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OER - Math, Chemistry & Physics: Calculus

Calculus

Joseph E. Fields, Southern Connecticut State University

This book is designed for the transition course between calculus and differential equations and the upper division mathematics courses with an emphasis on proof and abstraction.

 

Active Calculus 2.0

David Austin, Grand Valley State University
Matt Boelkins, Grand Valley State University
Steve Schlicker, Grand Valley State University

Active Calculus is different from most existing calculus texts in at least the following ways: the text is freely readable online in HTML format and is also available for in PDF; in the electronic format, graphics are in full color and there are live links to java applets; version 2.0 now contains WeBWorK exercises in each chapter, which are fully interactive in the HTML format and included in print in the PDF; the text is open source, and interested users can gain access to the original source files on GitHub; the style of the text requires students to be active learners — there are very few worked examples in the text, with there instead being 3-4 activities per section that engage students in connecting ideas, solving problems, and developing understanding of key calculus concepts; each section begins with motivating questions, a brief introduction, and a preview activity, all of which are designed to be read and completed prior to class; following the WeBW

Active Calculus Multivariable

David Austin, Grand Valley State University
Matthew Boelkins, Grand Valley State University
Steve Schlicker, Grand Valley State University

Active Calculus Multivariable is the continuation of Active Calculus to multivariable functions.

 

APEX Calculus

Brian Heinold, Mount St. Mary’s University
Dimplekumar Chalishajar, Virginia Military Institute
Gregory Hartman, Virginia Military Institute
Troy Siemers, Virginia Military Institute

APEX Calculus is a calculus textbook written for traditional college/university calculus courses. It has the look and feel of the calculus book you likely use right now (Stewart, Thomas & Finney, etc.). The explanations of new concepts is clear, written for someone who does not yet know calculus. Each section ends with an exercise set with ample problems to practice & test skills (odd answers are in the back).

Calculus

Gilbert Strang, MIT

Published in 1991 and still in print from Wellesley-Cambridge Press, the book is a straightforward introductory calculus textbook available free online to educators and self-learners alike. It is covers single variable and multivariable calculus, including applications.

Calculus for the Life Sciences: A Modeling Approach Volume 1

James L. Cornette, Iowa State University
Ralph A. Ackerman, Iowa State University

This text is a product of a two-semester calculus course for life sciences students in which students gathered biological data in a laboratory setting that was used to motivate the concepts of calculus.  The book contains data from experiments, but does not require that students do laboratory experiments.

Calculus for the Life Sciences: A Modeling Approach Volume 2

James L. Cornette, Iowa State University
Ralph A. Ackerman

This text is a product of a two-semester calculus course for life sciences students in which students gathered biological data in a laboratory setting that was used to motivate the concepts of calculus.  The book contains data from experiments, but does not require that students do laboratory experiments.

Calculus One

Multiple Authors, Mooculus

This text is based on David Guichard’s open-source calculus text which in turn is a modification and expansion of notes written by Neal Koblitz at the University of Washington.

Calculus Volume 1

Edwin Herman, University of Wisconsin-Stevens Point
Gilbert Strang, MIT

Calculus is designed for the typical two- or three-semester general calculus course, incorporating innovative features to enhance student learning.

Calculus Volume 2

Gilbert Strang, Massachusetts Institute of Technology

Calculus is designed for the typical two- or three-semester general calculus course, incorporating innovative features to enhance student learning. The book guides students through the core concepts of calculus and helps them understand how those concepts apply to their lives and the world around them.

Calculus Volume 3

Gilbert Strang, Massachusetts Institute of Technology

Calculus is designed for the typical two- or three-semester general calculus course, incorporating innovative features to enhance student learning. The book guides students through the core concepts of calculus and helps them understand how those concepts apply to their lives and the world around them.

Calculus: Early Transcendentals

David Guichard, Whitman College

Calculus: Early Transcendentals, originally by D. Guichard, has been redesigned by the Lyryx editorial team. Substantial portions of the content, examples, and diagrams have been redeveloped, with additional contributions provided by experienced and practicing instructors. This approachable text provides a comprehensive understanding of the necessary techniques and concepts of the typical Calculus course sequence, and is suitable for the standard Calculus I, II and III courses.

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Elementary Differential Equations with Boundary Value Problems

William F. Trench, Trinity University

Elementary Differential Equations with Boundary Value Problems is written for students in science, engineering, and mathematics who have completed calculus through partial differentiation.

 

Vector Calculus

Michael Corral, Schoolcraft College

This is a text on elementary multivariable calculus, designed for students who have completed courses in single-variable calculus. The traditional topics are covered: basic vector algebra; lines, planes and surfaces; vector-valued functions; functions of 2 or 3 variables; partial derivatives; optimization; multiple integrals; line and surface integrals.

Whitman Calculus

Dr David Guichard, Whitman College

An introductory level single variable calculus book, covering standard topics in differential and integral calculus, and infinite series. Late transcendentals and multivariable versions are also available.

Precalculus

Carl Stitz, Lakeland Community College
Jeff Zeager, Lorain County Community College

A casual glance through the Table of Contents of most of the major publishers’ College Algebra books reveals nearly isomorphic content in both order and depth. Our Table of Contents shows a different approach, one that might be labeled “Functions First.” To truly use The Rule of Four, that is, in order to discuss each new concept algebraically, graphically, numerically and verbally, it seems completely obvious to us that one would need to introduce functions first. (Take a moment and compare our ordering to the classic “equations first, then the Cartesian Plane and THEN functions” approach seen in most of the major players.) We then introduce a class of functions and discuss the equations, inequalities (with a heavy emphasis on sign diagrams) and applications which involve functions in that class.

Precalculus

Multiple Authors, Openstax College

Precalculus is intended for college-level precalculus students. Since precalculus courses vary from one institution to the next, we have attempted to meet the needs of as broad an audience as possible, including all of the content that might be covered in any particular course.

Precalculus

Holly Carley, NYC College of Technology
Thomas Tradler, NYC College of Technology

These are notes for a course in precalculus, as it is taught at New York City College of Technology - CUNY (where it is offered under the course number MAT 1375). Our approach is calculator based. For this, we will use the currently standard TI-84 calculator, and in particular, many of the examples will be explained and solved with it. However, we want to point out that there are also many other calculators that are suitable for the purpose of this course and many of these alternatives have similar functionalities as the calculator that we have chosen to use. An introduction to the TI-84 calculator together with the most common applications needed for this course is provided in appendix A. In the future we may expand on this by providing introductions to other calculators or computer algebra systems.

Precalculus: An Investigation of Functions

David Lippman, Pierce College
Melonie Rasmussen, Pierce College

Precalculus: An Investigation of Functions is a free, open textbook covering a two-quarter pre-calculus sequence including trigonometry.

Trigonometry

College Trigonometry

Carl Stitz, Lakeland Community College
Jeff Zeager, Lorain County Community College

Covers chapters 10-11 of Precalculus.

Trigonometry

Steven Schlicker, Grand Valley State University
Ted Sundstrom, Grand Valley State University

This trigonometry textbook is different than other trigonometry books in that it is free to download, and the reader is expected to do more than read the book and is expected to study the material in the book by working out examples rather than just reading about them.

 

Other

Jurg Nievergelt, ETH Zurich
Klaus Hinrichs, University of Muenster

An introductory coverage of algorithms and data structures with application to graphics and geometry.

Applied Combinatorics

Mitchel T. Keller, Washington and Lee University
William T. Trotter, Georgia Institute of Technology

Applied Combinatorics is an open-source textbook for a course covering the fundamental enumeration techniques (permutations, combinations, subsets, pigeon hole principle), recursion and mathematical induction, more advanced enumeration techniques (inclusion-exclusion, generating functions, recurrence relations, Polyá theory), discrete structures (graphs, digraphs, posets, interval orders), and discrete optimization (minimum weight spanning trees, shortest paths, network flows). There are also chapters introducing discrete probability, Ramsey theory, combinatorial applications of network flows, and a few other nuggets of discrete mathematics.

Applied Discrete Structures

Alan Doerr, University of Massachusetts Lowell
Kenneth Levasseur, University of Massachusetts Lowell

The text is divided into lecture-length sections, facilitating the organization of an instructor's presentation.Topics are presented in such a way that students' understanding can be monitored through thought-provoking exercises. The exercises require an understanding of the topics and how they are interrelated, not just a familiarity with the key words.

Applied Finite Mathematics

Applied Finite Mathematics covers topics including linear equations, matrices, linear programming, the mathematics of finance, sets and counting, probability, Markov chains, and game theory.

Discrete Mathematics: An Open Introduction

Oscar Levin, University of Northern Colorado

Discrete Mathematics: An Open Introduction is a free, open source textbook appropriate for a first or second year undergraduate course for math majors, especially those who will go on to teach.

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Basic Analysis: Introduction to Real Analysis

Jirí Lebl, Oklahoma State University

This free online textbook (e-book in webspeak) is a one semester course in basic analysis.

Book of Proof

Dr. Richard Hammack, Virginia Commonwealth University

Book of Proof is an introduction to the language and methods of mathematical proofs. The text is meant to bridge the computational courses that students typically encounter in their first years of college (such as calculus or differential equations) to more theoretical, proof-based courses such as topology, analysis and abstract algebra.  Topics include sets, logic, counting, methods of conditional and non-conditional proof, disproof, induction, relations, functions and infinite cardinality