30 Calculus
3D Interactive Plots for Multivariate Calculus 
Na Yu (Toronto Metropolitan University)
2022
Licence: CC BY-NC-SA
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.
Format: Online
Suggested for: MATH 365
Active Calculus Multivariable
Steve Schlicker, David Austin, and Matthew Boelkins (Grand Valley State University)
2017
Licence: CC BY-NC-SA
Active Calculus Multivariable is the continuation of Active Calculus to multivariable functions. In Active Calculus Multivariable, we endeavor to actively engage students in learning the subject through an activity-driven approach in which the vast majority of the examples are completed by students. Where many texts present a general theory of calculus followed by substantial collections of worked examples, we instead pose problems or situations, consider possibilities, and then ask students to investigate and explore. Following key activities or examples, the presentation normally includes some overall perspective and a brief synopsis of general trends or properties, followed by formal statements of rules or theorems. While we often offer plausibility arguments for such results, rarely do we include formal proofs. It is not the intent of this text for the instructor or author to demonstrate to students that the ideas of calculus are coherent and true, but rather for students to encounter these ideas in a supportive, leading manner that enables them to begin to understand for themselves why calculus is both coherent and true.
Formats: Online, PDF, and LaTex
Suggested for: MATH 365
Active Calculus 2.0
Matt Boelkins, David Austin, and Steve Schlicker (Grand Valley State University)
2017
Licence: CC BY-NC-SA
Active Calculus (2017 edition) may be used as a stand-alone textbook for a standard first-semester college calculus course or as a supplement to a more traditional text. Chapters 1–4 address the typical topics for differential calculus, while Chapters 5–8 provide the standard topics of integral calculus, including a chapter on differential equations (Chapter 7) and on infinite series (Chapter 8). In Active Calculus, we endeavor to actively engage students in learning the subject through an activity-driven approach in which the vast majority of the examples are completed by students. We pose problems or situations, consider possibilities, and then ask students to investigate and explore. It is not the intent of this text for the instructor or author to demonstrate to students that the ideas of calculus are coherent and true, but rather for students to encounter these ideas in a supportive, leading manner that enables them to begin to understand for themselves why calculus is both coherent and true.
Formats: Online and PDF
Suggested for: MATH 265, MATH 266
APEX Calculus
Gregory Hartman (Virginia Military Institute), Brian Heinold (Mount St. Mary’s University), Troy Siemers (Virginia Military Institute), Dimplekumar Chalishajar (Virginia Military Institute), and Jennifer Bowen (The College of Wooster)
2014
Licence: CC BY-NC
This text comprises a three–text series on Calculus. The first part covers material taught in many “Calc 1” courses: limits, derivatives, and the basics of integration, found in Chapters 1 through 6.1. The second text covers material often taught in “Calc 2:” integration and its applications, along with an introduction to sequences, series and Taylor Polynomials, found in Chapters 5 through 8. The third text covers topics common in “Calc 3” or “multivariable calc:” parametric equations, polar coordinates, vector–valued functions, and functions of more than one variable, found in Chapters 9 through 14.
Format: PDF
Suggested for: MATH 265, MATH 266
Applied Calculus
Shana Calaway (Shoreline Community College), Dale Hoffman (Bellevue College), and David Lippman (Pierce College Ft Steilacoom)
2014
Licence: CC BY
This text covers all of the concepts of first-year calculus with a balance of application and theory.
Format: PDF
Suggested for: MATH 260
Business Calculus with Excel
Mike May (Saint Louis University)
2024
Licence: CC BY-NC-SA
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.
Format: Online, PDF
Suggested for: MATH 260, MATH 244
Calculus
Gilbert Strang (MIT)
1991
Licence: CC BY-NC-SA
Originally published through traditional means, this textbook is now available as an open educational resource. This text includes single and multivariable calculus and was written by a professor of mathematics at the Massachusetts Institute of Technology.
Format: PDF
Suggested for: MATH 265, MATH 266, MATH 365
Calculus Early Transcendentals: Integral & Multi-Variable Calculus for Social Sciences
Petra Menz and Nicola Mulberry (Simon Fraser University)
2018
Licence: CC BY-NC-SA
Calculus Early Transcendentals: Integral & Multi-Variable Calculus for Social Sciences has been redesigned in the Department of Mathematics at Simon Fraser University from Calculus Early Transcendentals by Lyryx. Substantial portions of the content, examples, and diagrams have been redeveloped to meet the needs of social science calculus. Additional contributions have been provided by an experienced and practicing instructor. The textbook is approachable, cohesive, and suitable for standard integral calculus courses offering a comprehensive treatment of the necessary calculus techniques and concepts.
Format: PDF
Suggested for: MATH 260
Calculus Volume 1
Gilbert Strang (Massachusetts Institute of Technology) and Edwin Herman (University of Wisconsin-Stevens Point) (OpenStax)
2016
Licence: CC BY-NC-SA
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.
Formats: Online and PDF; online LibreTexts version
Suggested for: MATH 265
Calculus Volume 2
Gilbert Strang (Massachusetts Institute of Technology) (Open Stax)
2016
Licence: CC BY-NC-SA
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.
Formats: Online and PDF; online LibreTexts version
Suggested for: MATH 266
Calculus Volume 3
Gilbert Strang (Massachusetts Institute of Technology) (Open Stax)
2016
Licence: CC BY-NC-SA
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.
Formats: Online and PDF; online LibreTexts version
Suggested for: MATH 365
CLP-1 Differential Calculus
Joel Feldman, Andrew Rechnitzer, and Elyse Yeager
2023
Licence: CC BY-NC-SA
The CLP Calculus Textbooks and problem books were written for standard university Calculus 1, 2, 3 and 4 courses at the Department of Mathematics, UBC. The authors are three UBC Mathematics Department faculty, Joel Feldman, Andrew Rechnitzer and Elyse Yeager. Information on how to obtain the source files for the CLP texts can be found here.
Format: PDF
Suggested for: MATH 265
CLP-2 Integral Calculus
Joel Feldman, Andrew Rechnitzer, and Elyse Yeager
2023
Licence: CC BY-NC-SA
The CLP Calculus Textbooks and problem books were written for standard university Calculus 1, 2, 3 and 4 courses at the Department of Mathematics, UBC. The authors are three UBC Mathematics Department faculty, Joel Feldman, Andrew Rechnitzer and Elyse Yeager. Information on how to obtain the source files for the CLP texts can be found here.
Format: PDF
Suggested for: MATH 266
CLP-3 Multivariable Calculus
Joel Feldman, Andrew Rechnitzer, and Elyse Yeager
2023
Licence: CC BY-NC-SA
The CLP Calculus Textbooks and problem books were written for standard university Calculus 1, 2, 3 and 4 courses at the Department of Mathematics, UBC. The authors are three UBC Mathematics Department faculty, Joel Feldman, Andrew Rechnitzer and Elyse Yeager. Information on how to obtain the source files for the CLP texts can be found here.
Format: PDF
Suggested for: MATH 365
CLP-4 Vector Calculus
Joel Feldman, Andrew Rechnitzer, and Elyse Yeager
2023
Licence: CC BY-NC-SA
The CLP Calculus Textbooks and problem books were written for standard university Calculus 1, 2, 3 and 4 courses at the Department of Mathematics, UBC. The authors are three UBC Mathematics Department faculty, Joel Feldman, Andrew Rechnitzer and Elyse Yeager. Information on how to obtain the source files for the CLP texts can be found here.
Format: PDF
Suggested for: MATH 365
Community Calculus (Single, Multivariable)
David Guichard (Whitman College)
2023
Licence: CC BY-NC-SA
This online compilation of four calculus textbooks is frequently updated and has been used in courses. It has been positively reviewed by the Mathematical Association of America. It also covers early and late transcendentals.
Format: PDF
Suggested for: MATH 365. MATH 265, MATH 266
Contemporary Calculus
Dale Hoffman (Bellevue College) and Jeff Eldridge (Edmonds Community College)
2018
Licence: CC BY-SA
Chapters 0-3 cover differential calculus while chapters 4-8 cover integral calculus.
Formats: PDF and LaTeX
Suggested for: MATH 265, 266
Differential Calculus for the Life Sciences
Leah Edelstein-Keshet (University of British Columbia)
2017
Licence: CC BY-NC-SA
This textbook was written by a math professor at the University of British Columbia and is currently used as a textbook for introductory calculus courses for life sciences undergraduates.
Format: PDF
Suggested for: MATH 265, MATH 260
Elementary Calculus
Michael Corral, Schoolcraft College
2020
Licence: Free Documentation License (GNU)
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.
Formats: PDF, LaTex
Suggested for: MATH 265, MATH 266
Optimal, Integral, Likely: Optimization, Integral Calculus, and Probability
Bruno Belevan, Parham Hamidi, Nisha Malhotra, and Elisse Yeager (University of British Columbia)
2020
Licence: CC BY-NC-SA
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.
Format: PDF
Suggested for: MATH 260
Vector Calculus
Michael Corral (Schoolcraft College)
2022
GNU Free Documentation Licence
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.
Format: PDF
