{"product_id":"elementary-differential-equations-and-boundary-value-problems-international-adaptation","title":"Elementary Differential Equations and Boundary Value Problems, International Adaptation","description":"\u003cp\u003e\u003cb\u003eTABLE OF CONTENTS\u003c\/b\u003e \u003c\/p\u003e \u003cp\u003e\u003cb\u003e1 Introduction \u003c\/b\u003e \u003c\/p\u003e \u003cp\u003e1.1 Some Basic Mathematical Models  \u003c\/p\u003e \u003cp\u003e1.2 Solutions of Some Differential Equations  \u003c\/p\u003e \u003cp\u003e1.3 Classification of Differential Equations  \u003c\/p\u003e \u003cp\u003e  \u003c\/p\u003e \u003cp\u003e\u003cb\u003e2 First-Order Differential Equations \u003c\/b\u003e \u003c\/p\u003e \u003cp\u003e2.1 Linear Differential Equations; Method of Integrating Factors  \u003c\/p\u003e \u003cp\u003e2.2 Separable Differential Equations  \u003c\/p\u003e \u003cp\u003e2.3 Modeling with First-Order Linear Differential Equations  \u003c\/p\u003e \u003cp\u003e2.4 Differences Between Linear and Nonlinear Differential Equations  \u003c\/p\u003e \u003cp\u003e2.5 Autonomous Differential Equations and Population Dynamics  \u003c\/p\u003e \u003cp\u003e2.6 Exact Differential Equations and Integrating Factors  \u003c\/p\u003e \u003cp\u003e2.7 Numerical Approximations: Euler’s Method  \u003c\/p\u003e \u003cp\u003e2.8 The Existence and Uniqueness Theorem  \u003c\/p\u003e \u003cp\u003e2.9 First-Order Difference Equations  \u003c\/p\u003e \u003cp\u003e  \u003c\/p\u003e \u003cp\u003e\u003cb\u003e3 Second-Order Linear Differential Equations \u003c\/b\u003e \u003c\/p\u003e \u003cp\u003e3.1 Homogeneous Differential Equations with Constant Coefficients  \u003c\/p\u003e \u003cp\u003e3.2 Solutions of Linear Homogeneous Equations; the Wronskian  \u003c\/p\u003e \u003cp\u003e3.3 Complex Roots of the Characteristic Equation  \u003c\/p\u003e \u003cp\u003e3.4 Repeated Roots; Reduction of Order  \u003c\/p\u003e \u003cp\u003e3.5 Nonhomogeneous Equations; Method of Undetermined Coefficients  \u003c\/p\u003e \u003cp\u003e3.6 Variation of Parameters  \u003c\/p\u003e \u003cp\u003e3.7 Mechanical and Electrical Vibrations  \u003c\/p\u003e \u003cp\u003e3.8 Forced Periodic Vibrations  \u003c\/p\u003e \u003cp\u003e3.9 Central Gravitational Forces and Kepler’s Laws \u003c\/p\u003e \u003cp\u003e  \u003c\/p\u003e \u003cp\u003e\u003cb\u003e4 Higher-Order Linear Differential Equations \u003c\/b\u003e \u003c\/p\u003e \u003cp\u003e4.1 General Theory of n𝗍𝗁 Order Linear Differential Equations  \u003c\/p\u003e \u003cp\u003e4.2 Homogeneous Differential Equations with Constant Coefficients  \u003c\/p\u003e \u003cp\u003e4.3 The Method of Undetermined Coefficients  \u003c\/p\u003e \u003cp\u003e4.4 The Method of Variation of Parameters  \u003c\/p\u003e \u003cp\u003e  \u003c\/p\u003e \u003cp\u003e\u003cb\u003e5 Series Solutions of First-Order and\u003c\/b\u003e \u003cb\u003eSecond-Order Linear Equations \u003c\/b\u003e \u003c\/p\u003e \u003cp\u003e5.1 Review of Power Series  \u003c\/p\u003e \u003cp\u003e5.2 Series Solution of First Order Equations  \u003c\/p\u003e \u003cp\u003e5.3 Series Solutions Near an Ordinary Point, Part I  \u003c\/p\u003e \u003cp\u003e5.4 Series Solutions Near an Ordinary Point, Part II  \u003c\/p\u003e \u003cp\u003e5.5 Euler Equations; Regular Singular Points  \u003c\/p\u003e \u003cp\u003e5.6 Series Solutions Near a Regular Singular Point, Part I  \u003c\/p\u003e \u003cp\u003e5.7 Series Solutions Near a Regular Singular Point, Part II  \u003c\/p\u003e \u003cp\u003e5.8 Bessel’s Equation  \u003c\/p\u003e \u003cp\u003e  \u003c\/p\u003e \u003cp\u003e\u003cb\u003e6 Systems of First-Order Linear Equations \u003c\/b\u003e \u003c\/p\u003e \u003cp\u003e6.1 Introduction  \u003c\/p\u003e \u003cp\u003e6.2 Matrices  \u003c\/p\u003e \u003cp\u003e6.3 Systems of Linear Algebraic Equations; Linear Independence, Eigenvalues, Eigenvectors  \u003c\/p\u003e \u003cp\u003e6.4 Basic Theory of Systems of First-Order Linear Equations  \u003c\/p\u003e \u003cp\u003e6.5 Homogeneous Linear Systems with Constant Coefficients  \u003c\/p\u003e \u003cp\u003e6.6 Complex-Valued Eigenvalues  \u003c\/p\u003e \u003cp\u003e6.7 Fundamental Matrices  \u003c\/p\u003e \u003cp\u003e6.8 Repeated Eigenvalues  \u003c\/p\u003e \u003cp\u003e6.9 Nonhomogeneous Linear Systems  \u003c\/p\u003e \u003cp\u003e  \u003c\/p\u003e \u003cp\u003e7\u003cb\u003e The Laplace Transform \u003c\/b\u003e \u003c\/p\u003e \u003cp\u003e7.1 Definition of the Laplace Transform  \u003c\/p\u003e \u003cp\u003e7.2 Solution of Initial Value Problems  \u003c\/p\u003e \u003cp\u003e7.3 Step Functions  \u003c\/p\u003e \u003cp\u003e7.4 Differential Equations with Discontinuous Forcing Functions  \u003c\/p\u003e \u003cp\u003e7.5 Impulse Functions  \u003c\/p\u003e \u003cp\u003e7.6 The Convolution Integral  \u003c\/p\u003e \u003cp\u003e  \u003c\/p\u003e \u003cp\u003e\u003cb\u003e8 Numerical Methods of Solving First Order Equations\u003c\/b\u003e \u003c\/p\u003e \u003cp\u003e8.1 The Euler or Tangent Line Method  \u003c\/p\u003e \u003cp\u003e8.2 Improvements on the Euler Method  \u003c\/p\u003e \u003cp\u003e8.3 The Runge-Kutta Method  \u003c\/p\u003e \u003cp\u003e8.4 Multistep Methods  \u003c\/p\u003e \u003cp\u003e8.5 Systems of First-Order Equations  \u003c\/p\u003e \u003cp\u003e8.6 More on Errors; Stability  \u003c\/p\u003e \u003cp\u003e  \u003c\/p\u003e \u003cp\u003e\u003cb\u003e9 Nonlinear Differential Equations and Stability \u003c\/b\u003e \u003c\/p\u003e \u003cp\u003e9.1 The Phase Plane: Linear Systems  \u003c\/p\u003e \u003cp\u003e9.2 Autonomous Systems and Stability  \u003c\/p\u003e \u003cp\u003e9.3 Locally Linear Systems  \u003c\/p\u003e \u003cp\u003e9.4 Competing Species  \u003c\/p\u003e \u003cp\u003e9.5 Predator – Prey Equations  \u003c\/p\u003e \u003cp\u003e9.6 Lyapunov’s Second Method  \u003c\/p\u003e \u003cp\u003e9.7 Periodic Solutions and Limit Cycles  \u003c\/p\u003e \u003cp\u003e9.8 Chaos and Strange Attractors: The Lorenz Equations  \u003c\/p\u003e \u003cp\u003e  \u003c\/p\u003e \u003cp\u003e\u003cb\u003e10 Partial Differential Equations and Fourier Series \u003c\/b\u003e \u003c\/p\u003e \u003cp\u003e10.1 Two-Point Boundary Value Problems  \u003c\/p\u003e \u003cp\u003e10.2 Fourier Series  \u003c\/p\u003e \u003cp\u003e10.3 The Fourier Convergence Theorem  \u003c\/p\u003e \u003cp\u003e10.4 Even and Odd Functions  \u003c\/p\u003e \u003cp\u003e10.5 Separation of Variables; Heat Conduction in a Rod  \u003c\/p\u003e \u003cp\u003e10.6 Other Heat Conduction Problems  \u003c\/p\u003e \u003cp\u003e10.7 The Wave Equation: Vibrations of an Elastic String  \u003c\/p\u003e \u003cp\u003e10.8 Laplace’s Equation  \u003c\/p\u003e \u003cp\u003eA APPENDIX 537 \u003c\/p\u003e \u003cp\u003eB APPENDIX 541 \u003c\/p\u003e \u003cp\u003e  \u003c\/p\u003e \u003cp\u003e\u003cb\u003e11 Boundary Value Problems and Sturm-Liouville Theory \u003c\/b\u003e \u003c\/p\u003e \u003cp\u003e11.1 The Occurrence of Two-Point Boundary Value Problems  \u003c\/p\u003e \u003cp\u003e11.2 Sturm-Liouville Boundary Value Problems  \u003c\/p\u003e \u003cp\u003e11.3 Nonhomogeneous Boundary Value Problems  \u003c\/p\u003e \u003cp\u003e11.4 Singular Sturm-Liouville Problems  \u003c\/p\u003e \u003cp\u003e11.5 Further Remarks on the Method of Separation of Variables: A Bessel Series Expansion  \u003c\/p\u003e \u003cp\u003e11.6 Series of Orthogonal Functions: Mean Convergence  \u003c\/p\u003e \u003cp\u003e  \u003c\/p\u003e \u003cp\u003e\u003cb\u003eWeb Appendix\u003c\/b\u003e \u003c\/p\u003e \u003cp\u003e\u003cb\u003eSpecial Functions: \u003c\/b\u003eOn Legendre Polynomials and Functions  \u003c\/p\u003e \u003cp\u003e \u003c\/p\u003e \u003cp\u003eANSWERS TO PROBLEMS  \u003c\/p\u003e \u003cp\u003eINDEX \u003c\/p\u003e","brand":"Douglas B. Meade","offers":[{"title":"Default Title","offer_id":42850020753469,"sku":"9781119820512","price":234.86,"currency_code":"AUD","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0597\/7689\/2989\/files\/9781119820512_649d4c0c-a008-48cc-83de-ae1df62f32ee.jpg?v=1767069549","url":"https:\/\/www.palmleaf.com.au\/products\/elementary-differential-equations-and-boundary-value-problems-international-adaptation","provider":"Palmleaf","version":"1.0","type":"link"}