Calculus Unraveled: Intuition, Proofs, and Python

Transform your calculus skills with modern python coding Take your understanding of calculus to a whole new level with this hands-on, Python-based textbook by educator and neuroscientist Dr. Mike X Cohen. Spanning 605 pages and featuring 162 creative coding exercises, this book goes far beyond rote learning and memorization. Instead, you’ll build a deep, intuitive knowledge of calculus through modern computational methods that are applicable in machine learning, data science, engineering, physics, computational biology, and more. A Fresh Approach to Calculus Theory Meets Coding: Traditional calculus texts focus on formulas; this one merges conceptual rigor with practical Python code. You’ll see how calculus shapes cutting-edge technology and real-world numerical analyses. You’ll also learn how to find numerical approximations to equations that cannot be solved using traditional analytic methods. Comprehensive Coverage: From fundamentals of differentiation through multivariable integration, you’ll explore crucial topics like critical points, integration techniques, improper integrals, statistical applications, numerical algorithms, and more. Get Visual, Get Interactive: Code-based exercises bring equations to life, letting you simulate, plot, and investigate calculus concepts. Why This Book? Perfect for Self-Study: Whether you’re brushing up on basics or learning calculus for the first time, you can progress at your own pace. Ideal for Data Science & Machine Learning: Gain a solid grasp of the math behind algorithms. From gradient-based optimizations to integration in probability theory, see how calculus powers the ML world. Modern Python Workflows: Written with Jupyter/Colab notebooks in mind. Delve into libraries like NumPy, SciPy, Sympy, and Matplotlib to create dynamic visualizations. 162 Exercises to Level Up: These are not typical problem sets: Each exercise is a critical-thinking challenge requiring you to code, explore, and truly understand the math. Best part: full solutions are provided in the book’s github repository, and YouTube video explanations are provided for each exercise and their solutions. All book figures, concepts, and exercise solutions are available in Python in the book’s github repository. You can check your exercise solutions, adapt the code to continue your own mathematical explorations, and apply the theoretical and numerical approximation techniques to your own data, simulations, and projects. Who Should Read This Book? Students needing a supplementary resource to a standard calculus curriculum. Data Scientists, Engineers, and Tech Professionals craving deeper math fundamentals for machine learning, computational biology, or financial modeling, using libraries like sympy, numpy, scipy, and matplotlib. Math Enthusiasts eager for a new perspective, combining visualization, conceptual understanding, and real-world applications. About the Author Mike X Cohen is an accomplished neuroscientist professor and educator with over two decades of teaching experience. Renowned for his ability to distill advanced concepts into intuitive explanations, Mike blends mathematics, coding, and scientific thinking to make complex ideas accessible. Learn calculus by doing — not just by reading. With this innovative text, you’ll master everything from fundamental derivative rules to multivariable integration, all while coding each concept in Python. If you want to transform your calculus skills and gain valuable computational experience, this is the book for you.