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.

Word Count: 7000

(Note: This resource's metadata has been created automatically by reformatting and/or combining the information that the author initially provided as part of a bulk import process.)

The most important way to learn calculus is through problem-solving. While going through the solution to a problem, students are often faced with several issues. They may not see the connection between the concept taught in class and the solution. Others may not understand the solution because a step is missing or there are insufficient explanations. Or because they have weak algebra skills. The main goal of this exercise book is to address these issues to help students learn the material more efficiently and get better results. The book contains a wide variety of problems in integral calculus and multivariable calculus, with applications in differential equations, probability, management, and economics. Every problem has a very detailed solution, and the book is self-contained, as the summary for every concept is provided.

This 8-minute video lecture demonstrates how to use a position vector valued function to describe a curve or path. [Calculus playlist: Lesson 133 of 156]

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.

This series of videos focusing on calculus covers parameterizing a surface, surface integrals, stokes' theorem.

This series of videos focusing on calculus covers line integral of scalar and vector-valued functions, Green's Theorem and 2-D Divergence Teorem.

Word Count: 60034

(Note: This resource's metadata has been created automatically by reformatting and/or combining the information that the author initially provided as part of a bulk import process.)

Short Description:
Welcome to the OER companion to Baylor University's Math 1121: The Calculus Supplement Course, an optional, co-requisite course for students enrolled in Calculus 1. This OER was designed to provide 'just in time' support for the algebraic, trigonometric, and geometric relationships undergirding Calculus 1.

Long Description:
Welcome to the OER companion for Baylor University’s Math 1121: The Calculus Supplement Course! Math 1121 is an optional, co-requisite course for students enrolled in Calculus 1. This OER was designed to provide ‘just in time’ support for the algebraic, trigonometric, and geometric relationships undergirding Calculus 1. The topics and content were deliberately sequenced to coincide with the topics and content Calculus 1 students engage as they study limits, derivatives, applications of derivatives, and integration. Therefore, this text first reviews the essential functions from Pre-Calculus that students need to be successful in Calculus 1. Then, it examines the properties and algebraic transformations of those functions and reinforces strategies for analyzing functions. Finally, it bolsters the relationships between algebra and geometry that the Fundamental Theorem of Calculus and integrals bring together for Calculus 1 students. Although this OER was designed to support Calculus 1 students, there is almost no Calculus within these ‘pages.’ Rather, the focus is on everything that happens in a Calculus problem after that first Calculus step. Enjoy!

Word Count: 77096

(Note: This resource's metadata has been created automatically by reformatting and/or combining the information that the author initially provided as part of a bulk import process.)

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.

This course is a brief introduction to sequences and infinite series. We begin with a discussion of power series and develop tests for convergence and non-convergence. Taylor series are introduced and lead to an analysis of power series in general. This is a 1-credit course that can be taken any time after the student has completed Calculus I.

APEX Calculus is a freely-available comprehensive textbook. Using this textbook and specially created WeBWorK exercises, Drs. Ault and Goel implemented a no-cost option for Calculus I at Valdosta State University in Fall 2015.

This Project has been completed as part of a standard 10 weeks Calculus 1 face to face course during Summer 2022 semester at MassBay Community College, Wellesley Hills, MA.

This is a variation on 18.02 Multivariable Calculus. It covers the same topics as in 18.02, but with more focus on mathematical concepts.
Acknowledgement
Prof. McKernan would like to acknowledge the contributions of Lars Hesselholt to the development of this course.

Short Description:
Note: This OpenStax book was imported into Pressbooks on August 20, 2019, to make it easier for instructors to edit, build upon, and remix the content. The OpenStax import process isn't perfect, so there are a number of formatting errors in the book that need attention. As such, we don't recommend you use this book in the classroom. This also means that, while the original version of this book is accessible, this Pressbooks copy is not. For information about how to get your own copy of this book to work on, see the Add Content part in the Pressbooks Guide. You can access the original version of this textbook here: Calculus Volume 1: OpenStax.

Long Description:
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.

Please note that this title is published under a CC BY-NC-SA 4.0 license, which means that you are free to use and adapt, but not for commercial purposes. Changes you make need to be shared using this license.

Word Count: 204139

(Note: This resource's metadata has been created automatically as part of a bulk import process by reformatting and/or combining the information that the author initially provided. As a result, there may be errors in formatting.)

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.

Math of Biological/Management/Social Sciences presents intuitive development of the calculus of polynomial, exponential and logarithmic functions, and extrema theory and applications.

Course Outcomes:
1. Apply calculus to solve problems with confidence, persistence, and openness to alternate approaches.
2. Interpret and communicate the concepts of rates of change and derivatives.
3. Connect the graphical behavior, numerical patterns and symbolic representations of function and derivatives.
4. Collaborate to solve calculus problems related to their field of study.
5. Recognize when and how to proficiently apply calculus tools to solve problems in business management, social sciences and and biological sciences.
6. Use a graphing calculator and/or other technology to solve applied problems.

This is a lesson on finding the difference between an implicit and explicit function and finding the derivative of functions implicitly. It also covers finding the equation of a tangent line from a function in implicit form . There are self check throughout the lesson. The text that I use in my calculus class is Larson Calculus 11th edition. This corresponds to chapter 2 section 5 in that text but Implicit Differentiation is a common topic in any Calculus I or AP Calculus course.

Short Description:
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.

Word Count: 7075

(Note: This resource's metadata has been created automatically by reformatting and/or combining the information that the author initially provided as part of a bulk import process.)