tag:open.umn.edu,2005:/opentextbooks/subjects/calculusOpen Textbook Library - Calculus Textbooks2024-03-04T00:43:49Zhttps://open.umn.edu/assets/common/favicon/favicon-1594c2156c95ca22b1a0d803d547e5892bb0e351f682be842d64927ecda092e7.icohttps://open.umn.edu/assets/library/otl_logo-f9161d5c999f5852b38260727d49b4e7d7142fc707ec9596a5256a778f957ffc.png16102024-03-04T00:54:46Z2024-03-04T00:55:31ZBusiness Calculus with Excel<img alt="Read more about Business Calculus with Excel" title="Business Calculus with Excel cover image" class="cover " width="727" height="939" data-controller="cover" data-placeholder="/assets/common/placeholder-0e0607cbc50663ddb9e8fd188058bcd2630c730ef6ee322801278607b7d5af8e.png" src="/rails/active_storage/blobs/redirect/eyJfcmFpbHMiOnsiZGF0YSI6MTEyMzUsInB1ciI6ImJsb2JfaWQifX0=--84274e3eac03a3fc6b37c07b2279e23c8588b9be/buscalc.jpg" />This text is intended for a one semester calculus course for business students with the equivalent of a college algebra prerequisite. Rather than being a three-semester engineering calculus course that has been watered down to fit into one semester it is designed for the business students.12852022-11-21T15:36:01Z2024-01-22T14:52:35ZCalculus in Context - 2008 Edition<img alt="Read more about Calculus in Context - 2008 Edition" title="Calculus in Context - 2008 Edition cover image" class="cover " width="116" height="150" data-controller="cover" data-placeholder="/assets/common/placeholder-0e0607cbc50663ddb9e8fd188058bcd2630c730ef6ee322801278607b7d5af8e.png" src="/rails/active_storage/blobs/redirect/eyJfcmFpbHMiOnsiZGF0YSI6NDI5OCwicHVyIjoiYmxvYl9pZCJ9fQ==--30786bfc780aa576f7d44297142db57f19183910/thumbnail.jpeg" />Designing the curriculum We believe that calculus can be for students what it was for Euler and the Bernoullis: a language and a tool for exploring the whole fabric of science. We also believe that much of the mathematical depth and vitality of calculus lies in connections to other sciences. The mathematical questions that arise are compelling in part because the answers matter to other disciplines. We began our work with a "clean slate," not by asking what parts of the traditional course to include or discard. Our starting points are thus our summary of what calculus is really about. Our curricular goals are what we aim to convey about the subject in the course. Our functional goals describe the attitudes and behaviors we hope our students will adopt in using calculus to approach scientific and mathematical questions. Starting Points Calculus is fundamentally a way of dealing with functional relationships that occur in scientific and mathematical contexts. The techniques of calculus must be subordinate to an overall view of the questions that give rise to these relationships. Technology radically enlarges the range of questions we can explore and the ways we can answer them. Computers and graphing calculators are much more than tools for teaching the traditional calculus. The concept of a dynamical system is central to science. Therefore, differential equations belong at the center of calculus, and technology makes this possible at the introductory level. The process of successive approximation is a key tool of calculus, even when the outcome of the process--the limit--cannot be explicitly given in closed form. Curricular Goals Develop calculus in the context of scientific and mathematical questions. Treat systems of differential equations as fundamental objects of study. Construct and analyze mathematical models. Use the method of successive approximations to define and solve problems. Develop geometric visualization with hand-drawn and computer graphics. Give numerical methods a more central role. Functional Goals Encourage collaborative work. Enable students to use calculus as a language and a tool. Make students comfortable tackling large, messy, ill-defined problems. Foster an experimental attitude towards mathematics. Help students appreciate the value of approximate solutions. Teach students that understanding grows out of working on problems. Impact of Technology Differential equations can now be solved numerically, so they can take their rightful place in the introductory calculus course. The ability to handle data and perform many computations makes exploring messy, real-world problems possible. Since we can now deal with credible models, the role of modelling becomes much more central to the subject. The text illustrates how we have pursued the curricular goals. Each goal is addressed within the first chapter which begins with questions about describing and analyzing the spread of a contagious disease. A model is built: a model which is actually a system of coupled non-linear differential equations. We then begin a numerical exploration on those equations, and the door is opened to a solution by successive approximations. Our implementation of the functional goals is also evident. The text has many more words than the traditional calculus book--it is a book to be read. The exercises make unusual demands on students. Most are not just variants of examples that have been worked in the text. In fact, the text has rather few "template'' examples. Shifts in Emphasis It will also become apparent to you that the text reflects substantial shifts in emphasis in comparison to the traditional course. Here are some of the most striking: How the emphasis shifts: increase: concepts, geometry, graphs, brute force, numerical solutions decrease: techniques, algebra, formulas, elegance, closed-form solutions Since we all value elegance, let us explain what we mean by "brute force." Euler's method is a good example. It is a general method of wide applicability. Of course when we use it to solve a differential equation like y'(t) = t, we are using a sledgehammer to crack a peanut. But at least the sledgehammer works. Moreover, it works with coconuts (like y' = y(1 - y/10)), and it will even knock down a house (like y' = cos2(t)). Students also see the elegant special methods that can be invoked to solve y' = t and y' = y(1 - y/10) (separation of variables and partial fractions are discussed in chapter 11), but they understand that they are fortunate indeed when a real problem will succumb to such methods.10372021-08-16T15:51:57Z2024-01-22T14:52:26ZOptimal, Integral, Likely Optimization, Integral Calculus, and Probability for Students of Commerce and the Social Sciences<img alt="Read more about Optimal, Integral, Likely Optimization, Integral Calculus, and Probability for Students of Commerce and the Social Sciences" title="Optimal, Integral, Likely Optimization, Integral Calculus, and Probability for Students of Commerce and the Social Sciences cover image" class="cover " width="501" height="649" data-controller="cover" data-placeholder="/assets/common/placeholder-0e0607cbc50663ddb9e8fd188058bcd2630c730ef6ee322801278607b7d5af8e.png" src="/rails/active_storage/blobs/redirect/eyJfcmFpbHMiOnsiZGF0YSI6MjczMywicHVyIjoiYmxvYl9pZCJ9fQ==--1b53df3c71e355ecebf13e96d9872405e54035bf/new%20boosask.JPG" />Optimal, Integral, Likely is a free, open-source textbook intended for UBC’s course MATH 105: Integral Calculus with Applications to Commerce and Social Sciences. It is shared under the Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International License.9482021-01-12T19:46:24Z2024-01-22T14:52:19ZElementary Calculus<img alt="Read more about Elementary Calculus" title="Elementary Calculus cover image" class="cover " width="168" height="200" data-controller="cover" data-placeholder="/assets/common/placeholder-0e0607cbc50663ddb9e8fd188058bcd2630c730ef6ee322801278607b7d5af8e.png" src="/rails/active_storage/blobs/redirect/eyJfcmFpbHMiOnsiZGF0YSI6MTkzNCwicHVyIjoiYmxvYl9pZCJ9fQ==--69c475791ba78745db100f67fd2c2fff9f3a61d5/calc12book-small.png" />This textbook covers calculus of a single variable, suitable for a year-long (or two-semester) course. Chapters 1-5 cover Calculus I, while Chapters 6-9 cover Calculus II. The book is designed for students who have completed courses in high-school algebra, geometry, and trigonometry. Though designed for college students, it could also be used in high schools. The traditional topics are covered, but the old idea of an infinitesimal is resurrected, owing to its usefulness (especially in the sciences). There are 943 exercises in the book, with answers and hints to selected exercises.7802019-10-12T17:54:05Z2024-01-22T14:52:05ZMultivariable Calculus<img alt="Read more about Multivariable Calculus" title="Multivariable Calculus cover image" class="cover " width="760" height="986" data-controller="cover" data-placeholder="/assets/common/placeholder-0e0607cbc50663ddb9e8fd188058bcd2630c730ef6ee322801278607b7d5af8e.png" src="/rails/active_storage/blobs/redirect/eyJfcmFpbHMiOnsiZGF0YSI6NzM5LCJwdXIiOiJibG9iX2lkIn19--72d8691db19325f0b8925daeafd35b6ddb1ebd43/0000MulvarCal.png" />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.6742019-02-28T17:39:48Z2024-01-22T14:52:03ZAPEX PreCalculus<img alt="Read more about APEX PreCalculus" title="APEX PreCalculus cover image" class="cover " width="641" height="833" data-controller="cover" data-placeholder="/assets/common/placeholder-0e0607cbc50663ddb9e8fd188058bcd2630c730ef6ee322801278607b7d5af8e.png" src="/rails/active_storage/blobs/redirect/eyJfcmFpbHMiOnsiZGF0YSI6NjE5LCJwdXIiOiJibG9iX2lkIn19--e024b479ad3a18cf736ee2dd390243d1bf373b19/0000APEPreCal.png" />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.5572018-09-07T17:22:10Z2024-01-22T18:54:25ZIntroduction to GNU Octave: A brief tutorial for linear algebra and calculus students<img alt="Read more about Introduction to GNU Octave: A brief tutorial for linear algebra and calculus students" title="Introduction to GNU Octave: A brief tutorial for linear algebra and calculus students cover image" class="cover " width="2550" height="3300" data-controller="cover" data-placeholder="/assets/common/placeholder-0e0607cbc50663ddb9e8fd188058bcd2630c730ef6ee322801278607b7d5af8e.png" src="/rails/active_storage/blobs/redirect/eyJfcmFpbHMiOnsiZGF0YSI6NDgwLCJwdXIiOiJibG9iX2lkIn19--d84822615a72b4a50f7edc601d27f4d86886aa5d/0000IntroGNUO.png" />This brief book provides a noncomprehensive introduction to GNU Octave, a free open source alternative to MatLab. The basic syntax and usage is explained through concrete examples from the mathematics courses a math, computer science, or engineering major encounters in the first two years of college: linear algebra, calculus, and differential equations.5252018-09-07T17:22:07Z2024-01-22T14:51:57ZOrdinary Differential Equations<img alt="Read more about Ordinary Differential Equations" title="Ordinary Differential Equations cover image" class="cover " width="992" height="1352" data-controller="cover" data-placeholder="/assets/common/placeholder-0e0607cbc50663ddb9e8fd188058bcd2630c730ef6ee322801278607b7d5af8e.png" src="/rails/active_storage/blobs/redirect/eyJfcmFpbHMiOnsiZGF0YSI6NDUwLCJwdXIiOiJibG9iX2lkIn19--873e177a890dcc2ba4f0311c9af50a68cba0857a/0000OrdDifEqu.png" />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.4872018-09-07T17:22:05Z2024-01-22T14:52:16ZActive Calculus Multivariable<img alt="Read more about Active Calculus Multivariable" title="Active Calculus Multivariable cover image" class="cover " width="115" height="150" data-controller="cover" data-placeholder="/assets/common/placeholder-0e0607cbc50663ddb9e8fd188058bcd2630c730ef6ee322801278607b7d5af8e.png" src="/rails/active_storage/blobs/redirect/eyJfcmFpbHMiOnsiZGF0YSI6MTg4NCwicHVyIjoiYmxvYl9pZCJ9fQ==--e468f2fa00b3974f8cfa244ed63b8ec7ed0c8040/multivar.jpg" />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.4622018-09-07T17:22:03Z2024-01-22T14:51:56ZYet Another Calculus Text<img alt="Read more about Yet Another Calculus Text" title="Yet Another Calculus Text cover image" class="cover " width="918" height="982" data-controller="cover" data-placeholder="/assets/common/placeholder-0e0607cbc50663ddb9e8fd188058bcd2630c730ef6ee322801278607b7d5af8e.png" src="/rails/active_storage/blobs/redirect/eyJfcmFpbHMiOnsiZGF0YSI6MzkwLCJwdXIiOiJibG9iX2lkIn19--f1805b3a2845e36d11c47d73a12ced8699166fca/0000YetAnoCal.png" />I intend this book to be, firstly, a introduction to calculus based on the hyperrealnumber system. In other words, I will use infinitesimal and infinite numbers freely. Just as most beginning calculus books provide no logical justification for the real number system, I will provide none for the hyperreals. The reader interested in questions of foundations should consult books such asAbraham Robinson's Non-standard Analysis or Robert Goldblatt's Lectures onthe Hyperreals. Secondly, I have aimed the text primarily at readers who already have somefamiliarity with calculus. Although the book does not explicitly assume any prerequisites beyond basic algebra and trigonometry, in practice the pace istoo fast for most of those without some acquaintance with the basic notions of calculus.
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