Our writing is based on three premises. First, life sciences students are motivated by and respond well to actual data related to real life sciences problems. Second, the ultimate goal of calculus in the life sciences primarily involves modeling living systems with difference and differential equations. Understanding the concepts of derivative and integral are crucial, but the ability to compute a large array of derivatives and integrals is of secondary importance. Third, the depth of calculus for life sciences students should be comparable to that of the traditional physics and engineering calculus course; else life sciences students will be short changed and their faculty will advise them to take the 'best' (engineering) course.

Our writing is based on three premises. First, life sciences students are motivated by and respond well to actual data related to real life sciences problems. Second, the ultimate goal of calculus in the life sciences primarily involves modeling living systems with difference and differential equations. Understanding the concepts of derivative and integral are crucial, but the ability to compute a large array of derivatives and integrals is of secondary importance. Third, the depth of calculus for life sciences students should be comparable to that of the traditional physics and engineering calculus course; else life sciences students will be short changed and their faculty will advise them to take the 'best' (engineering) course.

In our text, mathematical modeling and difference and differential equations lead, closely follow, and extend the elements of calculus. Chapter one introduces mathematical modeling in which students write descriptions of some observed processes and from these descriptions derive first order linear difference equations whose solutions can be compared with the observed data. In chapters in which the derivatives of algebraic, exponential, or trigonometric functions are defined, biologically motivated differential equations and their solutions are included. The chapter on partial derivatives includes a section on the diffusion partial differential equation. There are two chapters on non-linear difference equations and on systems of two difference equations and two chapters on differential equations and on systems of differential equation.

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).

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.

These notes are intended to provide a brief, 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.

Our goal with this textbook is to provide students with a strong foundation in mathematical analysis. Such a foundation is crucial for future study of deeper topics of analysis. Students should be familiar with most of the concepts presented here after completing the calculus sequence. However, these concepts will be reinforced through rigorous proofs.
The textbook contain topics of real analysis usually covered in a 10-week course: the completeness axiom, sequences and convergence, continuity, and differentiation. The lecture notes also contain many well-selected exercises of various levels. Although these topics are written in a more abstract way compared with those available in some textbooks, teachers can choose to simplify them depending on the background of the students. For instance, rather than introducing the topology of the real line to students, related topological concepts can be replaced by more familiar concepts such as open and closed intervals. Some other topics such as lower and upper semicontinuity, differentiation of convex functions, and generalized differentiation of non-differentiable convex functions can be used as optional mathematical projects. In this way, the lecture notes are suitable for teaching students of different backgrounds.

This is a text for a two-term course in introductory real analysis for junior or senior mathematics majors and science students with a serious interest in mathematics. Prospective educators or mathematically gifted high school students can also benefit from the mathematical maturity that can be gained from an introductory real analysis course.

The book is designed to fill the gaps left in the development of calculus as it is usually presented in an elementary course, and to provide the background required for insight into more advanced courses in pure and applied mathematics. The standard elementary calculus sequence is the only specific prerequisite for Chapters 1–5, which deal with real-valued functions. (However, other analysis oriented courses, such as elementary differential equation, also provide useful preparatory experience.) Chapters 6 and 7 require a working knowledge of determinants, matrices and linear transformations, typically available from a first course in linear algebra. Chapter 8 is accessible after completion of Chapters 1–5.

This is a Calculus I interactive textbook with modules curated and created on The Ohio State University's Ximera platform.

The software upon which this interactive textbook was built is licensed under a GNU General Public License v.2.0, and therefore this resource caries the same license. Pursuant to this license, no warranties are made.

Review the license terms at https://github.com/XimeraProject/server/blob/master/LICENSE

This is a Calculus II interactive textbook with modules curated and created on The Ohio State University's Ximera platform.

The software upon which this interactive textbook was built is licensed under a GNU General Public License v.2.0, and therefore this resource caries the same license. Pursuant to this license, no warranties are made.

Review the license terms at https://github.com/XimeraProject/server/blob/master/LICENSE

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.

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.

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 is a short introduction to the fundamentals of real analysis. Although the prerequisites are few, I have written the text assuming the reader has the level of mathematical maturity of one who has completed the standard sequence of calculus courses, has had some exposure to the ideas of mathematical proof (including induction), and has an acquaintance with such basic ideas as equivalence relations and the elementary algebraic properties of the integers.

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.

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.

I intend this book to be, firstly, a introduction to calculus based on the hyperreal number 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 as Abraham Robinson's Non-standard Analysis or Robert Goldblatt's Lectures on the Hyperreals. Secondly, I have aimed the text primarily at readers who already have some familiarity with calculus. Although the book does not explicitly assume any prerequisites beyond basic algebra and trigonometry, in practice the pace is too fast for most of those without some acquaintance with the basic notions of calculus.