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ویرایش: 1 نویسندگان: Victor Henner, Tatyana Belozerova, Alexander Nepomnyashchy سری: Textbooks in Mathematics ISBN (شابک) : 1138339830, 9781138339835 ناشر: Chapman and Hall/CRC سال نشر: 2019 تعداد صفحات: 397 زبان: English فرمت فایل : PDF (درصورت درخواست کاربر به PDF، EPUB یا AZW3 تبدیل می شود) حجم فایل: 3 مگابایت
کلمات کلیدی مربوط به کتاب معادلات دیفرانسیل جزئی: روشها و کاربردهای تحلیلی (): ریاضیات، حساب دیفرانسیل و انتگرال، معادلات دیفرانسیل
در صورت تبدیل فایل کتاب Partial Differential Equations: Analytical Methods and Applications (Textbooks in Mathematics) به فرمت های PDF، EPUB، AZW3، MOBI و یا DJVU می توانید به پشتیبان اطلاع دهید تا فایل مورد نظر را تبدیل نمایند.
توجه داشته باشید کتاب معادلات دیفرانسیل جزئی: روشها و کاربردهای تحلیلی () نسخه زبان اصلی می باشد و کتاب ترجمه شده به فارسی نمی باشد. وبسایت اینترنشنال لایبرری ارائه دهنده کتاب های زبان اصلی می باشد و هیچ گونه کتاب ترجمه شده یا نوشته شده به فارسی را ارائه نمی دهد.
معادلات دیفرانسیل جزئی: روشها و کاربردهای تحلیلی تمام مباحث پایه یک دوره معادلات دیفرانسیل جزئی (PDE) برای دانشجویان مقطع کارشناسی یا دوره مبتدی برای دانشجویان کارشناسی ارشد را پوشش میدهد. . این توضیح فیزیکی کیفی نتایج ریاضی را ارائه می دهد و در عین حال سطح مورد انتظار دقت را حفظ می کند.
این متن مهارت های لازم برای حل مسئله را معرفی و ترویج می کند. ارائه مختصر و دوستانه برای خواننده است. رویکرد «تدریس بهمثال» مثالهای متعددی را ارائه میکند که با دقت انتخاب شدهاند که یادگیری گام به گام مفاهیم و تکنیکها را راهنمایی میکند. سری فوریه، مسئله Sturm-Liouville، تبدیل فوریه، و تبدیل لاپلاس گنجانده شده است. سطح ارائه و ساختار کتاب به خوبی برای استفاده در دروس مهندسی، فیزیک و ریاضیات کاربردی مناسب است.
نکات مهم :
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Partial Differential Equations: Analytical Methods and Applications covers all the basic topics of a Partial Differential Equations (PDE) course for undergraduate students or a beginners’ course for graduate students. It provides qualitative physical explanation of mathematical results while maintaining the expected level of it rigor.
This text introduces and promotes practice of necessary problem-solving skills. The presentation is concise and friendly to the reader. The "teaching-by-examples" approach provides numerous carefully chosen examples that guide step-by-step learning of concepts and techniques. Fourier series, Sturm-Liouville problem, Fourier transform, and Laplace transform are included. The book’s level of presentation and structure is well suited for use in engineering, physics and applied mathematics courses.
Highlights:
Cover Half Title Series Page Title Page Copyright Page Dedication Contents Preface 1. Introduction 1.1 Basic Definitions 1.2 Examples 2. First-Order Equations 2.1 Linear First-Order Equations 2.1.1 General Solution 2.1.2 Initial Condition 2.2 Quasilinear First-Order Equations 2.2.1 Characteristic Curves 2.2.2 Examples 3. Second-Order Equations 3.1 Classification of Second-Order Equations 3.2 Canonical Forms 3.2.1 Hyperbolic Equations 3.2.2 Elliptic Equations 3.2.3 Parabolic Equations 4. The Sturm-Liouville Problem 4.1 General Consideration 4.2 Examples of Sturm-Liouville Problems 5. One-Dimensional Hyperbolic Equations 5.1 Wave Equation 5.2 Boundary and Initial Conditions 5.3 Longitudinal Vibrations of a Rod and Electrical Oscillations 5.3.1 Rod Oscillations: Equations and Boundary Conditions 5.3.2 Electrical Oscillations in a Circuit 5.4 Traveling Waves: D'Alembert Method 5.5 Cauchy Problem for Nonhomogeneous Wave Equation 5.5.1 D'Alembert's Formula 5.5.2 Green's Function 5.5.3 Well-Posedness of the Cauchy Problem 5.6 Finite Intervals: The Fourier Method for Homogeneous Equations 5.7 The Fourier Method for Nonhomogeneous Equations 5.8 The Laplace Transform Method: Simple Cases 5.9 Equations with Nonhomogeneous Boundary Conditions 5.10 The Consistency Conditions and Generalized Solutions 5.11 Energy in the Harmonics 5.12 Dispersion of Waves 5.12.1 Cauchy Problem in an Infinite Region 5.12.2 Propagation of a Wave Train 5.13 Wave Propagation on an Inclined Bottom: Tsunami Effect 6. One-Dimensional Parabolic Equations 6.1 Heat Conduction and Diffusion: Boundary Value Problems 6.1.1 Heat Conduction 6.1.2 Diffusion Equation 6.1.3 One-dimensional Parabolic Equations and Initial and Boundary Conditions 6.2 The Fourier Method for Homogeneous Equations 6.3 Nonhomogeneous Equations 6.4 Green's Function and Duhamel's Principle 6.5 The Fourier Method for Nonhomogeneous Equations with Nonhomogeneous Boundary Conditions 6.6 Large Time Behavior of Solutions 6.7 Maximum Principle 6.8 The Heat Equation in an Infinite Region 7. Elliptic Equations 7.1 Elliptic Differential Equations and Related Physical Problems 7.2 Harmonic Functions 7.3 Boundary Conditions 7.3.1 Example of an Ill-posed Problem 7.3.2 Well-posed Boundary Value Problems 7.3.3 Maximum Principle and its Consequences 7.4 Laplace Equation in Polar Coordinates 7.5 Laplace Equation and Interior BVP for Circular Domain 7.6 Laplace Equation and Exterior BVP for Circular Domain 7.7 Poisson Equation: General Notes and a Simple Case 7.8 Poisson Integral 7.9 Application of Bessel Functions for the Solution of Poisson Equations in a Circle 7.10 Three-dimensional Laplace Equation for a Cylinder 7.11 Three-dimensional Laplace Equation for a Ball 7.11.1 Axisymmetric Case 7.11.2 Non-axisymmetric Case 7.12 BVP for Laplace Equation in a Rectangular Domain 7.13 The Poisson Equation with Homogeneous Boundary Conditions 7.14 Green's Function for Poisson Equations 7.14.1 Homogeneous Boundary Conditions 7.14.2 Nonhomogeneous Boundary Conditions 7.15 Some Other Important Equations 7.15.1 Helmholtz Equation 7.15.2 Schrödinger Equation 8. Two-Dimensional Hyperbolic Equations 8.1 Derivation of the Equations of Motion 8.1.1 Boundary and Initial Conditions 8.2 Oscillations of a Rectangular Membrane 8.2.1 The Fourier Method for Homogeneous Equations with Homogeneous Boundary Conditions 8.2.2 The Fourier Method for Nonhomogeneous Equations with Homogeneous Boundary Conditions 8.2.3 The Fourier Method for Nonhomogeneous Equations with Nonhomogeneous Boundary Conditions 8.3 Small Transverse Oscillations of a Circular Membrane 8.3.1 The Fourier Method for Homogeneous Equations with Homogeneous Boundary Conditions 8.3.2 Axisymmetric Oscillations of a Membrane 8.3.3 The Fourier Method for Nonhomogeneous Equations with Homogeneous Boundary Conditions 8.3.4 Forced Axisymmetric Oscillations 8.3.5 The Fourier Method for Equations with Nonhomogeneous Boundary Conditions 9. Two-Dimensional Parabolic Equations 9.1 Heat Conduction within a Finite Rectangular Domain 9.1.1 The Fourier Method for the Homogeneous Heat Equation (Free Heat Exchange) 9.1.2 The Fourier Method for Nonhomogeneous Heat Equation with Homogeneous Boundary Conditions 9.2 Heat Conduction within a Circular Domain 9.2.1 The Fourier Method for the Homogeneous Heat Equation 9.2.2 The Fourier Method for the Nonhomogeneous Heat Equation 9.2.3 The Fourier Method for the Nonhomogeneous Heat Equation with Nonhomogeneous Boundary Conditions 9.3 Heat Conduction in an Infinite Medium 9.4 Heat Conduction in a Semi-Infinite Medium 10. Nonlinear Equations 10.1 Burgers Equation 10.1.1 Kink Solution 10.1.2 Symmetries of the Burger's Equation 10.2 General Solution of the Cauchy Problem 10.2.1 Interaction of Kinks 10.3 Korteweg-de Vries Equation 10.3.1 Symmetry Properties of the KdV Equation 10.3.2 Cnoidal Waves 10.3.3 Solitons 10.3.4 Bilinear Formulation of the KdV Equation 10.3.5 Hirota's Method 10.3.6 Multisoliton Solutions 10.4 Nonlinear Schrödinger Equation 10.4.1 Symmetry Properties of NSE 10.4.2 Solitary Waves Appendix A: Fourier Series, Fourier and Laplace Transforms A.1 Periodic Processes and Periodic Functions A.2 Fourier Formulas A.3 Convergence of Fourier Series A.4 Fourier Series for Non-periodic Functions A.5 Fourier Expansions on Intervals of Arbitrary Length A.6 Fourier Series in Cosine or in Sine Functions A.7 Examples A.8 The Complex Form of the Trigonometric Series A.9 Fourier Series for Functions of Several Variables A.10 Generalized Fourier Series A.11 The Gibbs Phenomenon A.12 Fourier Transforms A.13 Laplace Transforms A.14 Applications of Laplace Transform for ODE Appendix B: Bessel and Legendre Functions B.1 Bessel Equation B.2 Properties of Bessel Functions B.3 Boundary Value Problems and Fourier-Bessel Series B.4 Spherical Bessel Functions B.5 The Gamma Function B.6 Legendre Equation and Legendre Polynomials B.7 Fourier-Legendre Series in Legendre Polynomials B.8 Associated Legendre Functions B.9 Fourier-Legendre Series in Associated Legendre Functions B.10 Airy Functions Appendix C: Sturm-Liouville Problem and Auxiliary Functions for One and Two Dimensions C.1 Eigenvalues and Eigenfunctions of 1D Sturm-Liouville Problem for Different Types of Boundary Conditions C.2 Auxiliary Functions Appendix D: The Sturm-Liouville Problem for Circular and Rectangular Domains D.1 The Sturm-Liouville Problem for a Circle D.2 The Sturm-Liouville Problem for the Rectangle Appendix E: The Heat Conduction and Poisson Equations for Rectangular Domains – Examples E.1 The Laplace and Poisson Equations for a Rectangular Domain with Nonhomogeneous Boundary Conditions – Examples E.2 The Heat Conduction Equations with Nonhomogeneous Boundary Conditions – Examples Bibliography Index