This book explores both the practical and theoretical aspects of the Discrete Fourier Transform, one of the most widely used tools in science, engineering, and computational mathematics. Designed to be accessible to an audience with diverse interests and mathematical backgrounds, the book is written in an informal style and is supported by many examples, figures, and problems. Conceived as an "owner's" manual, this comprehensive book covers such topics as the history of the DFT, derivations and properties of the DFT, comprehensive error analysis, issues concerning the implementation of the DFT in one and several dimensions, symmetric DFTs, a sample of DFT applications, and an overview of the FFT.

Topics covered include interpolation, the fast Fourier transform, iterative methods for solving systems of linear and nonlinear equations, numerical methods for solving ODEs, numerical methods for matrix eigenvalue problems, approximation theory, and computer arithmetic.".

Python Programming and Numerical Methods: A Guide for Engineers and Scientists introduces programming tools and numerical methods to engineering and science students, with the goal of helping the students to develop good computational problem-solving techniques through the use of numerical methods and the Python programming language. Part One introduces fundamental programming concepts, using simple examples to put new concepts quickly into practice. Part Two covers the fundamentals of algorithms and numerical analysis at a level that allows students to quickly apply results in practical settings. - Includes tips, warnings and "try this" features within each chapter to help the reader develop good programming practice - Summaries at the end of each chapter allow for quick access to important information - Includes code in Jupyter notebook format that can be directly run online

Mathematical models have become a crucial way for the Earth scientist to understand and predict how our planet functions and evolves through time and space. The finite element method (FEM) is a remarkably flexible and powerful tool with enormous potential in the Earth Sciences. This pragmatic guide explores how a variety of different Earth science problems can be translated and solved with FEM, assuming only basic programming experience. This book begins with a general introduction to numerical modeling and includes multiple sample Matlab codes to illustrate how FEM is implemented in practice. Textboxes have been included to provide additional detail, such as specialized Matlab usage or advanced topics. Covering all the key aspects, this is essential reading for those looking to master the technique, as well as those simply seeking to increase their basic level of understanding and appreciation of FEM.

An Introduction to Digital Signal Processing is written for those who need to understand and use digital signal processing and yet do not wish to wade through a multi-semester course sequence. Using only calculus-level mathematics, this book progresses rapidly through the fundamentals to advanced topics such as iterative least squares design of IIR filters, inverse filters, power spectral estimation, and multidimensional applications--all in one concise volume. This book emphasizes both the fundamental principles and their modern computer implementation. It presents and demonstrates how simple the actual computer code is for advanced modern algorithms used in DSP. Results of these programs, which the reader can readily duplicate and use on a PC, are presented in many actual computer drawn plots. - Assumes no previous knowledge of signal processing but leads up to very advanced techniquescombines exposition of fundamental principles with practical applications - Includes problems with each chapter - Presents in detail the appropriate computer algorithums for solving problems

The accelerating rate at which new materials are appearing, and transforming the engineering world, only serves to emphasize the vast potential for novel material structure and related performance. Microstructure Sensitive Design for Performance Optimization (MSDPO) embodies a new methodology for systematic design of material microstructure to meet the requirements of design in optimal ways. Intended for materials engineers and researchers in industry, government and academia as well as upper level undergraduate and graduate students studying material science and engineering, MSDPO provides a novel mathematical framework that facilitates a rigorous consideration of the material microstructure as a continuous design variable in the field of engineering design. Presents new methods and techniques for analysis and optimum design of materials at the microstructure level Authors' methodology introduces spectral approaches not available in previous texts, such as the incorporation of crystallographic orientation as a variable in the design of engineered components with targeted elastic properties Numerous illustrations and examples throughout the text help readers grasp the concepts

Introduces the fundamentals of numerical mathematics and illustrates its applications to a wide variety of disciplines in physics and engineering Applying numerical mathematics to solve scientific problems, this book helps readers understand the mathematical and algorithmic elements that lie beneath numerical and computational methodologies in order to determine the suitability of certain techniques for solving a given problem. It also contains examples related to problems arising in classical mechanics, thermodynamics, electricity, and quantum physics. Fundamentals of Numerical Mathematics for Physicists and Engineers is presented in two parts. Part I addresses the root finding of univariate transcendental equations, polynomial interpolation, numerical differentiation, and numerical integration. Part II examines slightly more advanced topics such as introductory numerical linear algebra, parameter dependent systems of nonlinear equations, numerical Fourier analysis, and ordinary differential equations (initial value problems and univariate boundary value problems). Chapters cover: Newton’s method, Lebesgue constants, conditioning, barycentric interpolatory formula, Clenshaw-Curtis quadrature, GMRES matrix-free Krylov linear solvers, homotopy (numerical continuation), differentiation matrices for boundary value problems, Runge-Kutta and linear multistep formulas for initial value problems. Each section concludes with Matlab hands-on computer practicals and problem and exercise sets. This book: Provides a modern perspective of numerical mathematics by introducing top-notch techniques currently used by numerical analysts Contains two parts, each of which has been designed as a one-semester course Includes computational practicals in Matlab (with solutions) at the end of each section for the instructor to monitor the student's progress through potential exams or short projects Contains problem and exercise sets (also with solutions) at the end of each section Fundamentals of Numerical Mathematics for Physicists and Engineers is an excellent book for advanced undergraduate or graduate students in physics, mathematics, or engineering. It will also benefit students in other scientific fields in which numerical methods may be required such as chemistry or biology.