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).
This text was written as a prequel to the APEXCalculus series, a three–volume series on Calculus. This text is not intended to fully prepare students with all of the mathematical knowledge they need to tackle Calculus, rather it is designed to review mathematical concepts that are often stumbling blocks in the Calculus sequence. It starts basic and builds to more complex topics. This text is written so that each section and topic largely stands on its own, making it a good resource for students in Calculus who are struggling with the supporting mathemathics found in Calculus courses. The topics were chosen based on experience; several instructors in the Applied Mathemathics Department at the Virginia Military Institute (VMI) compiled a list of topics that Calculus students commonly struggle with, giving the focus of this text. This allows for a more focused approach; at first glance one of the obvious differences from a standard Pre-Calculus text is its size.
This text is intended for a one- or two-semester undergraduate course in abstract algebra. Traditionally, these courses have covered the theoretical aspects of groups, rings, and fields. However, with the development of computing in the last several decades, applications that involve abstract algebra and discrete mathematics have become increasingly important, and many science, engineering, and computer science students are now electing to minor in mathematics. Though theory still occupies a central role in the subject of abstract algebra and no student should go through such a course without a good notion of what a proof is, the importance of applications such as coding theory and cryptography has grown significantly.
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.
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 WeBWorK exercises in each section, there are several challenging problems that require students to connect key ideas and write to communicate their understanding.
Active Calculus Multivariable is the continuation of Active Calculus to multivariable functions. The Active Calculus texts are different from most existing calculus texts in at least the following ways: the texts are 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 texts are open source, and interested instructors can gain access to the original source files upon request; the style of the texts requires students to be active learners — there are very few worked examples in the texts, 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.
This text is designed for college students who aspire to take calculus and who either need to take a course to prepare them for calculus or want to do some additional self-study. Many of the core topics of the course will be familiar to students who have completed high school. At the same time, we take a perspective on every topic that emphasizes how it is important in calculus.
This is book one in a six-book series on fundamental mathematics for adult learners. These books include glossaries, self tests, practice requests, grades records, and unit tests. Ancillary Resources include the Instructor's Manual. Topics in this book include: number and number operations, patterns, functions and relations, real life applications, geometry, and time.
: Fundamental mathematics for adult learners. Book 1 includes a Table of Contents, Glossary, Grades Records, Self Tests, Practice Tests and Unit Tests. Ancillary Resources include the Instructor's Manual. This is 1 of a series of 6 books in the ABE Math collection.
: Fundamental mathematics for adult learners. Book 2 includes a Table of Contents, Glossary, Grades Records, Self Tests, Practice Tests and Unit Tests. Ancillary Resources include the Instructor's Manual. This is 1 of a series of 6 books in the ABE Math collection.
: Fundamental mathematics for adult learners. Book 3 includes a Table of Contents, Glossary, Grades Records, Self Tests, Practice Tests and Unit Tests. Ancillary Resources include the Instructor's Manual. This is 1 of a series of 6 books in the ABE Math collection.
: Fundamental mathematics for adult learners. Book 4 includes a Table of Contents, Glossary, Grades Records, Self Tests, Practice Tests and Unit Tests. Ancillary Resources include the Instructor's Manual. This is 1 of a series of 6 books in the ABE Math collection.
: Fundamental mathematics for adult learners. Book 5 includes a Table of Contents, Glossary, Grades Records, Self Tests, Practice Tests and Unit Tests. Ancillary Resources include the Instructor's Manual. This is 1 of a series of 6 books in the ABE Math collection.
: Fundamental mathematics for adult learners. Book 6 includes a Table of Contents, Glossary, Grades Records, Self Tests, Practice Tests and Unit Tests. Ancillary Resources include the Instructor's Manual. This is 1 of a series of 6 books in the ABE Math collection.
This book is intended to help students prepare for entrance examinations in mathematics and scientific subjects, including STEP (Sixth Term Examination Papers). STEP examinations are used by Cambridge colleges as the basis for conditional offers in mathematics and sometimes in other mathematics-related subjects. They are also used by Warwick University, and many other mathematics departments recommend that their applicants practice on past papers to become accustomed to university-style mathematics.
Algebra and Trigonometry provides a comprehensive exploration of algebraic principles and meets scope and sequence requirements for a typical introductory algebra and trigonometry course. The modular approach and the richness of content ensures that the book meets the needs of a variety of courses. Algebra and Trigonometry offers a wealth of examples with detailed, conceptual explanations, building a strong foundation in the material before asking students to apply what they’ve learned.
This textbook is an introductory coverage of algorithms and data structures with application to graphics and geometry.
An openly licensed applied calculus textbook, covering derivatives, integrals, and an intro to multivariable calculus. This book is heavily remixed from Dale Hoffman's Contemporary Calculus textbook, and retains the same conceptual focus from that text.
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 Combinatorics began its life as a set of course notes we developed when Mitch was a TA for a larger than usual section of Tom’s MATH 3012: Applied Combinatorics course at Georgia Tech in Spring Semester 2006. Since then, the material has been greatly expanded and exercises have been added. The text has been in use for most MATH 3012 sections at Georgia Tech for several years now. Since the text has been available online for free, it has also been adopted at a number of other institutions for a wide variety of courses. In August 2016, we made the first release of Applied Combinatorics in HTML format, thanks to a conversion of the book’s source from LaTeX to MathBook XML. An inexpensive print-on-demand version is also available for purchase. Find out all about ways to get the book.
Since Fall 2016, Applied Combinatorics has been on the list of approved open textbooks from the American Institute of Mathematics.
The wide range of examples in the text are meant to augment the "favorite examples" that most instructors have for teaching the topcs in discrete mathematics.
To provide diagnostic help and encouragement, we have included solutions and/or hints to the odd-numbered exercises. These solutions include detailed answers whenever warranted and complete proofs, not just terse outlines of proofs.
Our use of standard terminology and notation makes Applied Discrete Structures a valuable reference book for future courses. Although many advanced books have a short review of elementary topics, they cannot be complete.
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.
An Instructor's Guide is available to any instructor who uses the text.
This applied mathematics textbook covers Matrices and Pathways, Statistics and Probability, Finance, Cyclic, Recursive and Fractal Patterns, Vectors, and Design. The approach used is primarily data driven, using numerical and geometrical problem-solving techniques.
This is a "first course" in the sense that it presumes no previous course in probability. The units are modules taken from the unpublished text: Paul E. Pfeiffer, ELEMENTS OF APPLIED PROBABILITY, USING MATLAB. The units are numbered as they appear in the text, although of course they may be used in any desired order. For those who wish to use the order of the text, an outline is provided, with indication of which modules contain the material.
The primary learning objective of this textbook is to introduce the reader to the fundamental statistical methods and basic analytical procedures associated with processing data in regard to healthcare research. It is intended that by working through the applications and practice problems, readers should be able to understand and apply some of the methods for developing, implementing, and applying healthcare statistic principles in research.
Arithmetic | Algebra provides a customized open-source textbook for the math developmental students at New York City College of Technology. The book consists of short chapters, addressing essential concepts necessary to successfully proceed to credit-level math courses. Each chapter provides several solved examples and one unsolved “Exit Problem”. Each chapter is also supplemented by its own WeBWork online homework assignment. The book can be used in conjunction with WeBWork for homework (online) or with the Arithmetic | Algebra Homework handbook (traditional). The content in the book, WeBWork and the homework handbook are also aligned to prepare students for the CUNY Elementary Algebra Final Exam (CEAFE).
Arithmetic | Algebra Homework book is a static version of the WeBWork online homework assignments that accompany the textbook Arithmetic | Algebra for the developmental math courses MAT 0630 and MAT 0650 at New York City College of Technology, CUNY.
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.
This free online textbook is a one semester course in basic analysis. These were my lecture notes for teaching Math 444 at the University of Illinois at Urbana-Champaign (UIUC) in fall 2009. The course is a first course in mathematical analysis aimed at students who do not necessarily wish to continue a graduate study in mathematics. A Sample Darboux sums prerequisite for the course is a basic proof course. The course does not cover topics such as metric spaces, which a more advanced course would. It should be possible to use these notes for a beginning of a more advanced course, but further material should be added.
This book provides a brief introduction to some common ideas in the study of probability. At the University of Minnesota, this material is included in a course on College Algebra designed to give students the basic skills to take an introductory Statistics course. The material itself is basic, and should be within the grasp of students who have successfully completed a high school Algebra I course. It comprises approximately three weeks worth of material at the college level; a typical college student would spend about 45 hours total learning this material.
This book will initiate you into an esoteric world. You will learn and apply the methods of thought that mathematicians use to verify theorems, explore mathematical truth and create new mathematical theories. This will prepare you for advanced mathematics courses, for you will be better able to understand proofs, write your own proofs and think critically and inquisitively about mathematics.
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 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.
This textbook was written to meet the needs of a twenty-first century student. It takes a systematic approach to helping students learn how to think and centers on a structured process termed the PUPP Model (Plan, Understand, Perform, and Present). This process is found throughout the text and in every guided example to help students develop a step-by-step problem-solving approach.
This textbook simplifies and integrates annuity types and variable calculations, utilizes relevant algebraic symbols, and is integrated with the Texas Instruments BAII+ calculator. It also contains structured exercises, annotated and detailed formulas, and relevant personal and professional applications in discussion, guided examples, case studies, and even homework questions.
This Business Mathematics courses aim to have students understand basic business problems, interpret them in mathematical terms, and use the tools of mathematics to solve these problems. The objective of this material is to provide mathematical theory, demonstration and practice for first-year Business students. A grade of C+ or better in Algebra 11 (or equivalent) is the prerequisite for this course; students requiring extensive review or remedial work are expected to have completed a preparatory course such as OPMT 0199, which is offered through part-time studies at BCIT. These notes explain the applications of basic mathematics to business and industry using ratios, functions and graphs, simple and compound interest, financial instruments and discounting, annuities, mortgages, loans, and leases. Cash-flow analysis applying rates of return, net present value, and payback is included.
Published in 1991 by Wellesley-Cambridge Press, the book is a useful resource for educators and self-learners alike. It is well organized, covers single variable and multivariable calculus in depth, and is rich with applications.
In addition to the Textbook, there is also an online Instructor's Manual and a student Study Guide. Prof. Strang has also developed a related series of videos, Highlights of Calculus, on the basic ideas of calculus.
Calculus-Based Physics is an introductory physics textbook designed for use in the two-semester introductory physics course typically taken by science and engineering students.
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.
To practice and develop an understanding of topics, this text offers a range of problems, from routine to challenging, with selected solutions. As this is an open text, instructors and students are encouraged to interact with the textbook through annotating, revising, and reusing to your advantage. Suggestions for contributions to this growing textbook are welcome.
Lyryx develops and supports open texts, with editorial services to adapt the text for each particular course. In addition, Lyryx provides content-specific formative online assessment, a wide variety of supplements, and in-house support available 7 days/week for both students and instructors.
Calculus is about the very large, the very small, and how things change—the surprise is that something seemingly so abstract ends up explaining the real world.
This course is a first and friendly introduction to calculus, suitable for someone who has never seen the subject before, or for someone who has seen some calculus but wants to review the concepts and practice applying those concepts to solve problems. One learns calculus by doing calculus, and so this course is based around doing practice problems.
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
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