems and over 200 illustrations, this accessible reference will equip students with the tools they need to succeed in the workplace.

Matrix, Numerical, and Optimization Methods in Science and Engineering
  • Kevin W. Cassel
  • Published online:
    18 February 2021
    Print publication:
    04 March 2021
  • Address vector and matrix methods necessary in numerical methods and optimization of linear systems in engineering with this unified text. Treats the mathematical models that describe and predict the evolution of our processes and systems, and the numerical methods required to obtain approximate solutions. Explores the dynamical systems theory used to describe and characterize system behaviour, alongside the techniques used to optimize their performance. Integrates and unifies matrix and eigenfunction methods with their applications in numerical and optimization methods. Consolidating, generalizing, and unifying these topics into a single coherent subject, this practical resource is suitable for advanced undergraduate students and graduate students in engineering, physical sciences, and applied mathematics.

Introduction to the Finite Element Method and Implementation with MATLAB®
  • Gang Li
  • Published online:
    09 December 2020
    Print publication:
    30 July 2020
  • Connecting theory with numerical techniques using MATLAB®, this practical textbook equips students with the tools required to solve finite element problems. This hands-on guide covers a wide range of engineering problems through nine well-structured chapters including solid mechanics, heat transfer and fluid dynamics; equilibrium, steady state and transient; and 1-D, 2-D and 3-D problems. Engineering problems are discussed using case study examples, which are solved using a systematic approach, both by examining the steps manually and by implementing a complete MATLAB®code. This topical coverage is supplemented by discourse on meshing with a detailed explanation and implementation of 2-D meshing algorithms. Introducing theory and numerical techniques alongside comprehensive examples this text increases engagement and provides students with the confidence needed to implement their own computer codes to solve given problems.

Competitive Programming in Python
  • 128 Algorithms to Develop your Coding Skills
  • Christoph Dürr, Jill-Jênn Vie
  • Translated by Greg Gibbons, Danièle Gibbons
  • Published online:
    03 December 2020
    Print publication:
    17 December 2020
  • Want to kill it at your job interview in the tech industry? Want to win that coding competition? Learn all the algorithmic techniques and programming skills you need from two experienced coaches, problem setters, and jurors for coding competitions. The authors highlight the versatility of each algorithm by considering a variety of problems and show how to implement algorithms in simple and efficient code. Readers can expect to master 128 algorithms in Python and discover the right way to tackle a problem and quickly implement a solution of low complexity. Classic problems like Dijkstra's shortest path algorithm and Knuth-Morris-Pratt's string matching algorithm are featured alongside lesser known data structures like Fenwick trees and Knuth's dancing links. The book provides a framework to tackle algorithmic problem solving, including: Definition, Complexity, Applications, Algorithm, Key Information, Implementation, Variants, In Practice, and Problems. Python code included in the book and on the companion website.

Finite Elements for Engineers with Ansys Applications
  • Mohamed S. Gadala
  • Published online:
    13 September 2020
    Print publication:
    09 July 2020
  • The finite element method (FEM) is indispensable in modeling and simulation in various engineering and physical systems, including structural analysis, stress, strain, fluid mechanics, heat transfer, dynamics, eigenproblems, design optimization, sound propagation, electromagnetics, and coupled field problems. This textbook integrates basic theory with real-life, design-oriented problems using ANSYS, the most commonly used computational software in the field. For students as well as practicing engineers and designers, each chapter is highly illustrated and presented in a step-by-step manner. Fundamental concepts are presented in detail with reference to easy to understand worked examples that clearly introduce the method before progressing to more advanced content. Included are step-by-step solutions for project type problems using modelling software, special chapters for modelling and the use of ANSYS and Workbench programs, and extensive sets of problems and projects round out each chapter.

Essential Mathematics for Engineers and Scientists
  • Thomas J. Pence, Indrek S. Wichman
  • Published online:
    30 April 2020
    Print publication:
    21 May 2020
  • This text is geared toward students who have an undergraduate degree or extensive coursework in engineering or the physical sciences and who wish to develop their understanding of the essential topics of applied mathematics. The methods covered in the chapters form the core of analysis in engineering and the physical sciences. Readers will learn the solutions, techniques, and approaches that they will use as academic researchers or industrial R&D specialists. For example, they will be able to understand the fundamentals behind the various scientific software packages that are used to solve technical problems (such as the equations describing the solid mechanics of complex structures or the fluid mechanics of short-term weather prediction and long-term climate change), which is crucial to working with such codes successfully. Detailed and numerous worked problems help to ensure a clear and well-paced introduction to applied mathematics. Computational challenge problems at the end of each chapter provide students with the opportunity for hands-on learning and help to ensure mastery of the concepts. Adaptable to one- and two-semester courses.

Modern Mathematical Methods for Physicists and Engineers
  • C. D. Cantrell
  • Published online:
    14 September 2019
    Print publication:
    09 October 2000
  • The advent of powerful desktop computers has revolutionized scientific analysis and engineering design in fields as disparate as particle physics and telecommunications. Modern Mathematical Methods for Physicists and Engineers provides a mathematical and computational education for students, researchers, and practising engineers. The author begins with a review of computation, and then deals with a range of key concepts including sets, fields, matrix theory, and vector spaces. He then goes on to cover more advanced subjects such as linear mappings, group theory, and special functions. In this way, he concentrates exclusively on the most important topics for the working physical scientist or engineer with the aim of helping them to make intelligent use of the latest computational and analytical methods. The book contains well over 400 homework problems and covers many topics not dealt with in other textbooks. It will be ideal for senior undergraduate and graduate students in the physical sciences and engineering, as well as a valuable reference for working engineers.

Introduction to Applied Linear Algebra
  • Vectors, Matrices, and Least Squares
  • Stephen Boyd, Lieven Vandenberghe
  • Published online:
    13 September 2019
    Print publication:
    07 June 2018
  • This groundbreaking textbook combines straightforward explanations with a wealth of practical examples to offer an innovative approach to teaching linear algebra. Requiring no prior knowledge of the subject, it covers the aspects of linear algebra - vectors, matrices, and least squares - that are needed for engineering applications, discussing examples across data science, machine learning and artificial intelligence, signal and image processing, tomography, navigation, control, and finance. The numerous practical exercises throughout allow students to test their understanding and translate their knowledge into solving real-world problems, with lecture slides, additional computational exercises in Julia and MATLAB®, and data sets accompanying the book online. Suitable for both one-semester and one-quarter courses, as well as self-study, this self-contained text provides beginning students with the foundation they need to progress to more advanced study.

Optimization Concepts and Applications in Engineering
  • 3rd edition
  • Ashok D. Belegundu, Tirupathi R. Chandrupatla
  • Published online:
    31 May 2019
    Print publication:
    06 June 2019
  • Organizations and businesses strive toward excellence, and solutions to problems are based mostly on judgment and experience. However, increased competition and consumer demands require that the solutions be optimum and not just feasible. Theory leads to algorithms. Algorithms need to be translated into computer codes. Engineering problems need to be modeled. Optimum solutions are obtained using theory and computers, and then interpreted. Revised and expanded in its third edition, this textbook integrates theory, modeling, development of numerical methods, and problem solving, thus preparing students to apply optimization to real-world problems. This text covers a broad variety of optimization problems using: unconstrained, constrained, gradient, and non-gradient techniques; duality concepts; multi-objective optimization; linear, integer, geometric, and dynamic programming with applications; and finite element-based optimization. It is ideal for advanced undergraduate or graduate courses in optimization design and for practicing engineers.

Numerical Methods
  • Fundamentals and Applications
  • Rajesh Kumar Gupta
  • Published online:
    26 April 2019
    Print publication:
    09 May 2019
  • Written in an easy-to-understand manner, this comprehensive textbook brings together both basic and advanced concepts of numerical methods in a single volume. Important topics including error analysis, nonlinear equations, systems of linear equations, interpolation and interpolation for Equal intervals and bivariate interpolation are discussed comprehensively. The textbook is written to cater to the needs of undergraduate students of mathematics, computer science, mechanical engineering, civil engineering and information technology for a course on numerical methods/numerical analysis. The text simplifies the understanding of the concepts through exercises and practical examples. Pedagogical features including solved examples and unsolved exercises are interspersed throughout the book for better understanding.

Numerical Methods with Chemical Engineering Applications
  • Kevin D. Dorfman, Prodromos Daoutidis
  • Published online:
    09 August 2018
    Print publication:
    11 January 2017
  • Designed primarily for undergraduates, but also graduates and practitioners, this textbook integrates numerical methods and programming with applications from chemical engineering. Combining mathematical rigor with an informal writing style, it thoroughly introduces the theory underlying numerical methods, its translation into MATLAB programs, and its use for solving realistic problems. Specific topics covered include accuracy, convergence and numerical stability, as well as stiffness and ill-conditioning. MATLAB codes are developed from scratch, and their implementation is explained in detail, all while assuming limited programming knowledge. All scripts employed are downloadable, and built-in MATLAB functions are discussed and contextualised. Numerous examples and homework problems - from simple questions to extended case studies - accompany the text, allowing students to develop a deep appreciation for the range of real chemical engineering problems that can be solved using numerical methods. This is the ideal resource for a single-semester course on numerical methods, as well as other chemical engineering courses taught over multiple semesters.

Linear Algebra
  • Elizabeth S. Meckes, Mark W. Meckes
  • Published online:
    21 June 2018
    Print publication:
    24 May 2018
  • Linear Algebra offers a unified treatment of both matrix-oriented and theoretical approaches to the course, which will be useful for classes with a mix of mathematics, physics, engineering, and computer science students. Major topics include singular value decomposition, the spectral theorem, linear systems of equations, vector spaces, linear maps, matrices, eigenvalues and eigenvectors, linear independence, bases, coordinates, dimension, matrix factorizations, inner products, norms, and determinants.

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