Applied Calculus with Python

Johns Hopkins University via Coursera

Go to Course: https://www.coursera.org/learn/applied-calculus-with-python

Introduction

# Course Review: Applied Calculus with Python on Coursera As someone who has a vested interest in both mathematics and programming, I recently completed the **Applied Calculus with Python** course offered on Coursera. This course stands out for its unique blend of mathematical theory and practical application through Python, making it a valuable resource for both aspiring programmers and math enthusiasts. Here’s an in-depth review detailing my experience, the course structure, and why I would highly recommend it. ## Course Overview The **Applied Calculus with Python** course is designed for individuals looking to deepen their understanding of calculus while harnessing the capabilities of Python. It's aimed at Python programmers wishing to explore foundational calculus concepts to tackle complex problems, as well as mathematics students eager to apply theoretical concepts through computational techniques. ### What You Will Learn By the end of the course, learners will have a firm grasp of essential calculus concepts and how to implement them in Python, specifically to solve real-world challenges. The course uses a combination of video lectures, readings, practical examples, and assessments to drive the learning experience. ## Syllabus Breakdown ### 1. Introduction to Python The course kicks off with an introduction to Python, ensuring that students build a solid foundation in programming. This module is not only about learning the syntax, but it emphasizes problem-solving in various real-life scenarios. The numerous examples and hands-on assignments encourage experimentation, allowing learners to explore and manipulative code directly. ### 2. Functions The module on functions dives deep into mathematical models, discussing how dependencies between variables are represented. Students are exposed to both the theory and implementation of functions within Python, reinforcing the connection between abstract mathematics and practical coding. ### 3. Rates of Change and the Derivative Perhaps one of the most significant concepts in calculus, the derivative represents how a quantity changes over time. This section introduces limits and helps students develop a thorough understanding of how to find derivatives analytically and using Python. The explanations are clear, and the visual aids used to represent these concepts are incredibly helpful. ### 4. Derivative Rules and Applications In this module, learners discover algebraic rules that simplify the process of finding derivatives without relying solely on limits. This understanding demystifies the derivative function and equips students with the knowledge necessary to tackle more advanced mathematical problems. The inclusion of Python in this section allows for practical application, demonstrating the utility of derivatives in computational tasks. ### 5. Accumulated Change and Integrals The exploration of integral calculus is fascinating, as it teaches students how to measure areas and volumes through accumulation. Students learn about the fundamental theorem of calculus, bridging the gap between integration and differentiation. The application of theoretical concepts to real-world problems in Python adds depth to the learning process. ## Recommendations **Who Should Take This Course?** - **Python Programmers**: If you're already familiar with Python and want to deepen your mathematical understanding, this course provides an excellent way to enhance your skill set. - **Math Students**: Those studying mathematics will benefit from seeing practical applications of calculus concepts as they learn. - **Professionals in STEM Fields**: Anyone working in fields like engineering, data science, or finance, where calculus and programming intersect, will find this course immensely useful. **Pros of the Course**: - **Hands-On Learning**: The course encourages active participation through coding exercises. - **Real-World Applications**: Every concept is tied back to solving genuine problems, making the content relevant. - **Structured Curriculum**: The careful progression through topics builds a comprehensive understanding of applied calculus. **Cons**: - **Steep Learning Curve**: For those completely new to either calculus or programming, the course may present challenges. It’s recommended to have basic knowledge in both fields. ## Conclusion The **Applied Calculus with Python** course on Coursera is an exceptional resource for anyone eager to marry the worlds of mathematics and programming. Not only does it lay down the theoretical foundations of calculus, but it also empowers learners to wield these concepts within the versatile Python environment. I highly recommend this course to anyone looking to enhance their skills and apply mathematical concepts to real-world problems effectively. Whether you want to advance your career or simply gain a more profound understanding of calculus, this course is definitely worth your time and investment.

Syllabus

Introduction to Python

Programming now has relevance well beyond just Computer Science. In this module and throughout this course, you will learn not only about programming using Python, but also how to use those skills to solve real, complex problems in future classes, at work, or elsewhere. To ensure this, copious amounts of examples are included, with explanations, throughout the course. You are strongly encouraged not only trace through them, but also experiment with (run, alter, break) them on your own. The assignments are linked to the respective module. Putting time in here will give you the opportunity to solve actual scientific problems and challenge you in a way that that’ll not only help you make use of the skills we’ll discuss in lecture, but also to leave you with that oh-so-satisfying feeling of having conquered the challenge when you’re done!

Functions

Functions arise whenever one quantity depends on another. Mathematically speaking, a function is a rule that assigns to each element x in a set D (called the domain) exactly one element, called f(x), in a set called the range. Because we continually make theories about dependencies between quantities in nature and society, functions are important tools in the construction of mathematical models. In this module, we will learn the theory of functions, see many examples and their graphs, as well as apply these functions. We will learn how to implement these functions in Python as well.

Rates of Change and the Derivative

Calculus is the science of measuring change. Early in its history, its tools were developed to solve problems involving the position, velocity, and acceleration of moving objects. Prior to the development of calculus, there was no way to express this change in a variable. In this section, we introduce the notion of limits to develop the derivative of a function. The derivative, commonly denoted as f'(x), will measure the instantaneous rate of change of a function at a certain point x = a. This number f'(a), when defined, will be graphically represented as the slope of the tangent line to a curve. We will see in this module how to find limits and derivatives both analytically and using Python.

Derivative Rules and Applications

The derivative is defined as a limit of the difference quotient. Computing this limit symbolically is very challenging for complicated functions. In this section, we develop rules that find the derivative without having to fall back on the limit definition each time. These rules are purely algebraic in nature and help us gain intuition into the behavior of a derivative function. More importantly, these rules help to demystify the Derivative() function and show the steps to produce the functions output. Understanding the process allows for mastery, adaptation, and more complicated applications of these concepts.

Accumulated Change and Integrals

One major topic in calculus is what is called "integral calculus," which involves finding areas or volumes of regions by adding up small slices. We start to think about areas or volumes as an accumulation of the smaller slices that make them and from that we can apply the theory of integral calculus to measure net change and total accumulations. Then, by the Fundamental Theorem of Calculus, this is then related back to where we started: derivatives. This module introduces some of the most beautiful and useful applications of calculus. Algebraic techniques will be shown alongside of numerical computations using Python.