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Fundamentals of Matrix Algebra
Gregory Hartman · Virginia Military Institute
Có trong mục lục: 01: Systems of Linear Equations · 1.01: Introduction to Linear Equations · 1.02: Using Matrices to Solve Systems of Linear Equations
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College Algebra for Liberal Arts and Humanities
Leif Jordan · College of the Desert
Có trong mục lục: 1.01: Linear and Absolute Value Equations · 1.04: Linear and Absolute Value Inequalities · 2.04: Systems of Linear Equations - Two Variables
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Introduction to Matrix Algebra
Autar Kaw · University of South Florida
Có trong mục lục: 1.06: Gaussian Elimination Method for Solving Simultaneous Linear Equations · 1.07: LU Decomposition Method for Solving Simultaneous Linear Equations
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MATH 95: Elementary Algebra II
Melissa Halling · Minnesota State Community and Technical College
Có trong mục lục: 01: Solving Linear Systems · 1.01: Review- Solving Linear Equations · 1.1.01: Simplifying Algebraic Expressions
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Quantitative Research Methods for Political Science, Public Policy and Public Administration (With Applications in R)
Hank Jenkins-Smith; Joseph Ripberger · University of Oklahoma Libraries · 2017
The focus of this book is on using quantitative research methods to test hypotheses and build theory in political science, public policy and public administration. It is designed for advanced undergraduate courses, or introductory and intermediate graduate-level courses. The first part of the book introduces the scientific method, then covers research design, measurement, descriptive statistics, probability, inference, and basic measures of association. The second part of the book covers bivariate and multiple linear regression using the ordinary least squares, the calculus and matrix algebra that are necessary for understanding bivariate and multiple linear regression, the assumptions that underlie these methods, and then provides a short introduction to generalized linear models.The book fully embraces the open access and open source philosophies. The book is freely available in the SHAREOK repository; it is written in R Markdown files that are available in a public GitHub repository; it uses and teaches R and RStudio for data analysis, visualization and data management; and it uses publically available survey data (from the Meso-Scale Integrated Socio-geographic Network) to illustrate important concepts and methods. We encourage students to download the data, replicate the examples, and explore further! We also encourage instructors to download the R Markdown files and modify the text for use in different courses.
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Multivariable Calculus
Don Shimamoto · Don Shimamoto · 2019
This book covers the standard material for a one-semester course in multivariable calculus. The topics include curves, differentiability and partial derivatives, multiple integrals, vector fields, line and surface integrals, and the theorems of Green, Stokes, and Gauss. Roughly speaking the book is organized into three main parts corresponding to the type of function being studied: vector-valued functions of one variable, real-valued functions of many variables, and finally the general case of vector-valued functions of many variables. As is always the case, the most productive way for students to learn is by doing problems, and the book is written to get to the exercises as quickly as possible. The presentation is geared towards students who enjoy learning mathematics for its own sake. As a result, there is a priority placed on understanding why things are true and a recognition that, when details are sketched or omitted, that should be acknowledged. Otherwise the level of rigor is fairly normal. Matrices are introduced and used freely. Prior experience with linear algebra is helpful, but not required.
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Fundamentals of Matrix Algebra
Gregory Hartman · APEX Calculus · 2011
A college (or advanced high school) level text dealing with the basic principles of matrix and linear algebra. It covers solving systems of linear equations, matrix arithmetic, the determinant, eigenvalues, and linear transformations. Numerous examples are given within the easy to read text. This third edition corrects several errors in the text and updates the font faces.
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Representation Theory
Jan Grabowski · Open Book Publishers · 2025
This volume offers a fresh and modern introduction to one of abstract algebra’s key topics. Guiding readers through the transition between structure theory and representation theory, this textbook explores how algebraic objects like groups and rings act as symmetries of other structures. Using the accessible yet powerful language of category theory, the book reimagines standard approaches to topics such as modules and algebras in a way that unlocks modern treatments of more advanced topics such as quiver representations and even representations of Hopf algebras and categories. Aimed at undergraduate students with prior exposure to linear algebra and basic group theory, the book introduces categories early and uses them throughout, providing a cohesive framework that mirrors current mathematical research. Though technically sophisticated, it also includes examples and exercises designed to develop intuition and understanding. Grabowski’s inclusion of computational tools such as SageMath offers a valuable and traditionally underdeveloped bridge between abstract theory and hands-on exploration. This is a uniquely valuable guide for students ready to stretch their understanding of the subject’s conceptual depth and evolving frontiers.
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Integral Calculus with Applications to Life Sciences
Paul Tsopméné · University of British Columbia Library · 2025
Integral Calculus with Applications to Life Sciences is an open educational resource (OER) that covers an unusually broad range of topics—including integration, infinite series, differential equations, linear algebra, probability, and statistics—rarely found in a single textbook. Each section begins with clear learning outcomes and a motivational paragraph, often tied to applications in the life sciences, helping students see the immediate relevance of what they learn. Examples are worked out in full detail. Every time a calculus or algebraic rule is applied, it is explicitly stated at the point of use. Rather than isolating algebra review in a preliminary chapter, this text integrates algebra throughout, allowing students to reinforce foundational skills while learning new material. This approach is especially supportive for students who may struggle with algebra. Practice problems with complete solutions follow each example, and most sections end with an application to biology, medicine, or related fields. The exercise sections include not only standard questions but also critical thinking problems such as finding errors in worked solutions, constructing counterexamples, and solving real-world problems. The text includes final answers for all exercises at the back. Hyperlinks allow students to jump seamlessly between exercises and final answers. By combining clarity, rigor, accessibility, and real-world relevance, one of the main goals of this OER is to help students not only to succeed in calculus but also to appreciate its power in understanding the living world.
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Linear Transformations on Vector Spaces
Scott Kaschner; Amber Russell · PALNI · 2023
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.
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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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Introductory Algebra
Anne Gloag · Independent · 2012
Introductory Algebra provides a comprehensive introduction of variables, functionsand linear equations and gives students a solid foundation in algebra.
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Introduction to Real Analysis
William Trench · A.T. Still University · 2013
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.
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Calculus for the Life Sciences: A Modeling Approach
James Cornette; Ralph Ackerman · A.T. Still University · 2013
Our writing is based on three premises. First, life sciences students are motivated by and respond well to actual data related to real life sciences problems. Second, the ultimate goal of calculus in the life sciences primarily involves modeling living systems with difference and differential equations. Understanding the concepts of derivative and integral are crucial, but the ability to compute a large array of derivatives and integrals is of secondary importance. Third, the depth of calculus for life sciences students should be comparable to that of the traditional physics and engineering calculus course; else life sciences students will be short changed and their faculty will advise them to take the 'best' (engineering) course. In our text, mathematical modeling and difference and differential equations lead, closely follow, and extend the elements of calculus. Chapter one introduces mathematical modeling in which students write descriptions of some observed processes and from these descriptions derive first order linear difference equations whose solutions can be compared with the observed data. In chapters in which the derivatives of algebraic, exponential, or trigonometric functions are defined, biologically motivated differential equations and their solutions are included. The chapter on partial derivatives includes a section on the diffusion partial differential equation. There are two chapters on non-linear difference equations and on systems of two difference equations and two chapters on differential equations and on systems of differential equation.
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Calculus for the Life Sciences: A Modeling Approach
James Cornette; Ralph Ackerman · A.T. Still University · 2011
Our writing is based on three premises. First, life sciences students are motivated by and respond well to actual data related to real life sciences problems. Second, the ultimate goal of calculus in the life sciences primarily involves modeling living systems with difference and differential equations. Understanding the concepts of derivative and integral are crucial, but the ability to compute a large array of derivatives and integrals is of secondary importance. Third, the depth of calculus for life sciences students should be comparable to that of the traditional physics and engineering calculus course; else life sciences students will be short changed and their faculty will advise them to take the 'best' (engineering) course. In our text, mathematical modeling and difference and differential equations lead, closely follow, and extend the elements of calculus. Chapter one introduces mathematical modeling in which students write descriptions of some observed processes and from these descriptions derive first order linear difference equations whose solutions can be compared with the observed data. In chapters in which the derivatives of algebraic, exponential, or trigonometric functions are defined, biologically motivated differential equations and their solutions are included. The chapter on partial derivatives includes a section on the diffusion partial differential equation. There are two chapters on non-linear difference equations and on systems of two difference equations and two chapters on differential equations and on systems of differential equation.
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Algebra 1
Lynn Marecek; MaryAnne Anthony-Smith; Andrea Honeycutt Mathis; Jay Abramson · OpenStax, Rice University
Algebra 1 is a complete high school algebra curriculum that is 100% aligned with the Texas Essential Knowledge and Skills (TEKS) and the English Language Proficiency Standards (ELPS). OpenStax Algebra 1 is a high-quality instructional material (HQIM) that is flexible enough for core adoption and adaptable enough to support a wide range of teaching strategies and student needs. Algebra 1 is a research-backed curriculum designed to strengthen teaching and learning in all classrooms. The OpenStax Algebra 1 curriculum is structured across nine units that guide students from linear to exponential to quadratic functions, emphasizing how these patterns differ. Students explore mathematical relationships through tables, equations, graphs, and real-world contexts, beginning with patterns of repeated addition or subtraction (linear), moving into multiplication or division (exponential), and culminating in models that both increase and decrease (quadratic). Each unit includes a readiness pre-assessment, multiple content sections, section assessments, and ends with a project, quizzes, and a wrap-up. The curriculum is designed to support coherent instruction, continuous assessment, and student engagement throughout the school year. Through our free, digital teacher guide (available within the “instructor resources” section of the website), teachers receive clear learning targets, prerequisite skill guidance, videos, and a breakdown of the Texas Essential Knowledge and Skills (TEKS) addressed in every lesson. Algebra 1 was authored by OpenStax and is based, in part, on the OpenStax Pre Algebra, Elementary Algebra, Intermediate Algebra, and College Algebra materials, and the IM 6-12TM by Illustrative Mathematics®. Based on OpenStax’s open (CC-BY-NC-SA) license, educators may remix and reuse the elements and content in Algebra 1 according to their approach and learning objectives. OpenStax textbooks are always available free online at openstax.org. If you have encountered a white s
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MAT 117: Mathematical Problem Solving in Liberal Arts
LibreTexts
Có trong mục lục: 6.02: Linear (Algebraic) Growth
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Beginning Algebra
Lumen Learning
Có trong mục lục: 1.02: Solving Linear Equations · 1.03: Multi-Step Linear Equations · 2.03: Graphing Linear Equations
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A Second Course in Ordinary Differential Equations: Dynamical Systems and Boundary Value Problems
Russell Herman · University of North Carolina Wilmington
Có trong mục lục: 2.10: Appendix- Diagonalization and Linear Systems · 03: Nonlinear Systems · 3.05: Nonlinear Pendulum
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College Algebra and Trigonometry- Expressions, Equations, and Graphs
Holly Carley and Ariane Masuda · New York City College of Technology
Có trong mục lục: 1.2.01: Linear Expressions · 2.01: Linear Equations · 3.01: Linear Equations with Two Variables