tag:open.umn.edu,2005:/opentextbooks/subjects/analysisOpen Textbook Library - Analysis Textbooks2023-01-25T13:37:42Zhttps://open.umn.edu/assets/common/favicon/favicon-1594c2156c95ca22b1a0d803d547e5892bb0e351f682be842d64927ecda092e7.icohttps://open.umn.edu/assets/library/otl_logo-f9161d5c999f5852b38260727d49b4e7d7142fc707ec9596a5256a778f957ffc.png13202023-01-25T13:37:42Z2024-01-22T14:52:38ZBasic Engineering Data Collection and Analysis<img alt="Read more about Basic Engineering Data Collection and Analysis" title="Basic Engineering Data Collection and Analysis cover image" class="cover " width="237" height="314" data-controller="cover" data-placeholder="/assets/common/placeholder-0e0607cbc50663ddb9e8fd188058bcd2630c730ef6ee322801278607b7d5af8e.png" src="/rails/active_storage/blobs/redirect/eyJfcmFpbHMiOnsiZGF0YSI6NDQ3OCwicHVyIjoiYmxvYl9pZCJ9fQ==--103735f76df76607eb0c037930ccb67f4669827b/Screen%20Shot%202023-01-25%20at%207.37.27%20AM.png" />In Basic Engineering Data Collection and Analysis, Stephen B. Vardeman and J. Marcus Jobe stress the practical over the theoretical. Step by step, students get real engineering data and scenario examples along with chapter-long case studies that illustrate concepts in realistic, thoroughly detailed situations. This approach encourages students to work through the material by carrying out data collection and analysis projects from problem formulation through the preparation of professional technical reports—just as if they were on the job.12432022-09-01T17:40:40Z2024-01-22T14:52:34ZThe Art of Polynomial Interpolation<img alt="Read more about The Art of Polynomial Interpolation" title="The Art of Polynomial Interpolation cover image" class="cover " width="768" height="1024" data-controller="cover" data-placeholder="/assets/common/placeholder-0e0607cbc50663ddb9e8fd188058bcd2630c730ef6ee322801278607b7d5af8e.png" src="/rails/active_storage/blobs/redirect/eyJfcmFpbHMiOnsiZGF0YSI6Mzk2OSwicHVyIjoiYmxvYl9pZCJ9fQ==--9f6157517a122f2bdea622d3b3957af7155069b0/The-Art-of-Polynomial-Interpolation_SMurphy_Cover-2-1-768x1024.png" />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.9252020-10-19T02:09:50Z2024-01-22T19:04:03ZFirst Semester in Numerical Analysis with Python<img alt="Read more about First Semester in Numerical Analysis with Python" title="First Semester in Numerical Analysis with Python cover image" class="cover " width="611" height="678" data-controller="cover" data-placeholder="/assets/common/placeholder-0e0607cbc50663ddb9e8fd188058bcd2630c730ef6ee322801278607b7d5af8e.png" src="/rails/active_storage/blobs/redirect/eyJfcmFpbHMiOnsiZGF0YSI6MTY1MywicHVyIjoiYmxvYl9pZCJ9fQ==--5c62bc2558ad896ff74a1077a2bebdfa5eef586a/Numerical%20analysis.PNG" />The book is based on “First semester in Numerical Analysis with Julia”, written by Giray Ökten. The contents of the original book are retained, while all the algorithms are implemented in Python (Version 3.8.0). Python is an open source (under OSI), interpreted, general-purpose programming language that has a large number of users around the world. Python is ranked the third in August 2020 by the TIOBE programming community index, a measure of popularity of programming languages, and is the top-ranked interpreted language. We hope this book will better serve readers who are interested in a first course in Numerical Analysis, but are more familiar with Python for the implementation of the algorithms. The first chapter of the book has a self-contained tutorial for Python, including how to set up the computer environment. Anaconda, the open-source individual edition, is recommended for an easy installation of Python and effortless management of Python packages, and the Jupyter environment, a web-based interactive development environment for Python as well as many other programming languages, was used throughout the book and is recommended to the readers for easy code development, graph visualization and reproducibility.7102019-05-15T23:37:43Z2024-03-05T02:11:42ZFirst Semester in Numerical Analysis with Julia<img alt="Read more about First Semester in Numerical Analysis with Julia" title="First Semester in Numerical Analysis with Julia cover image" class="cover " width="155" height="200" data-controller="cover" data-placeholder="/assets/common/placeholder-0e0607cbc50663ddb9e8fd188058bcd2630c730ef6ee322801278607b7d5af8e.png" src="/rails/active_storage/blobs/redirect/eyJfcmFpbHMiOnsiZGF0YSI6NjU2LCJwdXIiOiJibG9iX2lkIn19--ad942b5e610404311068b8a80f91f2b196c098d3/0000FSNumAnJu.jpg" />First Semester in Numerical Analysis with Julia presents the theory and methods, together with the implementation of the algorithms using the Julia programming language (version 1.1.0). The book covers computer arithmetic, root-finding, numerical quadrature and differentiation, and approximation theory. The reader is expected to have studied calculus and linear algebra. Some familiarity with a programming language is beneficial, but not required. The programming language Julia will be introduced in the book. The simplicity of Julia allows bypassing the pseudocode and writing a computer code directly after the description of a method while minimizing the distraction the presentation of a computer code might cause to the flow of the main narrative.4632018-09-07T17:22:03Z2024-01-22T14:51:56ZA Primer of Real Analysis<img alt="Read more about A Primer of Real Analysis" title="A Primer of Real Analysis cover image" class="cover " width="825" height="839" data-controller="cover" data-placeholder="/assets/common/placeholder-0e0607cbc50663ddb9e8fd188058bcd2630c730ef6ee322801278607b7d5af8e.png" src="/rails/active_storage/blobs/redirect/eyJfcmFpbHMiOnsiZGF0YSI6MzkxLCJwdXIiOiJibG9iX2lkIn19--864c61adae81eab2962f3b4d6c0f8f391a65765f/0000PriReaAna.png" />This is a short introduction to the fundamentals of real analysis. Although the prerequisites are few, I have written the text assuming the reader has the level of mathematical maturity of one who has completed the standard sequence of calculus courses, has had some exposure to the ideas of mathematical proof (including induction), and has an acquaintance with such basic ideas as equivalence relations and the elementary algebraic properties of the integers.2432018-09-07T17:21:50Z2024-01-22T14:51:57ZIntroduction to Mathematical Analysis I - Second Edition<img alt="Read more about Introduction to Mathematical Analysis I - Second Edition" title="Introduction to Mathematical Analysis I - Second Edition cover image" class="cover " width="1237" height="1620" data-controller="cover" data-placeholder="/assets/common/placeholder-0e0607cbc50663ddb9e8fd188058bcd2630c730ef6ee322801278607b7d5af8e.png" src="/rails/active_storage/blobs/redirect/eyJfcmFpbHMiOnsiZGF0YSI6MTk2LCJwdXIiOiJibG9iX2lkIn19--e9dad07c48820fcbdc9ea1dee74f7a9bf85672e7/9781365605529.png" />Our goal with this textbook is to provide students with a strong foundation in mathematical analysis. Such a foundation is crucial for future study of deeper topics of analysis. Students should be familiar with most of the concepts presented here after completing the calculus sequence. However, these concepts will be reinforced through rigorous proofs. The lecture notes contain topics of real analysis usually covered in a 10-week course: the completeness axiom, sequences and convergence, continuity, and differentiation. The lecture notes also contain many well-selected exercises of various levels. Although these topics are written in a more abstract way compared with those available in some textbooks, teachers can choose to simplify them depending on the background of the students. For instance, rather than introducing the topology of the real line to students, related topological concepts can be replaced by more familiar concepts such as open and closed intervals. Some other topics such as lower and upper semicontinuity, differentiation of convex functions, and generalized differentiation of non-differentiable convex functions can be used as optional mathematical projects. In this way, the lecture notes are suitable for teaching students of different backgrounds. The second edition includes a number of improvements based on recommendations from students and colleagues and on our own experience teaching the course over the last several years. In this edition we streamlined the narrative in several sections, added more proofs, many examples worked out in detail, and numerous new exercises. In all we added over 50 examples in the main text and 100 exercises (counting parts).1742018-09-07T17:21:47Z2024-01-22T14:52:22ZIntroduction to Real Analysis<img alt="Read more about Introduction to Real Analysis" title="Introduction to Real Analysis cover image" class="cover " width="107" height="150" data-controller="cover" data-placeholder="/assets/common/placeholder-0e0607cbc50663ddb9e8fd188058bcd2630c730ef6ee322801278607b7d5af8e.png" src="/rails/active_storage/blobs/redirect/eyJfcmFpbHMiOnsiZGF0YSI6MTk1NSwicHVyIjoiYmxvYl9pZCJ9fQ==--98acb3888fda07e56eadb9dd9e78494256450598/thumbnail.jpg" />This is a text for a two-term course in introductory real analysis for junior or senior mathematics majors and science students with a serious interest in mathematics. Prospective educators or mathematically gifted high school students can also benefit from the mathematical maturity that can be gained from an introductory real analysis course. The book is designed to fill the gaps left in the development of calculus as it is usually presented in an elementary course, and to provide the background required for insight into more advanced courses in pure and applied mathematics. The standard elementary calculus sequence is the only specific prerequisite for Chapters 1–5, which deal with real-valued functions. (However, other analysis oriented courses, such as elementary differential equation, also provide useful preparatory experience.) Chapters 6 and 7 require a working knowledge of determinants, matrices and linear transformations, typically available from a first course in linear algebra. Chapter 8 is accessible after completion of Chapters 1–5.952018-09-07T17:21:43Z2024-01-22T14:52:16ZBasic Analysis: Introduction to Real Analysis<img alt="Read more about Basic Analysis: Introduction to Real Analysis" title="Basic Analysis: Introduction to Real Analysis cover image" class="cover " width="240" height="312" data-controller="cover" data-placeholder="/assets/common/placeholder-0e0607cbc50663ddb9e8fd188058bcd2630c730ef6ee322801278607b7d5af8e.png" src="/rails/active_storage/blobs/redirect/eyJfcmFpbHMiOnsiZGF0YSI6MTkwNiwicHVyIjoiYmxvYl9pZCJ9fQ==--2dfd4d3adf8acebec7c76f0104ce83cab8fa5292/0000BasicAnal.png" />This free online textbook (e-book in webspeak) is a one semester course in basic analysis. This book started its life as my lecture notes for Math 444 at the University of Illinois at Urbana-Champaign (UIUC) in the fall semester of 2009, and was later enhanced to teach Math 521 at University of Wisconsin-Madison (UW-Madison). A prerequisite for the course is a basic proof course. It should be possible to use the book for both a basic course for students who do not necessarily wish to go to graduate school, but also as a first semester of a more advanced course that also covers topics such as metric spaces.