From STEM to STEAM : A Study of Art from the Perspective of Science, Technology, Engineering, and Mathematics

This book provides readers with an introductory overview of art from the perspective of science, technology, engineering, and mathematics. The author utilizes well-known and important works of art to demonstrate how STEM concepts apply to them. The book’s examples include a structural analysis of Michelangelo’s David. The author covers major breakthroughs in art history, such as the discovery of perspective. The book also discusses other important elements of art, such as color, from a scientific point of view. The author ensures that readers will understand the art terms used by comparing them with terms used in STEM fields of study.

this Book Provides A Comprehensive Introduction To Complex Variable Theory And Its Applications To Current Engineering Problems And Is Designed To Make The Fundamentals Of The Subject More Easily Accessible To Readers Who Have Little Inclination To Wade Through The Rigors Of The Axiomatic Approach. Modeled After Standard Calculus Books—both In Level Of Exposition And Layout—it Incorporates Physical Applications Throughout, So That The Mathematical Methodology Appears Less Sterile To Engineers. It Makes Frequent Use Of Analogies From Elementary Calculus Or Algebra To Introduce Complex Concepts, Includes Fully Worked Examples, And Provides A Dual Heuristic/analytic Discussion Of All Topics. A Downloadable Matlab Toolbox—a State-of-the-art Computer Aid—is Available.

Complex Numbers. Analytic Functions. Elementary Functions. Complex Integration. Series Representations For Analytic Functions. Residue Theory. Conformal Mapping. The Transforms Of Applied Mathematics. Matlab Toolbox For Visualization Of Conformal Maps. Numerical Construction Of Conformal Maps. Table Of Conformal Mappings. Features Coverage Of Julia Sets; Modern Exposition Of The Use Of Complex Numbers In Linear Analysis (e.g., Ac Circuits, Kinematics, Signal Processing); Applications Of Complex Algebra In Celestial Mechanics And Gear Kinematics; And An Introduction To Cauchy Integrals And The Sokhotskyi-plemeij Formulas.

For Mathematicians And Engineers Interested In Complex Analysis And Mathematical Physics.

This book presents a short introduction to the main tools of optimization methodology including linear programming, steepest descent, conjugate gradients, and the Karush-Kuhn-Tucker-John conditions. Each topic is developed in terms of a specific physical model, so that the strategy behind every step is motivated by a logical, concrete, easily visualized objective. A quick perusal of the Fibonacci search algorithm provides a simple and tantalizing first encounter with optimization theory, and a review of the max-min exposition of one-dimensional calculus prepares readers for the more sophisticated topics found later in the book. Notable features are the innovative perspectives on the simplex algorithm and Karush-Kuhn-Tucker-John conditions as well as a wealth of helpful diagrams. The author provides pointers to references for readers who would like to learn more about rigorous definitions, proofs, elegant reformulations and extensions, and case studies. However, the book is sufficiently self-contained to serve as a reliable resource for readers who wish to exploit commercially available optimization software without investing the time to develop expertise in its aspects.This book also:Features innovative perspectives on the simplex algorithm and Krushal-Kuhn-Tucker-John conditionsServes as a resource for readers to use the tools of optimization without needing to acquire expertise in the theoryFeatures plentiful resources that focus on rigorous definitions, proofs, and case studies This book provides a comprehensive introduction to complex variable theory and its applications to current engineering problems and is designed to make the fundamentals of the subject more easily accessible to readers who have little inclination to wade through the rigors of the axiomatic approach. Modeled after standard calculus books -- both in level of exposition and layout -- it incorporates physical applications throughout, so that the mathematical methodology appears less sterile to engineers. It makes frequent use of analogies from elementary calculus or algebra to introduce complex concepts, includes fully worked examples, and provides a dual heuristic/analytic discussion of all topics. A downloadable MATLAB toolbox -- a state-of-the-art computer aid -- is available. Complex Numbers. Analytic Functions. Elementary Functions. Complex Integration. Series Representations for Analytic Functions. Residue Theory. Conformal Mapping. The Transforms of Applied Mathematics. MATLAB ToolBox for Visualization of Conformal Maps. Numerical Construction of Conformal Maps. Table of Conformal Mappings. Features coverage of Julia Sets; modern exposition of the use of complex numbers in linear analysis (e.g., AC circuits, kinematics, signal processing); applications of complex algebra in celestial mechanics and gear kinematics; and an introduction to Cauchy integrals and the Sokhotskyi-Plemeij formulas. For mathematicians and engineers interested in Complex Analysis and Mathematical Physics. Preface Structure of the Book Choice of Subject Matter Creative Commons License Links Other Books by the Author Contents 1 Introduction 2 Sculpture 2.1 Michelangelo’s David 2.2 Estimating the Stress on David’s Knees 2.3 Transporting Michelangelo’s Sculptures 2.4 Other Davids 2.5 Other Michelangelos 2.6 Depictions of the Damned 2.7 Vasari 2.8 Michelangelo’s Rivals 3 Perspective 3.1 Examples of Perspective 3.2 Quantifying Perspective 3.3 Vector Analysis of Perspective 3.4 The Discovery of Perspective 3.5 Filippo Brunelleschi 3.6 Drawing in Perspective 3.7 Impossible Objects 4 Color Theory: Physics and Physiology 4.1 What is Light? 4.2 The Speed of Light 4.3 Wavelength, Frequency, and Color 4.4 Refraction 4.5 Dispersion 4.6 Frequency Analysis 4.7 The Eye 4.8 Additive Color Phenomena 4.9 Trichromatic Color Theory 5 Color Theory: Technology 5.1 Subtractive Mixing 5.2 Color Addition by Juxtaposition 5.3 Pointillism: Georges Seurat 5.4 The Munsell Color Tree 5.5 Amedeo Modigliani 5.6 Paul Cezanne 5.7 Vincent Willem van Gogh Postface Newly updated by the author, this text explores the solution of partial differential equations by separating variables, rather than by conducting qualitative theoretical analyses of their properties. These qualitative features--uniqueness, existence, elegance of composition, and convergence modes--are substantiated by physical reasoning, rather than rigorous arguments. Geared toward applied mathematicians, physicists, engineers, and others seeking explicit solutions,the bookoffers heuristic justifications for each construction. The first three chapters review the necessary tools for understanding the separation of variables technique: basics of ordinary differential equations, Frobenius-series construction and properties of Bessel functions, and Fourier analysis. Subsequent chapters explore the exposition of the algorithmic nature of the separation of variables process, based on a sequence of steps that infallibly leads to the solution expansion, regardless of the nature of the boundary conditions. This book offers an intuitive approach to random processes and educates the reader on how to interpret and predict their behavior. Premised on the idea that new techniques are best introduced by specific, low-dimensional examples, the mathematical exposition is easier to comprehend and more enjoyable, and it motivates the subsequent generalizations. It distinguishes between the science of extracting statistical information from raw data--e.g., a time series about which nothing is known a priori--and that of analyzing specific statistical models, such as Bernoulli trials, Poisson queues, ARMA, and Markov processes. The former motivates the concepts of statistical spectral analysis (such as the Wiener-Khintchine theory), and the latter applies and interprets them in specific physical contexts. The formidable Kalman filter is introduced in a simple scalar context, where its basic strategy is transparent, and gradually extended to the full-blown iterative matrix form. Fundamentals of Differential Equations presents the basic theory of differential equations and offers a variety of modern applications in science and engineering. Available in two versions, these flexible texts offer the instructor many choices in syllabus design, course emphasis (theory, methodology, applications, and numerical methods), and in using commercially available computer software.

Fundamentals of Differential Equations, Eighth Edition is suitable for a one-semester sophomore- or junior-level course. Fundamentals of Differential Equations with Boundary Value Problems, Sixth Edition, contains enough material for a two-semester course that covers and builds on boundary value problems. The Boundary Value Problems version consists of the main text plus three additional chapters (Eigenvalue Problems and Sturm-Liouville Equations; Stability of Autonomous Systems; and Existence and Uniqueness Theory).

The introductory text covers vector algebra; single variables; scalar and vector fields; line, surface, and volume integrals; and advanced topics. This seventh edition incorporates early introduction of curvilinear coordinate expressions, relegating deeper mathematical insights to the appendices on theorems of advanced calculus, constrained optimization, and vector equations of classical mechanics. Due to its optional reading sections, the text can be used at several levels. Includes exercises and selected answers. Annotation copyright Book News, Inc. Portland, Or. Focusing on vector analysis, this book aims to meet the professional needs of the engineer or scientist, and to give the mathematician an understanding of the three-dimensional versions of the theorems of higher geometry.