Calculus: Single Variable Part 2 - Differentiation

Go to Course: https://www.coursera.org/learn/differentiation-calculus

Introduction

**Course Review: Calculus: Single Variable Part 2 - Differentiation on Coursera** As a journey through the intricate world of mathematics, the course "Calculus: Single Variable Part 2 - Differentiation" stands out as an engaging introduction to the core concepts of single-variable calculus. Offered on Coursera, this course is not just another math class; it is a deep dive into the principles that drive both theoretical and practical applications across various disciplines, including engineering, physical sciences, and social sciences. ### Course Overview Calculus has long been celebrated as one of humanity's grand intellectual achievements. It provides the framework for understanding phenomena ranging from celestial mechanics to economic models and biological systems. This specific course focuses on differentiation, aiming to cultivate a robust conceptual understanding and practical skill set. Throughout the course, students are invited to explore the importance of derivatives beyond their typical interpretation as simple slopes. The instruction is brisk yet comprehensive, allowing for an expansive view of calculus while ensuring that students remain engaged and challenged. ### Syllabus Breakdown 1. **A New Look at Differentiation** In this initial module, students are introduced to a fresh perspective on derivatives, moving beyond the basic notion of slopes. The focus here is on asymptotic notation (big-O notation), which provides a powerful language for discussing rates of change. This new framing encourages critical thinking and deeper comprehension, setting the stage for future applications. 2. **Putting Derivatives to Work** The applicability of derivatives is unparalleled, making it a pivotal element of calculus. This module revisits essential applications of derivatives, demonstrating their utility across different contexts. By leveraging the knowledge gained about asymptotics, students will appreciate how derivatives can be utilized in various problem-solving scenarios. 3. **Differentials and Operators** The course takes a fascinating turn in this module by uncovering the mystery behind differentials. Rather than viewing derivatives as mere computational tools, students explore their role in implicit differentiation, leading to enriched understandings of what differentiation entails. This deeper exploration encourages learners to adopt a more nuanced perspective on the concepts. ### Why You Should Choose This Course - **Comprehensive Content**: The course strikes a balance between conceptual clarity and practical application, making it suitable for newcomers and those looking to reinforce existing knowledge. - **Engaging Learning Experience**: The combination of theoretical frameworks and real-world applications ensures that learners remain engaged and can see the relevance of calculus in their fields of study. - **Rigorous Understanding**: The emphasis on topics like asymptotic notation and the nuanced role of differentials prepares students for advanced calculus areas and other mathematical concepts. ### Recommendations I highly recommend "Calculus: Single Variable Part 2 - Differentiation" for students with interests in engineering, physical, or social sciences. Whether you are a college student preparing for rigorous coursework or a lifelong learner looking to brush up on calculus skills, this course provides an enriching experience that will enhance your understanding and application of mathematical principles. ### Final Thoughts In summary, this course serves as a crucial stepping stone in your academic journey through calculus. The engaging content, coupled with the expert instruction found on Coursera, makes it a perfect fit for anyone eager to grasp the nuances of differentiation and its broad applications. Set aside some time, grab a notebook, and embark on this mathematical adventure that promises to be both enlightening and enjoyable!

Syllabus

A New Look at Differentiation

Think derivatives mean "slopes"? Not anymore... In this module, we will reconsider what a derivative is and means in terms of the asymptotic (or big-O) notation from the previous chapter. This will give us a new language for describing and understanding rates of change and the rules that govern them.

Why exactly are derivatives so central to calculus? In part, it is because they are so ubiquitously useful! In this module, we will recall a few core applications of derivatives. In so doing, we'll see exactly how having an understanding of the asymptotics assists in building applications of the derivative.

There is much more to derivatives than simply their computation and applications. So much of how they arise is calculus is in the mysterious guise of *differentials*. These arise from implicit differentiation, which in turn reveals a deeper level of understanding of what differentiation means.