Fundamentals of Differential Equations

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Fundamentals Of Differential Equations

Książki Obcojęzyczne>Angielskie>Mathematics & science>Mathematics>Calculus & mathematical analysis>Differential calculus & equations

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Fundamentals of Differential Equations and Boundary Value Problems: Pearson New International Edition

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Introduction to Partial Differential Equations Springer International Publishing AG

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This textbook is designed for a one year course covering the fundamentals of partial differential equations, aimed towards advanced undergraduates and beginning graduate students. It features examples and exercises connected to real world problems.

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Introduction to Partial Differential Equations Springer International Publishing AG

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This textbook is designed for a one year course covering the fundamentals of partial differential equations, aimed towards advanced undergraduates and beginning graduate students in mathematics, science and engineering. Exercises appear at the end of almost every subsection, and come in a variety of flavors. Most exercise sets start with some straightforward computational problems to develop and reinforce the principal new techniques and ideas.

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Differential Equations and Linear Algebra Wellesley-Cambridge Press,U.S.

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Differential equations and linear algebra are two central topics in the undergraduate mathematics curriculum. This innovative textbook allows the two subjects to be developed either separately or together, illuminating the connections between two fundamental topics, and giving increased flexibility to instructors. It can be used either as a semester-long course in differential equations, or as a one-year course in differential equations, linear algebra, and applications. Beginning with the basics of differential equations, it covers first and second order equations, graphical and numerical methods, and matrix equations. The book goes on to present the fundamentals of vector spaces, followed by eigenvalues and eigenvectors, positive definiteness, integral transform methods and applications to PDEs. The exposition illuminates the natural correspondence between solution methods for systems of equations in discrete and continuous settings. The topics draw on the physical sciences, engineering and economics, reflecting the author's distinguished career as an applied mathematician and expositor.

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Fundamentals of Differential Geometry Springer, Berlin

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This book provides an introduction to the basic concepts in differential topology, differential geometry, and differential equations, and some of the main basic theorems in all three areas. This new edition includes new chapters, sections, examples, and exercises.§From the reviews: "There are many books on the fundamentals of differential geometry, but this one is quite exceptional; this is not surprising for those who know Serge Lang's books." --EMS NEWSLETTER§

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An Introduction to Ordinary Differential Equation LAP Lambert Academic Publishing

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In mathematics, a differential equation is an equation that relates one or more functions and their derivatives. This book deals with the basic concept of Differential Equations. It covers the basic discussions on ordinary differential equations as fundamentals for the study of differential equations. This consists of the lessons together with sample problems and exercises at the end of every topic to give way the student for him to solve it.

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Fundamentals of Mathematical Physics Dover Publications Inc.

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Indispensable for students of modern physics, this text provides the necessary background in mathematics to study the concepts of electromagnetic theory and quantum mechanics. Topics include vector algebra, matrix and tensor algebra, vector calculus, functions of a complex variable, integral transforms, linear differential equations, and partial differential equations. 1967 edition.

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Fundamentals of Matrix Computations 3e John Wiley & Sons Inc

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This new, modernized edition provides a clear and thorough introduction to matrix computations,a key component of scientific computing Retaining the accessible and hands-on style of its predecessor, Fundamentals of Matrix Computations , Third Edition thoroughly details matrix computations and the accompanying theory alongside the author's useful insights. The book presents the most important algorithms of numerical linear algebra and helps readers to understand how the algorithms are developed and why they work.Along with new and updated examples, the Third Edition features: A novel approach to Francis' QR algorithm that explains its properties without reference to the basic QR algorithm Application of classical Gram-Schmidt with reorthogonalization A revised approach to the derivation of the Golub-Reinsch SVD algorithm New coverage on solving product eigenvalue problems Expanded treatment of the Jacobi-Davidson method A new discussion on stopping criteria for iterative methods for solving linear equations Throughout the book, numerous new and updated exercises-ranging from routine computations and verifications to challenging programming and proofs-are provided, allowing readers to immediately engage in applying the presented concepts. The new edition also incorporates MATLAB to solve real-world problems in electrical circuits, mass-spring systems, and simple partial differential equations, and an index of MATLAB terms assists readers with understanding the basic concepts related to the software.Fundamentals of Matrix Computations , Third Edition is an excellent book for courses on matrix computations and applied numerical linear algebra at the upper-undergraduate and graduate level. The book is also a valuable resource for researchers and practitioners working in the fields of engineering and computer science who need to know how to solve problems involving matrix computations.

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Lectures on Vibrations Akademia Marynarki Wojennej

MECHANIKA

Owing to their flexibility, the components of structures and machinery are capable of relative motion when subjected to internal or external forces. If such motion is oscillatory in nature, the motion is referred to as vibration. Although applications exist where vibration performs a useful function, vibration in ships is undesirable as it tends to accelerate the wearing of parts such as bearings and gears, create excessive noise and transmit significant forces and/or motion to accommodation, working and recreation spaces as well as to other equipment. Humans may be exposed to vibrations transmitted to the whole body or to particular parts of the body, such as the head or limbs. Designers should primarily be concerned with vibrations transmitted to the body through supporting surfaces such as the buttocks or feet. Research shows that mechanical vibration interferes with work quality and productivity, safety, health, comfort, and causes motion sickness. The literature also shows that vibration may modify crewmember perception (e.g., reading text and instruments, depth perception), influence task control movements (e.g., tactile sense, head/hand movements, manual tracking) and lead to impairment of speech. These factors may result in increased crewmember reaction/response times and possibility of human error. There are many different sources of vibration in ships, such as propeller and stern wake, main engine and other machinery, wave loads and environmental effects. Due to the complexity of these sources of excitation and of the structural configuration of ships, harmful vibration problems still occur even though vibration prediction techniques have developed rapidly and are well established through the use of Finite Element Method software. Continuing research activities have shown that carrying out vibration control is a tend as well as requirement for ships and offshore structures. Also in many other engineering branches it is well known that the proper vibration control in the design process is necessary a safe and satisfactory working and living environment as well as to avoid abnormal wear and tear on the machinery and structures. Since vibration and noise disturb the surrounding medium, their levels should be low also from reason, particularly in submarines. The appropriately reduced acoustic emission and electromagnetic signature of submarines decrease a vessel

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Aerodynamics of Wings and Bodies Dover Publications Inc.

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1. Review of Fundamentals of Fuid Mechanics 1-1 General Assumptions and Basic Differential Equations 1-2 Conservation Laws for a Barotropic Fluid in a Conservative Body Force Field 1-3 Some Geometric or Kinematic Properties of the Velocity Field 1-4 The Independence of Scale in Inviscid Flows 1-5 Vortex Theorems for the Ideal Fluid 1-6 Integral Conservation Theorems for Inviscid Fluid 1-7 Irrotational Flow 1-8 The Acceleration Potential2. Constant-Density Inviscid Flow 2-1 Introduction 2-2 The Three-Dimensional Rigid Solid Moving Through a Liquid 2-3 The Representation of ? in Terms of Boundary Values 2-4 "Further Examination of the Rigid, Impermeable Solid Moving Through a Constant-Density Fluid Without Circulation" 2-5 Some Deductions from Lagrange's Equations of Motion in Particular Cases 2-6 Examples of Two- and Three-Dimensional Flows Without Circulation 2-7 Circulation and the Topology of Flow Regimes 2-8 Examples of Constant-Density Flows Where Circulation May Be Generated 2-9 "Two-Dimensional, Constant-Density Flow: Fundamental Ideas" 2-10 "Two-Dimensinal, Constant-Density Flow: Conformal Transformations and Their Uses" 2-11 The Kutta Condition and Lift3. Singular Perturbation Problems 3-1 Introduction 3-2 Expansion in a Small Parameter; Singular Peturbation Problems4. Effects of Viscosity 4-1 Introduction 4-2 Qualitative Effects of Viscosity 4-3 Boundary Layer on a Flat Plate5. Thin-Wing Theory 5-1 Introduction 5-2 Expansion Procedure for the Equations of Motion 5-3 Thin Airfoils in Incompressible Flow 5-4 Thin Airfoils in Supersonic Flow6. Slender-Body Theory 6-1 Introduction 6-2 Expansion Procedure for Axisymmetric Flow 6-3 Solutions for Subsonic and Supersonic Flows 6-4 General Slender Body 6-5 Examples of Lifting Slender-Body flow 6-6 The Pressure Drag of a Slender Body in Supersonic Flow 6-7 Transverse Forces and Moments on a Slender Body7. "Three-Dimensional Wings in Steady, Subsonic Flow" 7-1 Compressibility Corrections for Wings 7-2 Constant-Density Flow: the Thickness Problem 7-3 Constant-Density Flow: the Lifting Problem 7-4 Lifting-Line Theory 7-5 More Refined Theories of Lifting-Line type 7-6 Theories of Lifting-Surface Type8. Three-Dimensional Thin Wings in Steady Supersonic Flow 8-1 Introduction 8-2 Nonlifting Wings 8-3 Lifting Wings of Simple Planform 8-4 The Method of Evvard and Krasilshchikova 8-5 Conical Flows 8-6 Numerical Integration Schemes Appendix to Section 8-49. Drag at Supersonic Speeds 9-1 Introduction 9-2 Calculation of Supersonic Drag by Use of Momentum Theory 9-3 Drag of a Lineal Source Distribution 9-4 Optimum Shape of a Slender Body of Revolution 9-5 Drag of a General Source Distribution. Hayes' Method 9-6 Extension to Include Lift and Side Force Elements 9-7 The Supersonic Area Rule 9-8 Wave Drag Due to Lift10. Use of Flow-Reversal Theorems in Drag Minimization Problems 10-1 Introduction 10-2 "Drag of a General Singularity Distribution from a "Close" Viewpoint" 10-3 The Drag Due to Lift in Forward and Reverse Flows 10-4 The Drag Due to Thickness in Forward and Reverse Flows 10-5 The Drag of a General Distribution of Singularities in Steady Supersonic Forward or Reverse Flows 10-6 The Combined Flow Field 10-7 Use of the Combined Flow Field to Identify Minimum Drag Conditions 10-8 The Calculation of Minimum Drag by Solution of an Equivalent Two-Dimensional Potential Problem11. Interference and Nonplanar Lifting-Surfaces Theories 11-1 Introduction 11-2 Interfering or Nonplanar Lifting Surfaces in Subsonic Flow 11-3 Special Cases and Numerical Solution 11-4 Loads on Interfereing Surfaces in Subsonic Flow 11-5 Nonplanar Lifting Surfaces in Supersonic Flow12 Transonic Small-Disturbance flow 12-1 Introduction 12-2 Small-Perturbation Flow Equations 12-3 Similarity Rules 12-4 Methods of Solution13 Unsteady Flow 13-1 Statement of the Problem 13-2 "Two Dimensional, Constant-Density Flow" 13-3 Airfoils Oscillating at Supersonic and Subsonic Speeds 13-4 Indicial Motion in a Compressible Fluid 13-5 Three-Dimensional Oscillating Wings References and Author Index List of Symbols Index

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Wave Fields in Real Media Elsevier Science Publishing Co Inc

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Wave Fields in Real Media: Wave Propagation in Anisotropic, Anelastic, Porous and Electromagnetic Media examines the differences between an ideal and a real description of wave propagation, starting with the introduction of relevant stress-strain relations. The combination of this relation and the equations of momentum conservation lead to the equation of motion. The differential formulation is written in terms of memory variables, and Biot's theory is used to describe wave propagation in porous media. For each rheology, a plane-wave analysis is performed to show the physics of wave propagation.New topics covered in this edition include Fermat principle and its relation to Snell law; S-wave amplification function; bounds and averages of seismic Q; seismic attenuation in partially molten rocks; fluid-pressure diffusion in isotropic media; equivalent inclusion average stress model; cracks and pores effective medium model; Thermo-poroelasticity; the Kjartansson model of thermoelastic attenuation; magnetotellurics; machine learning in geophysics; and thermoelastic wave simulation with the Cole-Cole model. Wave Fields in Real Media contains a review of the main direct numerical methods for solving the equation of motion in the time and space domains. The emphasis is on geophysical applications for seismic exploration, but researchers in the fields of earthquake seismology, rock acoustics, and material science - including many branches of acoustics of fluids and solids - may also find this text useful. Examines the fundamentals of wave propagation in anisotropic, anelastic, and porous media Presents all equations and concepts necessary to understand the physics of wave propagation Emphasizes geophysics, particularly, seismic exploration for hydrocarbon reservoirs, which is essential for exploration and production of oil

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Methods of the Theory of Functions of Many Complex Variables Dover Publications Inc.

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This systematic exposition outlines the fundamentals of the theory of single sheeted domains of holomorphy. It further illustrates applications to quantum field theory, the theory of functions, and differential equations with constant coefficients. Students of quantum field theory will find this text of particular value. 1966 edition.

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Essential PTC (R) Mathcad Prime (R) 3.0 Elsevier Books

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Learn how to use PTC Mathcad Prime 3.0, one of the world's leading tools for technical computing, in the context of engineering, science, and math applications. Quickly harness the power of PTC Mathcad Prime 3.0 to solve both simple and complex problems. Essential PTC Mathcad Prime 3.0 is perfect for college students, first-time users, and experienced Mathcad 15 users who are moving to PTC Mathcad Prime 3.0. Updated from Maxfield's popular Essential Mathcad, this book introduces the most powerful functions and features of the new PTC Mathcad Prime 3.0 software and teaches how to apply them to create comprehensive calculations for any quantitative subject. Examples from several fields demonstrate the power and utility of PTC Mathcad's tools while also demonstrating how users can eff ectively incorporate Microsoft Excel spreadsheets into the software. * Learn the basics faster: Chapter 1 introduces many fundamentals of Mathcad, allowing the reader to begin using the program in less time.* Learn PTC Mathcad tools in context: Incorporates many applied examples and problems from a wide variety of disciplines.*Thorough discussion of many PTC Mathcad tools: Units, arrays, plotting, solving, symbolic calculations, programming, algebra, calculus, differential equations, reading from files, writing to files, and incorporating MS Excel spreadsheets.* Each copy of the book includes a code to download PTC Mathcad Prime 3.0 Student Edition, giving the user a full year of use from the time of installation. (The Student Edition software is intended for educational purposes only.)

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