Jacobian Matrices and Vector Calculus in JAX

Deep learning models rely on complex multi-dimensional derivatives to optimize parameters and train effectively. Understanding how to compute these derivatives efficiently is crucial for building custom neural networks and advanced scientific computing workflows. This text-based course guides you through the mathematical foundations of vector calculus and shows you how to implement them programmatically using modern tools. You will transition from basic calculus principles to writing clean, optimized differentiation code. What you will learn: Understand the mathematical foundations of Jacobians, gradients, and vector-valued functions; Compute Jacobian matrices using both forward-mode and reverse-mode automatic differentiation; Apply JAX transform functions like jacfwd and jacrev to complex tensor operations; Optimize computation times by combining vectorization with automatic differentiation; Write modular, type-hinted code suitable for modern research and production workflows. Starting with fundamental mathematical definitions, you will progress through step-by-step written explanations and code demonstrations that demystify high-dimensional derivatives. This course is designed for beginners in automatic differentiation, requiring only a basic familiarity with Python and linear algebra. Take the first step toward mastering vector calculus in modern machine learning.