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از ساعت 7 صبح تا 10 شب
ویرایش: 3
نویسندگان: Henry J. Ricardo
سری:
ISBN (شابک) : 0128234172, 9780128234174
ناشر: Academic Press
سال نشر: 2020
تعداد صفحات: 550
زبان: English
فرمت فایل : PDF (درصورت درخواست کاربر به PDF، EPUB یا AZW3 تبدیل می شود)
حجم فایل: 8 مگابایت
کلمات کلیدی مربوط به کتاب مقدمه ای مدرن بر معادلات دیفرانسیل: ریاضیات، حساب دیفرانسیل و انتگرال، معادلات دیفرانسیل
در صورت تبدیل فایل کتاب A Modern Introduction to Differential Equations 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 مقدمه ای مدرن بر معادلات دیفرانسیل 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.
مقدمه ای مدرن بر معادلات دیفرانسیل، ویرایش سوم، مقدمه ای بر مفاهیم اساسی معادلات دیفرانسیل ارائه می دهد. این کتاب با معرفی مفاهیم اولیه معادلات دیفرانسیل، با تمرکز بر جنبه های تحلیلی، گرافیکی و عددی معادلات مرتبه اول، از جمله میدان های شیب و خطوط فاز، آغاز می شود. منبع جامع سپس روشهای حل معادلات خطی همگن و ناهمگن مرتبه دوم با ضرایب ثابت، سیستمهای معادلات دیفرانسیل خطی، تبدیل لاپلاس و کاربردهای آن برای حل معادلات دیفرانسیل و سیستمهای معادلات دیفرانسیل، و سیستمهای معادلات غیرخطی را پوشش میدهد.
در سرتاسر متن، ویژگیهای آموزشی ارزشمند از یادگیری و آموزش پشتیبانی میکنند. هر فصل با خلاصه ای از مفاهیم مهم به پایان می رسد و شکل ها و جداول برای کمک به دانش آموزان در تجسم یا خلاصه کردن مفاهیم ارائه شده است. این کتاب همچنین شامل مثالها و تمرینهای بهروز شدهای است که از زیستشناسی، شیمی، و اقتصاد و همچنین ریاضیات خالص سنتی، فیزیک و مهندسی گرفته شدهاند.
A Modern Introduction to Differential Equations, Third Edition, provides an introduction to the basic concepts of differential equations. The book begins by introducing the basic concepts of differential equations, focusing on the analytical, graphical and numerical aspects of first-order equations, including slope fields and phase lines. The comprehensive resource then covers methods of solving second-order homogeneous and nonhomogeneous linear equations with constant coefficients, systems of linear differential equations, the Laplace transform and its applications to the solution of differential equations and systems of differential equations, and systems of nonlinear equations.
Throughout the text, valuable pedagogical features support learning and teaching. Each chapter concludes with a summary of important concepts, and figures and tables are provided to help students visualize or summarize concepts. The book also includes examples and updated exercises drawn from biology, chemistry, and economics, as well as from traditional pure mathematics, physics, and engineering.
Contents Preface Philosophy Use of technology Pedagogical features and writing style Preface New to the Third Edition Supplements Acknowledgments 1 Introduction to differential equations Introduction 1.1 Basic terminology 1.1.1 Ordinary and partial differential equations Ordinary differential equations Partial differential equations The order of an ordinary differential equation A general form for an ordinary differential equation Linear and nonlinear ordinary differential equations 1.1.2 Systems of ordinary differential equations 1.2 Solutions of differential equations 1.2.1 Basic notions Implicit solutions 1.2.2 Families of solutions I 1.3 Initial-value problems and boundary-value problems 1.3.1 An integral form of an IVP solution 1.3.2 Families of solutions II Boundary-value problems General solutions 1.3.3 Solutions of systems of ODEs Summary 2 First-order differential equations Introduction 2.1 Separable equations 2.2 Linear equations 2.2.1 The superposition principle 2.2.2 Variation of parameters and the integrating factor 2.3 Compartment problems 2.4 Slope fields 2.4.1 Autonomous and nonautonomous equations 2.5 Phase lines and phase portraits 2.5.1 The logistic equation 2.6 Equilibrium points: sinks, sources, and nodes 2.6.1 A test for equilibrium points 2.7 Bifurcations 2.7.1 Basic concepts 2.7.2 Application to differential equations 2.8 Existence and uniqueness of solutions 2.8.1 An Existence and Uniqueness Theorem 2.8.2 A sketch of a proof of the Existence and Uniqueness Theorem Summary 3 The numerical approximation of solutions Introduction 3.1 Euler's method 3.1.1 Stiff differential equations 3.2 The improved Euler method 3.3 More sophisticated numerical methods: Runge-Kutta and others Summary 4 Second- and higher-order equations Introduction 4.1 Homogeneous second-order linear equations with constant coefficients 4.1.1 The characteristic equation and eigenvalues 4.1.2 Real but unequal roots 4.1.3 Real but equal roots 4.1.4 Complex conjugate roots 4.1.5 The amplitude-phase angle form of a solution 4.1.6 Summary 4.2 Nonhomogeneous second-order linear equations with constant coefficients 4.2.1 The structure of solutions 4.3 The method of undetermined coefficients 4.4 Variation of parameters 4.5 Higher-order linear equations with constant coefficients 4.6 Existence and uniqueness 4.6.1 An Existence and Uniqueness Theorem 4.6.2 Many solutions 4.6.3 No solution 4.6.4 Exactly one solution Summary 5 The Laplace transform Introduction 5.1 The Laplace transform of some important functions 5.2 The inverse transform and the convolution 5.2.1 The inverse Laplace transform 5.2.2 The convolution 5.2.3 Integral equations and integro-differential equations 5.2.4 The Laplace transform and technology 5.3 Transforms of discontinuous functions 5.3.1 The Heaviside (unit step) function 5.4 Transforms of impulse functions-the Dirac delta function 5.5 Transforms of systems of linear differential equations 5.6 Laplace transforms of linear differential equations with variable coefficients Summary 6 Systems of linear differential equations Introduction 6.1 Higher-order equations and their equivalent systems 6.1.1 Conversion technique I: converting a higher-order equation into a system 6.1.2 Conversion technique II: converting a system into a higher-order equation 6.2 Existence and uniqueness 6.2.1 An Existence and Uniqueness Theorem 6.2.2 Many solutions 6.2.3 No solution 6.2.4 Exactly one solution 6.3 Numerical solutions of systems 6.3.1 Euler's method applied to systems 6.3.2 The fourth-order Runge-Kutta method for systems 6.4 The geometry of autonomous systems 6.4.1 Phase portraits for systems of equations 6.4.2 Equilibrium points 6.4.3 Three-dimensional systems 6.5 Systems and matrices 6.5.1 Matrices and vectors 6.5.2 The matrix representation of a linear system 6.5.3 Some matrix algebra 6.6 Two-dimensional systems of first-order linear equations 6.6.1 Eigenvalues and eigenvectors 6.6.2 Geometric interpretation of eigenvectors 6.6.3 The general problem 6.6.4 The geometric behavior of solutions 6.7 The stability of homogeneous linear systems: unequal real eigenvalues 6.7.1 Unequal real eigenvalues 6.7.2 The impossibility of dependent eigenvectors 6.7.3 Unequal positive eigenvalues 6.7.4 Unequal negative eigenvalues 6.7.5 Unequal eigenvalues with opposite signs 6.7.6 Unequal eigenvalues, one eigenvalue equal to zero 6.8 The stability of homogeneous linear systems: equal real eigenvalues 6.8.1 Equal nonzero eigenvalues, two independent eigenvectors 6.8.2 Equal nonzero eigenvalues, only one independent eigenvector 6.8.3 Both eigenvalues zero 6.9 The stability of homogeneous linear systems: complex eigenvalues 6.9.1 Complex eigenvalues and complex eigenvectors 6.10 Nonhomogeneous systems 6.10.1 The general solution 6.10.2 The method of undetermined coefficients 6.11 Spring-mass problems 6.11.1 Simple harmonic motion 6.11.2 Analysis 6.11.3 Another view-solution curves 6.11.4 Free damped motion 6.11.5 Different kinds of damping 6.11.6 Forced motion 6.11.7 Resonance 6.11.8 An analogy 6.12 Generalizations: the n xn case (n >=3) 6.12.1 Matrix representation 6.12.2 Eigenvalues and eigenvectors 6.12.3 Linear independence and linear dependence 6.12.4 Nonhomogeneous systems 6.12.5 Generalization to n xn systems Summary 7 Systems of nonlinear differential equations Introduction 7.1 Equilibria of nonlinear systems 7.2 Linear approximation at equilibrium points 7.2.1 Almost linear systems 7.3 The Hartman-Grobman theorem 7.4 Two important nonlinear systems 7.4.1 A predator-prey model: the Lotka-Volterra equations 7.4.2 A qualitative analysis of the Lotka-Volterra equations 7.4.3 Other graphical representations 7.4.4 The undamped pendulum 7.5 Bifurcations 7.6 Limit cycles and the Hopf bifurcation 7.6.1 Limit cycles 7.6.2 The Hopf bifurcation Summary A Some calculus concepts and results A.1 Local linearity: the tangent line approximation A.2 The chain rule A.3 The Taylor polynomial/Taylor series A.4 The fundamental theorem of calculus A.5 Partial fractions A.6 Improper integrals A.7 Functions of several variables/partial derivatives A.8 The tangent plane: the Taylor expansion of F(x,y) B Vectors and matrices B.1 Vectors and vector algebra; polar coordinates B.2 Matrices and basic matrix algebra B.3 Linear transformations and matrix multiplication B.4 Eigenvalues and eigenvectors C Complex numbers C.1 Complex numbers: the algebraic view C.2 Complex numbers: the geometric view C.3 The quadratic formula C.4 Euler's formula D Series solutions of differential equations D.1 Power series solutions of first-order equations D.2 Series solutions of second-order linear equations: ordinary points D.3 Regular singular points: the method of Frobenius D.4 The point at infinity D.5 Some additional special differential equations Answers and hints to odd-numbered exercises Index