tag:open.umn.edu,2005:/opentextbooks/subjects/mathematics?page=2Open Textbook Library - Mathematics Textbooks2023-09-28T22:02:32Zhttps://open.umn.edu/assets/common/favicon/favicon-1594c2156c95ca22b1a0d803d547e5892bb0e351f682be842d64927ecda092e7.icohttps://open.umn.edu/assets/library/otl_logo-f9161d5c999f5852b38260727d49b4e7d7142fc707ec9596a5256a778f957ffc.png14952023-09-28T22:10:35Z2024-01-22T15:05:54ZNumerical Methods in Scientific Computing<img alt="Read more about Numerical Methods in Scientific Computing" title="Numerical Methods in Scientific Computing cover image" class="cover " width="300" height="370" data-controller="common--cover" data-placeholder="/assets/common/placeholder-0e0607cbc50663ddb9e8fd188058bcd2630c730ef6ee322801278607b7d5af8e.png" src="/rails/active_storage/blobs/redirect/eyJfcmFpbHMiOnsiZGF0YSI6OTU4NSwicHVyIjoiYmxvYl9pZCJ9fQ==--4252392e602cdff5e054f9e09f20c2fca0f75246/submission_70_87_coverImage_en_US_t.png" />This is a book about numerically solving partial differential equations occurring in technical and physical contexts and the authors have set themselves a more ambitious target than to just talk about the numerics. Their aim is to show the place of numerical solutions in the general modeling process and this must inevitably lead to considerations about modeling itself. Partial differential equations usually are a consequence of applying first principles to a technical or physical problem at hand. That means, that most of the time the physics also have to be taken into account especially for validation of the numerical solution obtained. This book aims especially at engineers and scientists who have ’real world’ problems. It will concern itself less with pesky mathematical detail. For the interested reader though, we have included sections on mathematical theory to provide the necessary mathematical background. Since this treatment had to be on the superficial side we have provided further reference to the literature where necessary.10162023-09-01T00:00:00Z2024-01-14T06:56:03ZLinear Transformations on Vector Spaces<img alt="Read more about Linear Transformations on Vector Spaces" title="Linear Transformations on Vector Spaces cover image" class="cover " width="750" height="971" data-controller="common--cover" data-placeholder="/assets/common/placeholder-0e0607cbc50663ddb9e8fd188058bcd2630c730ef6ee322801278607b7d5af8e.png" src="/rails/active_storage/blobs/redirect/eyJfcmFpbHMiOnsiZGF0YSI6OTMxOCwicHVyIjoiYmxvYl9pZCJ9fQ==--430d90255dce93bf4772ad756327ee0baf94269f/Linear%20Transformations%20resized.png" />Linear Transformations on Vector Spaces serves primarily as a textbook for undergraduate Linear Algebra courses. While standard Linear Algebra books begin by focusing on solving systems of linear equations and associated procedural skills, our book begins by developing a conceptual framework for the topic using the central objects, vector spaces and linear transformations. It covers the same concepts, skills, and, applications as conventional texts in a one-semester course, but students walk away with a much richer and more useful mastery of the topics. The book is structured to facilitate the implementation of the flipped classroom. The text features a continuous narrative to illuminate the big picture of the material and is written to help students develop their textbook reading skills. Also, there are “Explorations” scattered throughout each section; these are quick first examples intended for students to complete while reading before class meetings. Additional materials include section overview homework assignments and worksheets that can be used for in-class practice.14412023-07-13T21:34:34Z2023-07-13T21:34:34ZIntroducing Mathematical Biology<img alt="Read more about Introducing Mathematical Biology" title="Introducing Mathematical Biology cover image" class="cover " width="520" height="693" data-controller="common--cover" data-placeholder="/assets/common/placeholder-0e0607cbc50663ddb9e8fd188058bcd2630c730ef6ee322801278607b7d5af8e.png" src="/rails/active_storage/blobs/redirect/eyJfcmFpbHMiOnsiZGF0YSI6Nzc4NCwicHVyIjoiYmxvYl9pZCJ9fQ==--5ee1b17feec958613bf3fbc6698e47829b4eb8a7/bookcover1.png" />Mathematical modelling plays an increasingly important role in almost any area of life sciences, and this interactive textbook focuses on the areas of population ecology, infectious diseases, immunology and cell dynamics, gene networks and pharmacokinetics. It is aimed at anyone who is interested in learning about how to model biological systems, including undergraduate and postgraduate mathematics students who have not studied mathematical biology before, life-sciences students with an interest in modelling, and post-16 mathematics students interested in university-level material. Some mathematical knowledge is assumed, and the mathematical models used are all in the form of ordinary differential equations.14002023-04-24T13:59:44Z2023-08-31T14:12:56ZFoundations of Biomedical Science: Quantitative Literacy: Theory and Problems<img alt="Read more about Foundations of Biomedical Science: Quantitative Literacy: Theory and Problems" title="Foundations of Biomedical Science: Quantitative Literacy: Theory and Problems cover image" class="cover " width="724" height="1024" data-controller="common--cover" data-placeholder="/assets/common/placeholder-0e0607cbc50663ddb9e8fd188058bcd2630c730ef6ee322801278607b7d5af8e.png" src="/rails/active_storage/blobs/redirect/eyJfcmFpbHMiOnsiZGF0YSI6NjAyNSwicHVyIjoiYmxvYl9pZCJ9fQ==--0d177e5a0940ae52a980fc4e6295862e8880bf6c/FoundationsOfBiomedicalScience_Cover_v2-724x1024.jpg" />Foundations of Biomedical Science: Quantitative Literacy Theory and Problems is designed to help students develop the fundamental mathematical and quantitative literacy required to navigate and interpret evidence-based Biomedical data. This will provide students with the skills and confidence to habitually question any quantitative data they come across and to use these skills to make informed judgements regarding their veracity.13992023-04-24T13:33:50Z2023-12-01T19:47:46ZContemporary Mathematics<img alt="Read more about Contemporary Mathematics" title="Contemporary Mathematics cover image" class="cover " width="546" height="716" data-controller="common--cover" data-placeholder="/assets/common/placeholder-0e0607cbc50663ddb9e8fd188058bcd2630c730ef6ee322801278607b7d5af8e.png" src="/rails/active_storage/blobs/redirect/eyJfcmFpbHMiOnsiZGF0YSI6NjAxOCwicHVyIjoiYmxvYl9pZCJ9fQ==--b2f6a20d0e4484c956b64f00e97f9ea48aa7e97e/Screenshot%202023-04-24%20at%208.31.58%20AM.png" />Contemporary Mathematics is designed to meet the scope and sequence requirements for a liberal arts mathematics course. This resource provides stand-alone sections with a focus on showing relevance in the features as well as the examples, exercises, and exposition. Contemporary Mathematics integrates technology applications, projects, and highlights a diverse group of contributors to mathematics, statistics, and related fields. Print copies of this book will be available for the fall 2023 semester. You can sign up to be notified when print copies are available.13912023-04-09T22:41:53Z2024-01-22T14:52:43ZAn Intuitive, Interactive, Introduction to Biostatistics<img alt="Read more about An Intuitive, Interactive, Introduction to Biostatistics" title="An Intuitive, Interactive, Introduction to Biostatistics cover image" class="cover " width="155" height="200" data-controller="common--cover" data-placeholder="/assets/common/placeholder-0e0607cbc50663ddb9e8fd188058bcd2630c730ef6ee322801278607b7d5af8e.png" src="/rails/active_storage/blobs/redirect/eyJfcmFpbHMiOnsiZGF0YSI6NDY3NCwicHVyIjoiYmxvYl9pZCJ9fQ==--b99fc2d656c8ecfa620b9bb865642df72d6a570b/9984376757802771.jpeg" />"An Intuitive, Interactive Introduction to Biostatistics" is an introductory statistics textbook oriented towards towards undergraduate students in the health sciences. While covering the breadth of material typically presented in a first semester statistics course, including introductions to probability and distributions, study design, CLT, hypothesis testing, and inference, IIIB distinguishes itself with its focus on cultivating student intuition through the use of guided questions and interactive simulation-based applets. Written in R, this open-source text has been created with customizability in mind, offering instructors maximal flexibility in arranging and modifying the content.3762023-03-29T21:48:03Z2024-01-22T14:51:53ZIntroductory Algebra<img alt="Read more about Introductory Algebra" title="Introductory Algebra cover image" class="cover " width="606" height="769" data-controller="common--cover" data-placeholder="/assets/common/placeholder-0e0607cbc50663ddb9e8fd188058bcd2630c730ef6ee322801278607b7d5af8e.png" src="/rails/active_storage/blobs/redirect/eyJfcmFpbHMiOnsiZGF0YSI6MzExLCJwdXIiOiJibG9iX2lkIn19--9d2122042f549507d6bd7d8449ad2bf98e492fc7/9781607826590.png" />Introductory Algebra provides a comprehensive introduction of variables, functionsand linear equations and gives students a solid foundation in algebra.13842023-03-27T14:14:13Z2024-01-29T14:36:07ZIntroduction to Arithmetic Groups<img alt="Read more about Introduction to Arithmetic Groups" title="Introduction to Arithmetic Groups cover image" class="cover " width="1018" height="1220" data-controller="common--cover" data-placeholder="/assets/common/placeholder-0e0607cbc50663ddb9e8fd188058bcd2630c730ef6ee322801278607b7d5af8e.png" src="/rails/active_storage/blobs/redirect/eyJfcmFpbHMiOnsiZGF0YSI6NDY0OCwicHVyIjoiYmxvYl9pZCJ9fQ==--9d8572cf0162c498ad1f7fb3b358bdac98bfef1a/Screenshot%202023-03-27%20at%209.08.45%20AM.png" />Introduction to Arithmetic Groups13702023-03-13T17:53:13Z2023-09-07T04:51:59ZIntroduction to Systems Biology: Workbook for Flipped-Classroom Teaching<img alt="Read more about Introduction to Systems Biology: Workbook for Flipped-Classroom Teaching" title="Introduction to Systems Biology: Workbook for Flipped-Classroom Teaching cover image" class="cover " width="1876" height="2430" data-controller="common--cover" data-placeholder="/assets/common/placeholder-0e0607cbc50663ddb9e8fd188058bcd2630c730ef6ee322801278607b7d5af8e.png" src="/rails/active_storage/blobs/redirect/eyJfcmFpbHMiOnsiZGF0YSI6NDYxNSwicHVyIjoiYmxvYl9pZCJ9fQ==--630187190d84d0b85709381828819784fcb8b7a6/obp.0291.jpg" />This book is an introduction to the language of systems biology, which is spoken among many disciplines, from biology to engineering. Authors Thomas Sauter and Marco Albrecht draw on a multidisciplinary background and evidence-based learning to facilitate the understanding of biochemical networks, metabolic modeling and system dynamics. Their pedagogic approach briefly highlights core ideas of concepts in a broader interdisciplinary framework to guide a more effective deep dive thereafter. The learning journey starts with the purity of mathematical concepts, reveals its power to connect biological entities in structure and time, and finally introduces physics concepts to tightly align abstraction with reality. This workbook is all about self-paced learning, supports the flipped-classroom concept, and kick-starts with scientific evidence on studying. Each chapter comes with links to external YouTube videos, learning checklists, and Integrated real-world examples to gain confidence in thinking across scientific perspectives. The result is an integrated approach that opens a line of communication between theory and application, enabling readers to actively learn as they read. This overview of capturing and analyzing the behavior of biological systems will interest adherers of systems biology and network analysis, as well as related fields such as bioinformatics, biology, cybernetics, and data science.13492023-02-20T14:44:23Z2024-01-22T14:52:40ZNumerical Methods for Ordinary Differential Equations<img alt="Read more about Numerical Methods for Ordinary Differential Equations" title="Numerical Methods for Ordinary Differential Equations cover image" class="cover " width="300" height="370" data-controller="common--cover" data-placeholder="/assets/common/placeholder-0e0607cbc50663ddb9e8fd188058bcd2630c730ef6ee322801278607b7d5af8e.png" src="/rails/active_storage/blobs/redirect/eyJfcmFpbHMiOnsiZGF0YSI6NDU1NSwicHVyIjoiYmxvYl9pZCJ9fQ==--fd3b68009deeeda4d91b01a1623ef2844da77abd/submission_57_74_coverImage_en_US_t.png" />In this book we discuss several numerical methods for solving ordinary differential equations. We emphasize the aspects that play an important role in practical problems. We confine ourselves to ordinary differential equations with the exception of the last chapter in which we discuss the heat equation, a parabolic partial differential equation. The techniques discussed in the intro-ductory chapters, for instance interpolation, numerical quadrature and the solution to nonlinear equations, may also be used outside the context of differential equations. They have been in-cluded to make the book self-contained as far as the numerical aspects are concerned. Chapters, sections and exercises marked with a * are not part of the Delft Institutional Package. The numerical examples in this book were implemented in Matlab, but also Python or any other programming language could be used. A list of references to background knowledge and related literature can be found at the end of this book. Extra information about this course can be found at http://NMODE.ewi.tudelft.nl, among which old exams, answers to the exercises, and a link to an online education platform. We thank Matthias Moller for his thorough reading of the draft of this book and his helpful suggestions.
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