Exploring Calculus
Labs and Projects with Mathematica
📘 About This Book
This text is meant to be a hands-on lab manual that can be used in class every day to guide the exploration of the theory and applications of differential and integral calculus. For the most part, labs can be used individually or in a sequence. Each lab consists of an explanation of material with integrated exercises. Some labs are split into multiple subsections and thus exercises are separated by those subsections. The exercise sections integrate problems, technology, Mathematica R visualization, and Mathematica CDFs that allow students to discover the theory and applications of differential and integral calculus in a meaningful and memorable way. Employs Mathematica to calculate and explore concepts and theories of calculus Uses engaging labs to inspire learning Includes many applications to a variety of fields that can promote research projects User-friendly approach that can be used for classroom work or independent exploratory learning
📖 Summary
Exploring Calculus by Crista Arangala, published in 2016, is a concise 121-page text designed to serve as a hands-on lab manual for students and instructors navigating the theoretical and practical worlds of differential and integral calculus. Moving away from traditional, passive lecture formats, this book is crafted to be used in class every single day to guide active exploration and discovery. The structural design of the book centers around a series of engaging labs that can be utilized either individually or woven together in a logical sequence, depending on the specific curriculum and pacing of a course. Each lab begins with a clear, accessible explanation of the mathematical material, seamlessly integrated with exercises that prompt students to apply what they have just learned. To prevent cognitive overload, some of the labs are thoughtfully divided into multiple subsections, ensuring that the accompanying exercises are broken down and appropriately paired with the specific concepts covered in those sections. A defining characteristic of Arangalas work is its heavy integration of modern technology, specifically leveraging Mathematica to calculate and explore the foundational concepts and intricate theories of calculus. Through the use of Mathematica visualizations and Mathematica CDFs (Computable Document Format), students are not merely told how calculus works; they are given the digital tools to actively visualize, manipulate, and observe mathematical phenomena in real time. This technological approach bridges the gap between abstract mathematical theory and tangible real-world applications, helping learners discover principles in a way that is both meaningful and memorable. By encouraging students to get their hands dirty with computation and visual experimentation, the manual fosters a deeper intuition for rates of change, accumulation, and the fundamental theorem of calculus. Furthermore, the inclusion of numerous practical applications ensures that learners understand why these mathematical tools matter beyond the classroom walls. Whether used to supplement a standard course or as the primary daily driver for an inquiry-based classroom, Exploring Calculus transforms the traditional calculus journey into an interactive laboratory experience, making complex mathematical ideas approachable, visual, and deeply engaging for everyone involved.
🎯 Key Lessons
⚖️ Pros & Cons
✅ Pros
Promotes active, hands-on learning through daily classroom labs
Integrates modern technology like Mathematica for powerful visualizations
Breaks down complex topics into digestible subsections
Includes numerous practical applications to inspire learning
⚠️ Cons
Requires access to Mathematica and familiarity with the software
May be too brief at 121 pages to serve as a standalone textbook without a primary text
❓ FAQ
Who wrote Exploring Calculus? +
Crista Arangala is the author of the book.
When was the book published? +
It was published in 2016.
How many pages long is the book? +
The text spans 121 pages.
What software tool is used in the book? +
The book employs Mathematica for calculations, visualizations, and CDFs.
How are the labs structured? +
The labs consist of material explanations with integrated exercises, sometimes split into subsections.
