Indeed, such equations are crucial to mathematical physics. Although simplifications can be made that reduce these equations to ordinary differential equations, nevertheless the complete description of physical systems resides in the general area of partial differential equations.This highly useful text shows the reader how to formulate a partial differential equation from the physical problem (constructing the mathematical model) and how to solve the equation (along with initial and boundary conditions). Written for advanced undergraduate and graduate students, as well as professionals working in the applied sciences, this clearly written book offers realistic, practical coverage of diffusion-type problems, hyperbolic-type problems, elliptic-type problems, and numerical and approximate methods. Each chapter contains a selection of relevant problems (answers are provided) and suggestions for further reading.

    The book will teach you about:* Neural networks, a beautiful biologically-inspired programming paradigm which enables a computer to learn from observational data* Deep learning, a powerful set of techniques for learning in neural networksNeural networks and deep learning currently provide the best solutions to many problems in image recognition, speech recognition, and natural language processing. This book will teach you the core concepts behind neural networks and deep learning.

    They can navigate more data than a doctor or lawyer and act with greater precision. For many years we’ve taken solace in the notion that they can’t create. But now that algorithms can learn and adapt, does the future of creativity belong to machines, too?It is hard to imagine a better guide to the bewildering world of artificial intelligence than Marcus du Sautoy, a celebrated Oxford mathematician whose work on symmetry in the ninth dimension has taken him to the vertiginous edge of mathematical understanding. In The Creativity Code he considers what machine learning means for the future of creativity. The Pollockizer can produce drip paintings in the style of Jackson Pollock, Botnik spins off fanciful (if improbable) scenes inspired by J. K. Rowling, and the music-composing algorithm Emmy managed to fool a panel of Bach experts. But do these programs just mimic, or do they have what it takes to create? Du Sautoy argues that to answer this question, we need to understand how the algorithms that drive them work―and this brings him back to his own subject of mathematics, with its puzzles, constraints, and enticing possibilities.While most recent books on AI focus on the future of work, The Creativity Code moves us to the forefront of creative new technologies and offers a more positive and unexpected vision of our future cohabitation with machines. It challenges us to reconsider what it means to be human―and to crack the creativity code.