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.

These OpenStax Calculus I ancillary materials, including guided notes and questions using Edfinity, were developed as a result of a Round 17 Affordable Materials Grant.

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.

Continuation of Physics 1. Topics include: simple harmonic motion, gravitation, fluid mechanics, waves, the kinetic theory of gases, and the first and second laws of thermodynamics. This course is a calculus-based physics course that is required by four-year colleges in science and engineering studies.

These thoroughly illustrated sheets make use of multiple representations and can be used for unit-end summaries in inquiry-based/modeling-style courses as well as for direct instruction in didactic courses.

During this activity students will learn how to estimate population size using two techniques, density extrapolation and the mark-recapture method.

Open Textbooks for Rural Arizona participants are invited to remix this template to share their courses, textbooks, and other OER material on our Hub.

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 Project has been completed as part of a standard 10 weeks Calculus 1 asynchronous online course with optional WebEx sessions during Summer 2021 Semester at MassBay Community College, Wellesley Hills, MA.

This resource contains 95 multiple choice quiz questions inspired by Examples in the 12 chapters of University Physics Volume 2 Unit 2: Electricity and Magnetism. The quizzes have randomized numerical values, and can be printed out in two versions for students sitting side-by-side in a classroom. The current configuration creates 3-question quizzes. A study guide leads students to a practice quiz for each chapter. The number of questions in the study guide ranges from 4 to 11. The small number of questions in certain chapters does not imply that these chapters are less important -- not all examples make for good multiple choice test questions that involve numerical calculations. After this system has been field tested, more questions can be added where needed. Conceptual questions can also be added.

The selection of 3 questions from a given chapter was achieved by a random number generator. For this reason, the question selections might be less than ideal. These quizzes are not intended to have a large impact on the students' grade, but instead to encourage students to *read the textbook*. Also, since instructors know the contents of the quizzes in advance, they can compensate for idiosyncratic question selection as they prep students for the quiz.

The advantage of this system is that it is extremely convenient for instructors to use the browser's "print" option to print and distribute a quiz to the students. The disadvantage is that students and instructor have equal access to everything. Fortunately we can "hide the quizzes in plain sight". The current configuration provides 20 "renditions" of each quiz, and only the instructor knows which is selected.

The transparent nature of this unorthodox system has some advantages: Traditional methods of hiding the content of upcoming classroom exams are plagued by the fact that it is difficult to keep information secret. Instructors who use the same or similar exams for consecutive years will discover that students begin to exchange information with each other between semesters. An even more intractable problem is that testbank questions can be purchased on the internet. In this regard, the OER efforts might gain advantage over commercial ventures that sell text questions to instructors or students. The legitimate vendors (who sell to instructors) attempt to solve the "secrecy" problem by continuously modifying the textbooks, exams, and other ancillary materials. While all this ensures future revenues for the vendors, it also perpetuates costs for students.

In contrast, there is no need to modify an OER textbook by artificially creating a "new" edition. In fact, it is my experience that OER are created at a painfully slow pace, so it is unlikely that OER materials could evolve even if we wanted them to. This relatively "static" nature of OER textbooks suggests that the exams and homework problems be also "static". Instead of asking students to solve a homework problem at home, they should be quizzed on their ability to solve a problem whose solution is readily available online. Unfortunately all this tends to reduce the quality of lessons to that of rote memorization. So instead of finding interesting homework problems for which there is not solution available on the internet, we should task students with creating new homework problems and test questions. Those with less ability can be tasked with improving the posted solutions to problems that have already been solved.

Differential Equations and Linear Algebra is a free and open textbook introducing the basics of differential equations and linear algebra to undergraduate students. Students should have taken courses in Differential and Integral Calculus before using this textbook. This book is a combination of 3 open educational resources: 1. Elementary Differential Equations by William F. Trench, licensed under CC BY-NC-SA 3.0. 2. Differential Equations for Engineers by Jiří Lebl, licensed under CC BY-NC-SA 3.0. 3. A First Course in Linear Algebra (an open text) by Lyryx Learning – based on original text by Ken Kuttler, licensed under CC BY.

This Project has been completed as part of a standard 10 weeks Calculus 1 asynchronous online course with optional WebEx sessions during Summer 2021 Semester at MassBay Community College, Wellesley Hills, MA.

RocketModeler was developed at the NASA Glenn Research Center in an effort to foster hands-on, inquiry-based learning in science and math. RocketModeler is a simulator that models the design and flight of a model rocket. The program works in two modes: Design Mode or Flight Mode. In the Design Mode, you can change design variables including the size of the rocket body, the fins, and the nose cone. You can also select different materials for each component. You can select from a variety of standard solid rocket engines. The program computes the center of gravity and pressure for your rocket and determines the stability. When you have a design that you like, you can switch to the Flight Mode (shown below), where you can launch your rocket and observe its flight trajectory. You can pause at any time to record data and then continue the flight through parachute deploy and recovery. This program has recently (Oct 8, 2004) been upgraded to support stomp rockets, bottle rockets, and ballistic shells in addition to solid model rockets. It also supports both English and metric units.

Single Variable Calculus: An Introduction to Integration is a free and open textbook and is a great introduction to integration for students who have already taken courses in differential calculus. The book explains Calculus II concepts adequately, comprehensively, and concisely, and its topics are reflective of the content areas in other published Calculus textbooks. Problems in the textbook do not only test computational skills, but are also applicable and related to real-life problems and areas that students are interested in. The text gives an adequate picture of Calculus II – Integral Calculus and prepares students for other disciplines like Engineering and Physics, as well as higher-level Mathematics courses.

This Project has been completed as part of a standard 10 weeks Calculus 3 asynchronous online course with optional WebEx sessions during Summer 2021 Semester at MassBay Community College, Wellesley Hills, MA.

Calculus 1 & 2 course collection video from the UNC System OER project. This one-minute video is meant for students. It focuses on what students may think they know about the topic, what students could learn from taking the course, and a brief introduction to open educational resources.

The information shared within this website was carefully curated and designed to promote quality online teaching and learning experiences for Calculus faculty and students within the University of North Carolina System.

The information shared within this website was carefully curated and designed to promote quality online teaching and learning experiences for Calculus faculty and students within the University of North Carolina System.