Short Description:
An open textbook created to improve both teaching and learning vital concepts and techniques in multivariable calculus, one of the fundamental courses across the undergraduate curriculum in science and engineering. The goals of this resource are to help learners develop their geometric intuition about abstract and complex mathematical concepts (e.g., partial derivatives, multiple integrals, vector fields), and train them to make connections between concepts visually (e.g., connecting “vectors” in mathematics with “magnitude” and “direction” in physics) in order to more fully understand engineering, physics and mathematical problems (e.g., differential equations) in their subsequent STEM coursework.

Word Count: 7075

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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).

Active Calculus is different from most existing calculus texts in at least the following ways: the text is free for download by students and instructors in .pdf format; in the electronic format, graphics are in full color and there are live html links to java applets; the text is open source, and interested instructors can gain access to the original source files upon request; 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; the exercises are few in number and challenging in nature.

Applied Calculus instructs students in the differential and integral calculus of elementary functions with an emphasis on applications to business, social and life science. Different from a traditional calculus course for engineering, science and math majors, this course does not use trigonometry, nor does it focus on mathematical proofs as an instructional method.

The text is mostly an adaptation of two other excellent open- source calculus textbooks: Active Calculus by Dr. Matt Boelkins of Grand Valley State University and Drs. Gregory Hartman, Brian Heinold, Troy Siemers, Dimplekumar Chalishajar, and Jennifer Bowen of the Virginia Military Institute and Mount Saint Mary's University. Both of these texts can be found at http://aimath.org/textbooks/approved-textbooks/.
The authors of this text have combined sections, examples, and exercises from the above two texts along with some of their own content to generate this text. The impetus for the creation of this text was to adopt an open-source textbook for Calculus while maintaining the typical schedule and content of the calculus sequence at our home institution.

Short Description:
Welcome to the OER companion to Baylor University's Math 1121: The Calculus Supplement Course, an optional, co-requisite course for students enrolled in Calculus 1. This OER was designed to provide 'just in time' support for the algebraic, trigonometric, and geometric relationships undergirding Calculus 1.

Long Description:
Welcome to the OER companion for Baylor University’s Math 1121: The Calculus Supplement Course! Math 1121 is an optional, co-requisite course for students enrolled in Calculus 1. This OER was designed to provide ‘just in time’ support for the algebraic, trigonometric, and geometric relationships undergirding Calculus 1. The topics and content were deliberately sequenced to coincide with the topics and content Calculus 1 students engage as they study limits, derivatives, applications of derivatives, and integration. Therefore, this text first reviews the essential functions from Pre-Calculus that students need to be successful in Calculus 1. Then, it examines the properties and algebraic transformations of those functions and reinforces strategies for analyzing functions. Finally, it bolsters the relationships between algebra and geometry that the Fundamental Theorem of Calculus and integrals bring together for Calculus 1 students. Although this OER was designed to support Calculus 1 students, there is almost no Calculus within these ‘pages.’ Rather, the focus is on everything that happens in a Calculus problem after that first Calculus step. Enjoy!

Word Count: 77096

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This short text is designed more for self-study or review than for classroom use; full solutions are given for nearly all the end-of-chapter problems. For a more traditional text designed for classroom use, see Fundamentals of Calculus (http://www.lightandmatter.com/fund/). The focus is mainly on integration and differentiation of functions of a single variable, although iterated integrals are discussed. Infinitesimals are used when appropriate, and are treated more rigorously than in old books like Thompson's Calculus Made Easy, but in less detail than in Keisler's Elementary Calculus: An Approach Using Infinitesimals. Numerical examples are given using the open-source computer algebra system Yacas, and Yacas is also used sometimes to cut down on the drudgery of symbolic techniques such as partial fractions. Proofs are given for all important results, but are often relegated to the back of the book, and the emphasis is on teaching the techniques of calculus rather than on abstract results.

This course provides an introduction to applied concepts in Calculus that are relevant to the managerial, life, and social sciences. Students should have a firm grasp of the concept of functions to succeed in this course. Topics covered include derivatives of basic functions and how they can be used to optimize quantities such as profit and revenues, as well as integrals of basic functions and how they can be used to describe the total change in a quantity over time.

This is an online textbook for a one semester calculus course aimed at business students.
The material covered is fairly standard: differentiation and integration without trigonometry, partial derivatives and optimization of functions of several variables.
There are several characteristics that differentiate the text from other texts:
Excel is used as the main computational engine throughout the text and the needed Excel skills are taught rather than assumed.
Examples, exercises, and vocabulary are tailored to uses in a business curriculum.
There is a modeling thread throughout the text.
Webwork versions of exercises are available on request.

Le contenu de ce manuel couvre la grande majorité des sujets présentés dans les cours de calcul différentiel et intégral pour les étudiants en sciences et génie. Les seuls préalables sont les mathématiques normalement enseignées au secondaire en Ontario. Ce manuel peut être utilisé pour trois des variantes des cours de calcul différentiel et intégral que nous retrouvons dans la majorité des universités en Ontario : Calcul différentiel et intégral pour les étudiants en génie, Calcul différentiel et intégral pour les étudiants en sciences de la vie et Calcul différentiel et intégral pour les étudiants en administration.

This course begins with a review of algebra specifically designed to help and prepare the student for the study of calculus, and continues with discussion of functions, graphs, limits, continuity, and derivatives. The appendix provides a large collection of reference facts, geometry, and trigonometry that will assist in solving calculus problems long after the course is over. Upon successful completion of this course, the student will be able to: calculate or estimate limits of functions given by formulas, graphs, or tables by using properties of limits and LĺÎĺ_ĺĚĺ_hopitalĺÎĺ_ĺĚĺ_s Rule; state whether a function given by a graph or formula is continuous or differentiable at a given point or on a given interval and justify the answer; calculate average and instantaneous rates of change in context, and state the meaning and units of the derivative for functions given graphically; calculate derivatives of polynomial, rational, common transcendental functions, and implicitly defined functions; apply the ideas and techniques of derivatives to solve maximum and minimum problems and related rate problems, and calculate slopes and rates for function given as parametric equations; find extreme values of modeling functions given by formulas or graphs; predict, construct, and interpret the shapes of graphs; solve equations using NewtonĺÎĺ_ĺĚĺ_s Method; find linear approximations to functions using differentials; festate in words the meanings of the solutions to applied problems, attaching the appropriate units to an answer; state which parts of a mathematical statement are assumptions, such as hypotheses, and which parts are conclusions. This free course may be completed online at any time. It has been developed through a partnership with the Washington State Board for Community and Technical Colleges; the Saylor Foundation has modified some WSBCTC materials. (Mathematics 005)

The most important way to learn calculus is through problem-solving. While going through the solution to a problem, students are often faced with several issues. They may not see the connection between the concept taught in class and the solution. Others may not understand the solution because a step is missing or there are insufficient explanations. Or because they have weak algebra skills. The main goal of this exercise book is to address these issues to help students learn the material more efficiently and get better results. The book contains a wide variety of problems in integral calculus and multivariable calculus, with applications in differential equations, probability, management, and economics. Every problem has a very detailed solution, and the book is self-contained, as the summary for every concept is provided.

The most important way to learn calculus is through problem-solving. While going through the solution to a problem, students often face several issues. They may not see the connection between the concept taught in class and the solution. Others may not understand the solution because a step is missing or there are insufficient explanations. Or because they have weak algebra skills. The main goal of this exercise book is to address these issues to help students learn the material more efficiently and get better results. The book contains a wide variety of problems in differential calculus with applications in management and economics. Every problem has a very detailed solution, and the book is self-contained, as the summary for every concept is provided.

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. Due to the comprehensive nature of the material, we are offering the book in three volumes for flexibility and efficiency. Volume 1 covers functions, limits, derivatives, and integration

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. Due to the comprehensive nature of the material, we are offering the book in three volumes for flexibility and efficiency. Volume 2 covers integration, differential equations, sequences and series, and parametric equations and polar coordinates.

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. Due to the comprehensive nature of the material, we are offering the book in three volumes for flexibility and efficiency. Volume 3 covers parametric equations and polar coordinates, vectors, functions of several variables, multiple integration, and second-order differential equations.

Word Count: 7000

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This open-source book by Crowell, Robbin, and Angenent is a spin-off of a previous open-source book by Robbin and Angenent. It covers the first semester of a freshman calculus course.

With Applications to Biology and Environmental Science

Short Description:
This book is an approachable introduction to calculus with applications to biology and environmental science. For example, one application in the book is determining the volume of earth moved in the 1959 earthquake that created Quake Lake. Another application uses differential equations to model various biological examples, including moose and wolf populations at Isle Royale National Park, ranavirus in amphibians, and competing species of protozoa. The text focuses on intuitive understanding of concepts, but still covers most of the algebra and calculations common in a survey of calculus course.

Word Count: 37976

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An Open Education Resource

Short Description:
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.

Word Count: 41598

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