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Classical Numerical Methods in Scientific Computing
Jos van Kan; Guus Segal; Fred Vermolen; Hans Kraaijevanger · TU Delft Open · 2023
Partial differential equations are paramount in mathematical modelling with applications in engineering and science. The book starts with a crash course on partial differential equations in order to familiarize the reader with fundamental properties such as existence, uniqueness and possibly existing maximum principles. The main topic of the book entails the description of classical numerical methods that are used to approximate the solution of partial differential equations. The focus is on discretization methods such as the finite difference, finite volume and finite element method. The manuscript also makes a short excursion to the solution of large sets of (non)linear algebraic equations that result after application of discretization method to partial differential equations. The book treats the construction of such discretization methods, as well as some error analysis, where it is noted that the error analysis for the finite element method is merely descriptive, rather than rigorous from a mathematical point of view. The last chapters focus on time integration issues for classical time-dependent partial differential equations. After reading the book, the reader should be able to derive finite element methods, to implement the methods and to judge whether the obtained approximations are consistent with the solution to the partial differential equations. The reader will also obtain these skills for the other classical discretization methods. Acquiring such fundamental knowledge will allow the reader to continue studying more advanced methods like meshfree methods, discontinuous Galerkin methods and spectral methods for the approximation of solutions to partial differential equations.
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COMPUTATIONAL PHYSICS: A Practical Introduction to Computational Physics and Scientific Computing (using C++)
Konstantinosn Anagnostopoulos · National Technical University of Athens · 2016
This book is an introduction to the computational methods used in physics, but also in other scientific fields. It is addressed to an audience that has already been exposed to the introductory level of college physics, usually taught during the first two years of an undergraduate program in science and engineering. It assumes no prior knowledge of numerical analysis, programming or computers and teaches whatever is necessary for the solution of the problems addressed in the text. It can be used as a textbook in introductory computational physics or scientific computing classes. The book starts with very simple problems in particle motion and ends with an in-depth discussion of advanced techniques used in Monte Carlo simulations in statistical mechanics. The level of instruction rises slowly, while discussing problems like the diffusion equation, electrostatics on the plane, quantum mechanics and random walks. All the material can be taught in two semesters, but a selection of topics can form the material of a one semester course. The book aims to provide the students with the background and the experience needed in order to advance to high performance computing projects in science and engineering. It puts emphasis on hands--on programming of numerical code but also on the production, analysis and interpretation of data. But it also tries to keep the students motivated by considering interesting applications in physics, like chaos, quantum mechanics, special relativity and the physics of phase transitions. There is a C++ and a Fortran edition for the core programming. Data analysis is performed using the powerful tools of the GNU/Linux environment. All the necessary software is open source and freely available. The book and the accompanying software are given under a Creative Commons License/GNU public License as a service to the community. It can be used freely as a whole, or any part of it, in any form, by anyone. There is no official distribution of hard copies, b
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The Art of Polynomial Interpolation
Stuart Murphy · Pennsylvania State University
The inspiration for this text grew out of a simple question that emerged over a number of years of teaching math to Middle School, High School and College students. Practically speaking, what is the origin of a particular polynomial? So much time is spent analyzing, factoring, simplifying and graphing polynomials that it is easy to lose sight of the fact that polynomials have a wealth of practical uses. Exploring the techniques of interpolating data allows us to view the development and birth of a polynomial. This text is focused on laying a foundation for understanding and applying several common forms of polynomial interpolation. The principal goals of the text are: Breakdown the process of developing polynomials to demonstrate and give the student a feel for the process and meaning of developing estimates of the trend (s) a collection of data may represent. Introduce basic matrix algebra to assist students with understanding the process without getting bogged down in purely manual calculations. Some manual calculations have been included, however, to assist with understanding the concept. Assist students in building a basic foundation allowing them to add additional techniques, of which there are many, not covered in this text.
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Learning Statistics with R: A tutorial for psychology students and other beginners
Danielle Navarro · Danielle Navarro · 2018
Learning Statistics with R covers the contents of an introductory statistics class, as typically taught to undergraduate psychology students, focusing on the use of the R statistical software. The book discusses how to get started in R as well as giving an introduction to data manipulation and writing scripts. From a statistical perspective, the book discusses descriptive statistics and graphing first, followed by chapters on probability theory, sampling and estimation, and null hypothesis testing. After introducing the theory, the book covers the analysis of contingency tables, t-tests, ANOVAs and regression. Bayesian statistics are covered at the end of the book.
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Introduction to Modern Statistics
Mine Çetinkaya-Rundel; Jo Hardin · OpenIntro · 2024
Introduction to Modern Statistics is a re-imagining of a previous title, Introduction to Statistics with Randomization and Simulation. The new book puts a heavy emphasis on exploratory data analysis (specifically exploring multivariate relationships using visualization, summarization, and descriptive models) and provides a thorough discussion of simulation-based inference using randomization and bootstrapping, followed by a presentation of the related Central Limit Theorem based approaches. The second edition of IMS has updated datasets, additional exercises, a new application for chapter 3, and updated text and code to reflect changes in best practices. You can access the full PDF by clicking the Read Free Sample button at the PDF link.
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Yet Another Calculus Text
Dan Sloughter · Dan Sloughter · 2007
I intend this book to be, firstly, a introduction to calculus based on the hyperrealnumber system. In other words, I will use infinitesimal and infinite numbers freely. Just as most beginning calculus books provide no logical justification for the real number system, I will provide none for the hyperreals. The reader interested in questions of foundations should consult books such asAbraham Robinson's Non-standard Analysis or Robert Goldblatt's Lectures onthe Hyperreals. Secondly, I have aimed the text primarily at readers who already have somefamiliarity with calculus. Although the book does not explicitly assume any prerequisites beyond basic algebra and trigonometry, in practice the pace istoo fast for most of those without some acquaintance with the basic notions of calculus.
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Introductory Business Statistics
Thomas Tiemann · BCcampus · 2010
The book "Introductory Business Statistics" by Thomas K. Tiemann explores the basic ideas behind statistics, such as populations, samples, the difference between data and information, and most importantly sampling distributions. The author covers topics including descriptive statistics and frequency distributions, normal and t-distributions, hypothesis testing, t-tests, f-tests, analysis of variance, non-parametric tests, and regression basics. Using real-world examples throughout the text, the author hopes to help students understand how statistics works, not just how to "get the right number."
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Applied Probability
Paul Pfeiffer · OpenStax CNX · 2009
This is a "first course" in the sense that it presumes no previous course in probability. The mathematical prerequisites are ordinary calculus and the elements of matrix algebra. A few standard series and integrals are used, and double integrals are evaluated as iterated integrals. The reader who can evaluate simple integrals can learn quickly from the examples how to deal with the iterated integrals used in the theory of expectation and conditional expectation. Appendix B provides a convenient compendium of mathematical facts used frequently in this work. And the symbolic toolbox, implementing MAPLE, may be used to evaluate integrals, if desired. In addition to an introduction to the essential features of basic probability in terms of a precise mathematical model, the work describes and employs user defined MATLAB procedures and functions (which we refer to as m-programs, or simply programs) to solve many important problems in basic probability. This should make the work useful as a stand-alone exposition as well as a supplement to any of several current textbooks. Most of the programs developed here were written in earlier versions of MATLAB, but have been revised slightly to make them quite compatible with MATLAB 7. In a few cases, alternate implementations are available in the Statistics Toolbox, but are implemented here directly from the basic MATLAB program, so that students need only that program (and the symbolic mathematics toolbox, if they desire its aid in evaluating integrals). Since machine methods require precise formulation of problems in appropriate mathematical form, it is necessary to provide some supplementary analytical material, principally the so-called minterm analysis. This material is not only important for computational purposes, but is also useful in displaying some of the structure of the relationships among events.
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Mathematical Reasoning: Writing and Proof, Version 2.1
Ted Sundstrom · Grand Valley State University · 2014
Mathematical Reasoning: Writing and Proofis designed to be a text for the ?rst course in the college mathematics curriculum that introduces students to the processes of constructing and writing proofs and focuses on the formal development of mathematics. The primary goals of the text are to help students: Develop logical thinking skills and to develop the ability to think more abstractly in a proof oriented setting. Develop the ability to construct and write mathematical proofs using standard methods of mathematical proof including direct proofs, proof by contradiction, mathematical induction, case analysis, and counterexamples. Develop the ability to read and understand written mathematical proofs. Develop talents for creative thinking and problem solving. Improve their quality of communication in mathematics. This includes improving writing techniques, reading comprehension, and oral communication in mathematics. Better understand the nature of mathematics and its language. This text also provides students with material that will be needed for their further study of mathematics.
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Linear Algebra, Theory And Applications
Kenneth Kuttler · Saylor Foundation · 2012
This is a book on linear algebra and matrix theory. While it is self contained, it will work best for those who have already had some exposure to linear algebra. It is also assumed that the reader has had calculus. Some optional topics require more analysis than this, however. This book features an ugly, elementary, and complete treatment of determinants early in the book. Thus it might be considered as Linear algebra done wrong. I have done this because of the usefulness of determinants. However, all major topics are also presented in an alternative manner which is independent of determinants. The book has an introduction to various numerical methods used in linear algebra. This is done because of the interesting nature of these methods. The presentation here emphasizes the reasons why they work. It does not discuss many important numerical considerations necessary to use the methods effectively. These considerations are found in numerical analysis texts.
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Becoming a Climate Conscious Lawyer: Climate and the Australian Legal System
Anna Huggins; Ellen Hawkins; Steven Tudor; Nicole Rogers · La Trobe University · 2024
As the world grapples with the escalating challenges of climate change, the legal profession finds itself at a crossroads. Becoming a Climate Conscious Lawyer: Climate and the Australian Legal System provides an original, innovative, and accessible analysis of the impact of climate change on legal doctrines and principles. It offers an overview of cutting-edge developments and how the transition to a low-carbon society is reshaping a wide range of laws, from corporate to criminal law, and beyond. This valuable new resource supports legal professionals, law students, and legal educators to understand current legal challenges – providing the know-how to strategically navigate, and positively influence, the development of law to respond to a climate changed world. The book delivers a transformative approach to legal education: equipping law students to become climate-conscious professionals with the confidence and competency to deliver legal solutions to a diverse range of clients, and promote climate justice across diverse communities.
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Legal Writing I & II: Legal Research and Writing & Introduction to Litigation Practice
Ben Fernandez · Ben Fernandez · 2020
Legal Writing I & II; Legal Research and Writing & Introduction to Litigation Practice contains a brief discussion of all of the topics covered in a law school courses on legal writing, including a typical first semester course on legal research, analysis and writing an objective memorandum, as well as a second semester course on persuasion and writing an appellate brief, motion to dismiss or motion for summary judgment. The discussion focuses on the basics of analogical reasoning and persuasion and leaves out the minutiae. Each topic is taken one step at a time, with each step building on the step before it. The sources of law are presented first, then legal research, and reading and analyzing cases and statutes. The book covers analogizing a case to a fact pattern and marshaling the relevant facts to the elements of a statutory rule next. And then first section of the book concludes with legal citation, CRAC and CREAC, and writing a legal research memorandum. The text also includes a lot of samples and examples of how the author would write a case brief, a legal memoranda and an appellate brief, as well as an appendix with charts, outlines and exercises students can use to practice these skills. Legal Writing I & II; Legal Research and Writing & Introduction to Litigation Practice covers all the skills students need to know to work at a law firm, and everything students have to learn to begin practicing in litigation department of a firm.
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Sales and Leases: A Problem-based Approach
Scott Burnham; Kristen Juras · CALI's eLangdell® Press · 2023
Sales and Leases is a coursebook for a 3-credit course in personal property sales and leases – the subject matter of UCC Articles 2 and 2A. Adjustments could be made for other credit allocations and chapters can be used on a stand-alone basis. The course is designed so that students both review the rules and principles they studied in their first-year course in Contracts and learn the rules that apply to the subset of contracts for the sale and lease of goods. Students taking this course should be well-prepared to solve legal problems in contracts and sales, and should be well-prepared for those parts of the bar exam as well. While the course in Contracts focuses on the rules of common-law contracts, the focus of this course is the rules found in legislation. Therefore, instead of emphasizing case analysis, the book contains a good deal of narrative that assists students in working through the complexity of the statutes. Students will need to supplement the book with a complete copy of the UCC that includes the Official Comments. Discussion of other statutes, such as UETA and Magnuson-Moss, is incorporated where appropriate. The approach is problem-based, which we believe is more appropriate for an upper-division course based primarily on statutes. The narrative is interspersed with problems for class discussion that require students to apply the principles and rules to particular fact situations. Many times there is an issue of interpretation or policy in the Code, however, and therefore each chapter also contains at least one case that explores an issue arising under the statute.
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Contract Doctrine, Theory & Practice
J.H. Verkerke · CALI's eLangdell® Press · 2012
This is Volume 3 in a three volume series written for Contracts Law. Its former title is "Collaborative Teaching Materials for Contracts." The first semester of law school is mostly about learning to speak a new legal language (but emphatically not “legalese”), to formulate and evaluate legal arguments, to become comfortable with the distinctive style of legal analysis. We could teach these skills using almost any legal topic. But we begin the first-year curriculum with subjects that pervade the entire field of law. Contract principles have a long history and they form a significant part of the way that lawyers think about many legal problems. As you will discover when you study insurance law, employment law, family law, and dozens of other practice areas, your knowledge of contract doctrine and theory will be invaluable.
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University Academic Writing for International Students: A Usage-based Approach
Carol Lynn Moder; Alys Avalos-Rivera; Ho'omana Nathan Horton; Miriam Kinfe · Oklahoma State University · 2020
This resource is designed specifically to meet the academic writing needs of international students studying at universities in the United States. The materials in the book can be covered within a 14-week semester, but each chapter or section may also be used independently. Based on a series of needs analysis projects, this resource provides an overview of major rhetorical patterns of writing that are commonly used in university settings in the United States. These commonly required genres include descriptive and evaluative summaries, short essays, comparison and contrast assignments, literature reviews, descriptive reports, and proposals. The resource includes chapters that address the structure and purpose of these more common genres, including an awareness of the ways that the target audience and situation should shape the writing of each.
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Technical Writing Essentials: Introduction to Professional Communications in the Technical Fields
Suzan Last · University of Victoria · 2019
This open textbook is designed to introduce readers to the basics of technical communication: audience and task analysis in workplace contexts, clear and concise communications style, effective document design, teamwork and collaboration, and fundamental research skills.
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Messages that Matter: Public Speaking in the Information Age
Josh Misner; Geoff Carr · North Idaho College · 2023
Messages that Matter: Public Speaking in the Information Age is a student-focused textbook that provides practical and real-world instruction in the art of public speaking, with a focus on how speakers can learn to communicate with diverse audiences to achieve their primary goal of being understood as intended. Using an audience-centered approach, Messages that Matter provides instruction on: audience analysis, overcoming speaker anxiety, research techniques for speakers, how to practice and refine delivery, persuasion techniques, and group presentation fundamentals.
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Introduction to Communication and Media Studies
J.J. Sylvia IV · ROTEL · 2024
Introduction to Communication and Media Studies is an in-depth exploration of how communication shapes our world. This book traces the historical evolution of media, from the early days of the printing press to today’s digital age, examining key developments such as the telegraph, radio, television, and the internet. It also covers critical theories that explain media’s impact on society, including the effects of advertising, the role of public relations, and the emergence of social media as a powerful force in modern communication. Chapters on media literacy, critical thinking, and rhetorical analysis help students develop critical skills for understanding and analyzing media messages.
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Studying the Bible: The Tanakh and Early Christian Writings
Gregory Eiselein; Anna Goins; Naomi Wood · New Prairie Press · 2019
Studying the Bible: The Tanakh and Early Christian Writings is a university-level, textbook introduction to the study of the Bible, its literary forms, and historical and cultural contexts. This textbook is a companion to the Bible courses taught in the English Department at Kansas State University, in particular ENGL 470 The Bible, though it is available for use in other courses and contexts. This textbook examines the Hebrew Bible (also known as the Tanakh) and the early Christian writings of the New Testament. It is an introduction to the analysis of biblical texts, their histories, and their interpretations. The emphasis throughout this textbook is on the literary qualities of these biblical texts as well as their cultural and historical contexts.
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Metaethics from a First Person Standpoint: An Introduction to Moral Philosophy
Catherine Wilson · Open Book Publishers · 2016
Metaethics from a First Person Standpoint addresses in a novel format the major topics and themes of contemporary metaethics, the study of the analysis of moral thought and judgement. Metathetics is less concerned with what practices are right or wrong than with what we mean by ‘right’ and ‘wrong.’ Looking at a wide spectrum of topics including moral language, realism and anti-realism, reasons and motives, relativism, and moral progress, this book engages students and general readers in order to enhance their understanding of morality and moral discourse as cultural practices. Catherine Wilson innovatively employs a first-person narrator to report step-by-step an individual’s reflections, beginning from a position of radical scepticism, on the possibility of objective moral knowledge. The reader is invited to follow along with this reasoning, and to challenge or agree with each major point. Incrementally, the narrator is led to certain definite conclusions about ‘oughts’ and norms in connection with self-interest, prudence, social norms, and finally morality. Scepticism is overcome, and the narrator arrives at a good understanding of how moral knowledge and moral progress are possible, though frequently long in coming.Accessibly written, Metaethics from a First Person Standpoint presupposes no prior training in philosophy and is a must-read for philosophers, students and general readers interested in gaining a better understanding of morality as a personal philosophical quest.