{"product_id":"elementary-differential-equations-and-boundary-value-problems-isbn-9781119777694","title":"Elementary Differential Equations and Boundary Value Problems","description":"\u003cp\u003e\u003ci\u003eElementary Differential Equations and Boundary Value Problems, 12th Edition\u003c\/i\u003e is written from the viewpoint of the applied mathematician, whose interest in differential equations may sometimes be quite theoretical, sometimes intensely practical, and often somewhere in between. In this revision, new author Douglas Meade focuses on  developing students conceptual understanding with new concept questions and worksheets for each chapter. Meade builds upon Boyce and DiPrima’s work to combine a sound and accurate (but not abstract) exposition of the elementary theory of differential equations with considerable material on methods of solution, analysis, and approximation that have proved useful in a wide variety of applications. The main prerequisite for engaging with the program is a working knowledge of calculus, gained from a normal two or three semester course sequence or its equivalent. Some familiarity with matrices will also be helpful in the chapters on systems of differential equations. \u003c\/p\u003e \u003cp\u003ePreface v\u003c\/p\u003e \u003cp\u003e\u003cb\u003e1 Introduction 1\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e1.1 Some Basic Mathematical Models; Direction Fields 1\u003c\/p\u003e \u003cp\u003e1.2 Solutions of Some Differential Equations 9\u003c\/p\u003e \u003cp\u003e1.3 Classification of Differential Equations 17\u003c\/p\u003e \u003cp\u003e\u003cb\u003e2 First-Order Differential Equations 26\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e2.1 Linear Differential Equations; Method of Integrating Factors 26\u003c\/p\u003e \u003cp\u003e2.2 Separable Differential Equations 34\u003c\/p\u003e \u003cp\u003e2.3 Modeling with First-Order Differential Equations 41\u003c\/p\u003e \u003cp\u003e2.4 Differences Between Linear and Nonlinear Differential Equations 53\u003c\/p\u003e \u003cp\u003e2.5 Autonomous Differential Equations and Population Dynamics 61\u003c\/p\u003e \u003cp\u003e2.6 Exact Differential Equations and Integrating Factors 72\u003c\/p\u003e \u003cp\u003e2.7 Numerical Approximations: Euler’s Method 78\u003c\/p\u003e \u003cp\u003e2.8 The Existence and Uniqueness Theorem 86\u003c\/p\u003e \u003cp\u003e2.9 First-Order Difference Equations 93\u003c\/p\u003e \u003cp\u003e\u003cb\u003e3 Second-Order Linear Differential Equations 106\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e3.1 Homogeneous Differential Equations with Constant Coefficients 106\u003c\/p\u003e \u003cp\u003e3.2 Solutions of Linear Homogeneous Equations; the Wronskian 113\u003c\/p\u003e \u003cp\u003e3.3 Complex Roots of the Characteristic Equation 123\u003c\/p\u003e \u003cp\u003e3.4 Repeated Roots; Reduction of Order 130\u003c\/p\u003e \u003cp\u003e3.5 Nonhomogeneous Equations; Method of Undetermined Coefficients 136\u003c\/p\u003e \u003cp\u003e3.6 Variation of Parameters 145\u003c\/p\u003e \u003cp\u003e3.7 Mechanical and Electrical Vibrations 150\u003c\/p\u003e \u003cp\u003e3.8 Forced Periodic Vibrations 161\u003c\/p\u003e \u003cp\u003e\u003cb\u003e4 Higher-Order Linear Differential Equations 173\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e4.1 General Theory of \u003ci\u003en\u003c\/i\u003e;;;; Order Linear Differential Equations 173\u003c\/p\u003e \u003cp\u003e4.2 Homogeneous Differential Equations with Constant Coefficients 178\u003c\/p\u003e \u003cp\u003e4.3 The Method of Undetermined Coefficients 185\u003c\/p\u003e \u003cp\u003e4.4 The Method of Variation of Parameters 189\u003c\/p\u003e \u003cp\u003e\u003cb\u003e5 Series Solutions of Second-Order Linear Equations 194\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e5.1 Review of Power Series 194\u003c\/p\u003e \u003cp\u003e5.2 Series Solutions Near an Ordinary Point, Part I 200\u003c\/p\u003e \u003cp\u003e5.3 Series Solutions Near an Ordinary Point, Part II 209\u003c\/p\u003e \u003cp\u003e5.4 Euler Equations; Regular Singular Points 215\u003c\/p\u003e \u003cp\u003e5.5 Series Solutions Near a Regular Singular Point, Part I 224\u003c\/p\u003e \u003cp\u003e5.6 Series Solutions Near a Regular Singular Point, Part II 228\u003c\/p\u003e \u003cp\u003e5.7 Bessel’s Equation 235\u003c\/p\u003e \u003cp\u003e\u003cb\u003e6 The Laplace Transform 247\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e6.1 Definition of the Laplace Transform 247\u003c\/p\u003e \u003cp\u003e6.2 Solution of Initial Value Problems 254\u003c\/p\u003e \u003cp\u003e6.3 Step Functions 263\u003c\/p\u003e \u003cp\u003e6.4 Differential Equations with Discontinuous Forcing Functions 270\u003c\/p\u003e \u003cp\u003e6.5 Impulse Functions 275\u003c\/p\u003e \u003cp\u003e6.6 The Convolution Integral 280\u003c\/p\u003e \u003cp\u003e\u003cb\u003e7 Systems of First-Order Linear Equations 288\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e7.1 Introduction 288\u003c\/p\u003e \u003cp\u003e7.2 Matrices 293\u003c\/p\u003e \u003cp\u003e7.3 Systems of Linear Algebraic Equations; Linear Independence, Eigenvalues, Eigenvectors 301\u003c\/p\u003e \u003cp\u003e7.4 Basic Theory of Systems of First-Order Linear Equations 311\u003c\/p\u003e \u003cp\u003e7.5 Homogeneous Linear Systems with Constant Coefficients 315\u003c\/p\u003e \u003cp\u003e7.6 Complex-Valued Eigenvalues 325\u003c\/p\u003e \u003cp\u003e7.7 Fundamental Matrices 335\u003c\/p\u003e \u003cp\u003e7.8 Repeated Eigenvalues 342\u003c\/p\u003e \u003cp\u003e7.9 Nonhomogeneous Linear Systems 351\u003c\/p\u003e \u003cp\u003e\u003cb\u003e8 Numerical Methods 363\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e8.1 The Euler or Tangent Line Method 363\u003c\/p\u003e \u003cp\u003e8.2 Improvements on the Euler Method 372\u003c\/p\u003e \u003cp\u003e8.3 The Runge-Kutta Method 376\u003c\/p\u003e \u003cp\u003e8.4 Multistep Methods 380\u003c\/p\u003e \u003cp\u003e8.5 Systems of First-Order Equations 385\u003c\/p\u003e \u003cp\u003e8.6 More on Errors; Stability 387\u003c\/p\u003e \u003cp\u003e\u003cb\u003e9 Nonlinear Differential Equations and Stability 400\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e9.1 The Phase Plane: Linear Systems 400\u003c\/p\u003e \u003cp\u003e9.2 Autonomous Systems and Stability 410\u003c\/p\u003e \u003cp\u003e9.3 Locally Linear Systems 419\u003c\/p\u003e \u003cp\u003e9.4 Competing Species 429\u003c\/p\u003e \u003cp\u003e9.5 Predator – Prey Equations 439\u003c\/p\u003e \u003cp\u003e9.6 Liapunov’s Second Method 446\u003c\/p\u003e \u003cp\u003e9.7 Periodic Solutions and Limit Cycles 455\u003c\/p\u003e \u003cp\u003e9.8 Chaos and Strange Attractors: The Lorenz Equations 465\u003c\/p\u003e \u003cp\u003e\u003cb\u003e10 Partial Differential Equations and Fourier Series 476\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e10.1 Two-Point Boundary Value Problems 476\u003c\/p\u003e \u003cp\u003e10.2 Fourier Series 482\u003c\/p\u003e \u003cp\u003e10.3 The Fourier Convergence Theorem 490\u003c\/p\u003e \u003cp\u003e10.4 Even and Odd Functions 495\u003c\/p\u003e \u003cp\u003e10.5 Separation of Variables; Heat Conduction in a Rod 501\u003c\/p\u003e \u003cp\u003e10.6 Other Heat Conduction Problems 508\u003c\/p\u003e \u003cp\u003e10.7 The Wave Equation: Vibrations of an Elastic String 516\u003c\/p\u003e \u003cp\u003e10.8 Laplace’s Equation 527\u003c\/p\u003e \u003cp\u003eA Appendix 537\u003c\/p\u003e \u003cp\u003eB Appendix 541\u003c\/p\u003e \u003cp\u003e\u003cb\u003e11 Boundary Value Problems and Stur-Liouville Theory 544\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e11.1 The Occurrence of Two-Point Boundary Value Problems 544\u003c\/p\u003e \u003cp\u003e11.2 Sturm-Liouville Boundary Value Problems 550\u003c\/p\u003e \u003cp\u003e11.3 Nonhomogeneous Boundary Value Problems 561\u003c\/p\u003e \u003cp\u003e11.4 Singular Sturm-Liouville Problems 572\u003c\/p\u003e \u003cp\u003e11.5 Further Remarks on the Method of Separation of Variables: A Bessel Series Expansion 578\u003c\/p\u003e \u003cp\u003e11.6 Series of Orthogonal Functions: Mean Convergence 582\u003c\/p\u003e \u003cp\u003eAnswers to Problems 591\u003c\/p\u003e \u003cp\u003eIndex 624\u003c\/p\u003e","brand":"Wiley","offers":[{"title":"Default Title","offer_id":47989118533861,"sku":"NP9781119777694","price":111.0,"currency_code":"USD","in_stock":false}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/1842\/7735\/files\/9781119777694.jpg?v=1761782870","url":"https:\/\/k12savings.com\/es\/products\/elementary-differential-equations-and-boundary-value-problems-isbn-9781119777694","provider":"K12savings","version":"1.0","type":"link"}