Digital library
Textbooks, references and open learning resources.
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Math 125: Hope College
Katharine Vance · Hope College
This course covers the material typically taught in the first half of a Calculus I course. The calculus material is supplemented by reviewing topics of high school mathematics as needed. The calculus topics are also taught at a slower pace. Topics include function review, limits and continuity, the concept (and definition) of a derivative, and differentiation rules (product rule, quotient rule, chain rule are included).
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Elementary Abstract Algebra
W Edwin Clark · University of South Florida
This book is intended for a one semester introduction to abstract algebra. We assume that students have some familiarity with basic set theory linear algebra and calculus. But very little of this nature will be needed To a great extent the course is self contained except for the requirement of a certain amount of mathematical maturity. And hopefully the student's level of mathematical maturity will increase as the course progresses.
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Manchester University Physical Chemistry I (CHEM 341)
Kathy Davis · Manchester University
Textbook for CHEM 341 at Manchester University (Physical Chemistry I). Foundations of quantum mechanics for describing atomic structure, molecular motion and chemical bonding, with specific applications to spectroscopy and chemical reactivity. Prerequisite(s): CHEM 113 (General Chemistry II), MATH 122 (Calculus II).
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Fundamentals of Transportation
David Levinson et al. · Wikibook
This text is aimed at undergraduate civil engineering students, though the material may provide a useful review for practitioners and graduate students in transportation. Often this is the first engineering course students take, which requires a switch in thinking from simply solving given problems to formulating the problem mathematically before solving it, i.e. from straight-forward calculation often found in undergraduate Calculus to vaguer word problems more reflective of the real world.
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Trigonometry
Ted Sundstrom & Steven Schlicker · Grand Valley State University
This trigonometry textbook this book is not just about mathematical content but is also about the process of learning and doing mathematics. That is, this book is designed not to be just casually read but rather to be engaged. Since this can be a difficult task, there are several features of the book designed to assist students in this endeavor. In particular, most sections of the book start with a beginning activity that review prior mathematical work that is necessary for the new section.
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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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Intermediate Microeconomics
Patrick Emerson · Oregon State University · 2019
Intermediate Microeconomics is a comprehensive microeconomic theory text that uses real world policy questions to motivate and illustrate the material in each chapter. Intermediate Microeconomics is an approachable yet rigorous textbook that covers the entire scope of traditional microeconomic theory and includes two mathematical approaches, allowing instructors to teach the material with or without calculus. With real-world policy topics as an entree into each subject, Intermediate Microeconomics will help students engage with the material and facilitate learning not only the concepts, but their importance and application as well.
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Principles of Microeconomics
Doug Curtis; Ian Irvine · Lyryx · 2021
Principles of Microeconomics is an adaptation of the textbook, Microeconomics: Markets, Methods, and Models by D. Curtis and I. Irvine, which provides concise yet complete coverage of introductory microeconomic theory, application and policy in a Canadian and global environment. This adaptation employs methods that use equations sparingly and do not utilize calculus. The key issues in most chapters are analyzed by introducing a numerical example or case study at the outset. Students are introduced immediately to the practice of taking a data set, examining it numerically, plotting it, and again analyzing the material in that form. The end-of-chapter problems involve numerical and graphical analysis, and a small number of problems in each chapter involve solving simple linear equations (intersecting straight lines). However, a sufficient number of questions is provided for the student to test understanding of the material without working through that subset of questions. This textbook is intended for a one-semester course, and can be used in a two-semester sequence with the companion textbook, Principles of Macroeconomics. The three introductory chapters are common to both textbooks.
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The Economics of Food and Agricultural Markets
Andrew Barkley · New Prairie Press · 2016
The Second Edition of Economics of Food and Agricultural Markets (2019) is written for applied intermediate microeconomics courses. The book showcases the power of economic principles to explain and predict issues and current events in the food, agricultural, agribusiness, international trade, labor markets, and natural resource sectors. The field of agricultural economics is relevant, important and interesting. The study of market structures, also called industrial organization, provides powerful, timely, and useful tools for any individual or group making personal choices, business decisions, or public policies in food and agricultural industries. Readers will benefit from a large number of real-world examples and applications of the economic concepts under discussion. The book introduces economic principles in a succinct and reader-friendly format, providing students and instructors with a clear, up-to-date, and straightforward approach to learning how a market-based economy functions, and how to use simple economic principles for improved decision making. The principles are applied to timely, interesting, and important real-world issues through words, graphs, and simple algebra and calculus. This book is intended for students who study agricultural economics, microeconomics, rural development and/or environmental policy. The goal of the book is to encourage students to learn to “think like an economist” through application of benefits and costs to every decision, idea, and strategic decision. This objective is accomplished by including extended examples that cover a broad range of topics including the analysis of consumer decisions, supply and demand, and market efficiency; the design of pricing strategies; advertising and marketing decisions; and public policy analysis. Contents The book begins with a review and introduction of economic principles, including markets, scarcity, and the scientific method. Supply and demand are examined carefully and completely, w
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Introduction to Economic Analysis
Preston McAfee; Tracy Lewis · Saylor Foundation · 2009
This book presents standard intermediate microeconomics material and some material that, in the authors' view, ought to be standard but is not. Introductory economics material is integrated. Standard mathematical tools, including calculus, are used throughout. The book easily serves as an intermediate microeconomics text, and can be used for a relatively sophisticated undergraduate who has not taken a basic university course in economics. The focus of this book is on the conceptual tools and not on fluff. As such, it reflects the approach actually adopted by the majority of economists for understanding economic activity. There are lots of models and equations, and no pictures of economists ;-) Economic analysis is used in many situations. When British Petroleum sets the price for Alaskan crude oil, it uses an estimated demand model, both for gasoline consumers and also for the refineries to which BP sells. Economic analysis was used by experts in the antitrust suit brought by the U.S. Department of Justice both to understand Microsoft's incentive to foreclose (eliminate from the market) rival Netscape and consumer behavior in the face of alleged foreclosure. Stock market analysts use economic models to forecast the profits of companies to predict the price of their stocks. When the government forecasts the budget deficit or considers a change in environmental regulations, it uses economic models. This book presents the building blocks of the models in common use by an army of economists thousands of times per day. This book, plus econometrics, provides most of the economic analysis tools to take upper division economics courses of any type.
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University Physics I: Classical Mechanics
Julio Gea-Banacloche · University of Arkansas · 2019
This is a “minimalist” textbook for a first semester of university, calculus-based physics, covering classical mechanics (including one chapter on mechanical waves, but excluding fluids), plus a brief introduction to thermodynamics. The presentation owes much to Mazur’s The Principles and Practice of Physics: conservation laws, momentum and energy, are introduced before forces, and one-dimensional setups are thoroughly explored before two-dimensional systems are considered. It contains both problems and worked-out examples.
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University Physics
Jeff Sanny; Samuel Ling · OpenStax · 2016
University Physics is a three-volume collection that meets the scope and sequence requirements for two- and three-semester calculus-based physics courses. Volume 1 covers mechanics, sound, oscillations, and waves. This textbook emphasizes connections between between theory and application, making physics concepts interesting and accessible to students while maintaining the mathematical rigor inherent in the subject. Frequent, strong examples focus on how to approach a problem, how to work with the equations, and how to check and generalize the result.
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Light and Matter
Benjamin Crowell · Benjamin Crowell · 2010
This is an introductory text intended for a one-year introductory course of the type typically taken by biology majors, or for AP Physics B. Algebra and trig are used, and there are optional calculus-based sections.
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Transition to Higher Mathematics: Structure and Proof
Bob Dumas; John McCarthy · Open Scholarship · 2015
This book is written for students who have taken calculus and want to learn what “real mathematics" is. We hope you will find the material engaging and interesting, and that you will be encouraged to learn more advanced mathematics. This is the second edition of our text. It is intended for students who have taken a calculus course, and are interested in learning what higher mathematics is all about. It can be used as a textbook for an "Introduction to Proofs" course, or for self-study. Chapter 1: Preliminaries, Chapter 2: Relations, Chapter 3: Proofs, Chapter 4: Principles of Induction, Chapter 5: Limits, Chapter 6: Cardinality, Chapter 7: Divisibility, Chapter 8: The Real Numbers, Chapter 9: Complex Numbers. The last 4 chapters can also be used as independent introductions to four topics in mathematics: Cardinality; Divisibility; Real Numbers; Complex Numbers.
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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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First Semester in Numerical Analysis with Julia
Giray Ökten · Florida State University · 2023
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.
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Functions, Trigonometry, and Systems of Equations
Vanessa Coffelt · Texas A&M University · 2025
This is the second edition of a Precalculus textbook designed specifically for Math 150: Functions, Trigonometry, and Systems of Equations at Texas A&M University.
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Geometry with an Introduction to Cosmic Topology
Michael Hitchman · Michael P. Hitchman · 2020
Motivated by questions in cosmology, the open-content text Geometry with an Introduction to Cosmic Topology uses Mobius transformations to develop hyperbolic, elliptic, and Euclidean geometry - three possibilities for the global geometry of the universe. The text, written for students who have taken vector calculus, also explores the interplay between the shape of a space and the type of geometry it admits. Geometry is suitable for a semester course in non-Euclidean geometry or as a guide to independent study, with over 200 exercises and several essays on topics including the history of geometry, parallax and curvature, and research aimed at determining the shape of the universe.
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Modeling, Functions, and Graphs
Katherine Yoshiwara · Bruce Yoshiwara · 2018
Modeling, Functions, and Graphs covers the content of a typical college algebra course with an emphasis on functions and modeling; when combined with a trigonometry text or supplement, this text can be used in a precalculus course. The text employs a variety of applications to motivate mathematical thinking. Each chapter opens with a problem of historical or contemporary significance highlighting the material in the chapter, and includes by an Investigation that previews the skills to be introduced. These Investigations can be used in class as guided explorations or as projects for small groups. We have also provided a set of more challenging Projects at the end of each chapter.
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Ordinary Differential Equations
Stephen Wiggins · Stephen Wiggins · 2017
This book consists of ten weeks of material given as a course on ordinary differential equations (ODEs) for second year mathematics majors at the University of Bristol. It is the first course devoted solely to differential equations that these students will take. This book consists of 10 chapters, and the course is 12 weeks long. Each chapter is covered in a week, and in the remaining two weeks I summarize the entire course, answer lots of questions, and prepare the students for the exam. I do not cover the material in the appendices in the lectures. Some of it is basic material that the students have already seen that I include for completeness and other topics are "tasters" for more advanced material that students will encounter in later courses or in their project work. Students are very curious about the notion of chaos, and I have included some material in an appendix on that concept. The focus in that appendix is only to connect it with ideas that have been developed in this course related to ODEs and to prepare them for more advanced courses in dynamical systems and ergodic theory that are available in their third and fourth years.