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This handbook focuses on special functions in physics in the real and complex domain. It covers more than 170 different functions with additional numerical hints for efficient computation, which are useful to anyone who needs to program with other programming languages as well. The book comes with MATLAB-based programs for each of these functions and a detailed html-based documentation. Some of the explained functions are: Gamma and Beta functions; Legendre functions, which are linked to quantum mechanics and electrodynamics; Bessel functions; hypergeometric functions, which play an important role in mathematical physics; orthogonal polynomials, which are largely used in computational physics; and Riemann zeta functions, which play an important role, e.g., in quantum chaos or string theory. The book’s primary audience are scientists, professionals working in research areas of industries, and advanced students in physics, applied mathematics, and engineering.
A unique textbook for an undergraduate course on mathematical modeling, Differential Equations with MATLAB: Exploration, Applications, and Theory provides students with an understanding of the practical and theoretical aspects of mathematical models involving ordinary and partial differential equations (ODEs and PDEs). The text presents a unifying picture inherent to the study and analysis of more than 20 distinct models spanning disciplines such as physics, engineering, and finance. The first part of the book presents systems of linear ODEs. The text develops mathematical models from ten disparate fields, including pharmacokinetics, chemistry, classical mechanics, neural networks, physiology, and electrical circuits. Focusing on linear PDEs, the second part covers PDEs that arise in the mathematical modeling of phenomena in ten other areas, including heat conduction, wave propagation, fluid flow through fissured rocks, pattern formation, and financial mathematics. The authors engage students by posing questions of all types throughout, including verifying details, proving conjectures of actual results, analyzing broad strokes that occur within the development of the theory, and applying the theory to specific models. The authors’ accessible style encourages students to actively work through the material and answer these questions. In addition, the extensive use of MATLAB® GUIs allows students to discover patterns and make conjectures.
Solid state physics, the study and prediction of the fundamental physical properties of materials, forms the backbone of modern materials science and has many technological applications. The unique feature of this text is the MATLAB®-based computational approach with several numerical techniques and simulation methods included. This is highly effective in addressing the need for visualization and a direct hands-on approach in learning the theoretical concepts of solid state physics. The code is freely available to all textbook users. Additional Features: Uses the pedagogical tools of computational physics that have become important in enhancing physics teaching of advanced subjects such as solid state physics Adds visualization and simulation to the subject in a way that enables students to participate actively in a hand-on approach Covers the basic concepts of solid state physics and provides students with a deeper understanding of the subject matter Provides unique example exercises throughout the text Obtains mathematical analytical solutions Carries out illustrations of important formulae results using programming scripts that students can run on their own and reproduce graphs and/or simulations Helps students visualize solid state processes and apply certain numerical techniques using MATLAB®, making the process of learning solid state physics much more effective Reinforces the examples discussed within the chapters through the use of end-of-chapter exercises Includes simple analytical and numerical examples to more challenging ones, as well as computational problems with the opportunity to run codes, create new ones, or modify existing ones to solve problems or reproduce certain results
Master the tools of MATLAB through hands-on examples Shows How to Solve Math Problems Using MATLAB The mathematical software MATLAB® integrates computation, visualization, and programming to produce a powerful tool for a number of different tasks in mathematics. Focusing on the MATLAB toolboxes especially dedicated to science, finance, and engineering, MATLAB® with Applications to Engineering, Physics and Finance explains how to perform complex mathematical tasks with relatively simple programs. This versatile book is accessible enough for novices and users with only a fundamental knowledge of MATLAB, yet covers many sophisticated concepts to make it helpful for experienced users as well. The author first introduces the basics of MATLAB, describing simple functions such as differentiation, integration, and plotting. He then addresses advanced topics, including programming, producing executables, publishing results directly from MATLAB programs, and creating graphical user interfaces. The text also presents examples of Simulink® that highlight the advantages of using this software package for system modeling and simulation. The applications-dedicated chapters at the end of the book explore the use of MATLAB in digital signal processing, chemical and food engineering, astronomy, optics, financial derivatives, and much more.
Mathematics of Computing -- Numerical Analysis.
Broadly organized around the applications of Fourier analysis, "Methods of Applied Mathematics with a MATLAB Overview" covers both classical applications in partial differential equations and boundary value problems, as well as the concepts and methods associated to the Laplace, Fourier, and discrete transforms. Transform inversion problems are also examined, along with the necessary background in complex variables. A final chapter treats wavelets, short-time Fourier analysis, and geometrically-based transforms. The computer program MATLAB is emphasized throughout, and an introduction to MATLAB is provided in an appendix. Rich in examples, illustrations, and exercises of varying difficulty, this text can be used for a one- or two-semester course and is ideal for students in pure and applied mathematics, physics, and engineering.
This book may be used by students and professionals in physics and engineering that have completed first-year calculus and physics. An introductory chapter reviews algebra, trigonometry, units and complex numbers that are frequently used in physics. Examples using MATLAB and Maple for symbolic and numerical calculations in physics with a variety of plotting features are included in all 16 chapters. The book applies many of mathematical concepts covered in Chapters 1-9 to fundamental physics topics in mechanics, electromagnetics; quantum mechanics and relativity in Chapters 10-16. Companion files are included with MATLAB and Maple worksheets and files, and all of the figures from the text. Features: • Each chapter includes the mathematical development of the concept with numerous examples • MATLAB & Maple examples are integrated in each chapter throughout the book • Applies the mathematical concepts to fundamental physics principles such as relativity, mechanics, electromagnetics, etc. • Introduces basic MATLAB and Maple commands and programming structures • Includes companion files with MATLAB and Maple files and worksheets, and all of the figures from the text
Self-contained text, useful for classroom or independent study, covers Bessel functions of zero order, modified Bessel functions, definite integrals, asymptotic expansions, and Bessel functions of any real order. 226 problems.
Mathematical physics provides physical theories with their logical basis and the tools for drawing conclusions from hypotheses. Introduction to Mathematical Physics explains to the reader why and how mathematics is needed in the description of physical events in space. For undergraduates in physics, it is a classroom-tested textbook on vector analysis, linear operators, Fourier series and integrals, differential equations, special functions and functions of a complex variable. Strongly correlated with core undergraduate courses on classical and quantum mechanics and electromagnetism, it helps the student master these necessary mathematical skills. It contains advanced topics of interest to graduate students on relativistic square-root spaces and nonlinear systems. It contains many tables of mathematical formulas and references to useful materials on the Internet. It includes short tutorials on basic mathematical topics to help readers refresh their mathematical knowledge. An appendix on Mathematica encourages the reader to use computer-aided algebra to solve problems in mathematical physics. A free Instructor's Solutions Manual is available to instructors who order the book for course adoption.