{"product_id":"calculus-for-machine-learning-and-artificial-intelligence-from-derivatives-to-backpropagation-9798299388251","title":"Calculus for machine learning and artificial intelligence: From derivatives to backpropagation","description":"\u003cp\u003e • Author(s): Anshuman Mishra\u003cbr\u003e • Publisher: Independently Published\u003cbr\u003e • Publisher Imprint: Independently Published\u003cbr\u003e • BISAC: Calculus\u003c\/p\u003e\u003cp\u003eMathematics has always been the language of science, providing the framework through which humanity understands the natural world. Among the branches of mathematics, \u003cb\u003ecalculus\u003c\/b\u003e has held a special place as a tool for describing continuous change, modeling dynamic systems, and solving complex problems in physics, engineering, economics, and beyond. In the modern era, calculus has gained renewed importance due to the rapid rise of \u003cb\u003eArtificial Intelligence (AI)\u003c\/b\u003e and \u003cb\u003eMachine Learning (ML)\u003c\/b\u003e. The algorithms that power modern AI systems-ranging from simple linear regression models to deep neural networks-are built upon the fundamental principles of calculus.\u003cbr\u003eThis book, \u003ci\u003eCalculus for Machine Learning and AI\u003c\/i\u003e, is designed to provide readers with a clear, rigorous, and application-oriented understanding of calculus as it applies to machine learning. Unlike traditional calculus books that focus solely on mathematical theory, this book emphasizes \u003cb\u003ewhy and how calculus is the backbone of AI systems\u003c\/b\u003e, making it a bridge between pure mathematics and applied machine learning practice.\u003cbr\u003eOur goal is to \u003cb\u003edemystify calculus\u003c\/b\u003e for computer scientists, data scientists, engineers, and students who want to understand not just how to compute derivatives or integrals, but also why these operations are essential for optimization, learning, and intelligent decision-making. \u003c\/p\u003e\u003cp\u003e\u003c\/p\u003e\u003cb\u003eWhy Calculus Matters in AI and Machine Learning\u003c\/b\u003e\u003cbr\u003eTo appreciate the value of this book, one must first understand why calculus is indispensable in AI: \u003col\u003e\n\u003cli\u003e\n\u003cb\u003eDerivatives and Gradients as Learning Tools\u003c\/b\u003e\u003cbr\u003eAt the heart of machine learning lies optimization. Models learn by minimizing errors, and this requires gradients-mathematical tools derived from calculus. Whether adjusting the weights of a neural network or fine-tuning parameters in a regression model, derivatives guide learning by showing the direction of steepest descent.\u003c\/li\u003e\n\u003cli\u003e\n\u003cb\u003eBackpropagation and Neural Networks\u003c\/b\u003e\u003cbr\u003eNeural networks are among the most powerful AI architectures, and their training is made possible through backpropagation-a process entirely dependent on calculus. Without derivatives, there is no mechanism to update weights systematically, making learning impossible.\u003c\/li\u003e\n\u003cli\u003e\n\u003cb\u003eOptimization and Loss Functions\u003c\/b\u003e\u003cbr\u003eThe concepts of minima, maxima, and saddle points are deeply rooted in calculus. Gradient Descent, Stochastic Gradient Descent, and their numerous variants are all grounded in differential calculus and partial derivatives.\u003c\/li\u003e\n\u003cli\u003e\n\u003cb\u003eProbability and Continuous Distributions\u003c\/b\u003e\u003cbr\u003eIn AI, many probabilistic models require integration to compute likelihoods, marginal probabilities, and expectations. Calculus enables us to handle these continuous distributions, which are central to Bayesian models and probabilistic AI.\u003c\/li\u003e\n\u003cli\u003e\n\u003cb\u003eDynamic Models and Reinforcement Learning\u003c\/b\u003e\u003cbr\u003eReinforcement learning often involves continuous state and action spaces where calculus helps model transitions, expected rewards, and optimal policies. Calculus is also essential for solving Bellman equations and Hamilton-Jacobi equations in advanced AI.\u003c\/li\u003e\n\u003cli\u003e\n\u003cb\u003eUnderstanding Transformations\u003c\/b\u003e\u003cbr\u003eMany machine learning techniques, such as Principal Component Analysis (PCA) and dimensionality reduction, rely on continuous transformations of data. Calculus helps in understanding these transformations and their impact on learning systems.\u003c\/li\u003e\n\u003c\/ol\u003eIn short, calculus is not just an academic requirement-it is the \u003cb\u003eengine that makes AI possible\u003c\/b\u003e. \u003cp\u003e\u003c\/p\u003e\u003cb\u003eHow This Book is Beneficial for Study\u003c\/b\u003e\u003cbr\u003e\u003cb\u003e1. \u003cb\u003eBridging Theory and Practice\u003c\/b\u003e\u003c\/b\u003e\u003cbr\u003eOne of the greatest challenges for learners is connecting abstract mathematical concepts with practical AI applications. This book narrows that gap. Instead of treating calculus as an isolated subject, it demonstrates how every concept directly powers real-world AI tasks.","brand":"Independently Published","offers":[{"title":"Paperback","offer_id":47594666164375,"sku":"9798299388251","price":1742.0,"currency_code":"INR","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0666\/3471\/1191\/files\/9798299388251.webp?v=1774986734","url":"https:\/\/atlanticbooks.com\/products\/calculus-for-machine-learning-and-artificial-intelligence-from-derivatives-to-backpropagation-9798299388251","provider":"Atlantic Books","version":"1.0","type":"link"}