微分方程及其应用-第4版-(影印版)

Chapter 1 First-order differential equations1．1 Introduction1．2 First-orderlinear differential equations1．3 The Van Meegeren art forgeries1．4 Separableequations1．5 Populationmodels1．6 The spread of technological innovations1．7 An atomic waste disposal problem1．8 The dynamics of tumor growth， nuxing problems， and orthogonal trajectories1．9 Exact equations， and why we cannot solve very many differential equations1．10 The existence-uniqueness theorem； Picard iteration1．11 Finding roots of equations by iteration1．11．1 Newton’s method1．12 Difference equations， and how to compute the interest due on your student loans1．13 Numerical approximations； Euler’s method1．13．1 Error analysis for Euler’s method1．14 The three term Taylor series method1．15 An improved Euler method1．16 The Runge-Kutta method1．17 What to do in practiceChapter 2 Second-order linear differential equations2．1 Algebraic properties of solutions2．2 Linear equations with constant coefficients2．2．1 Complexroots2．2．2 Equal roots； reduction of order2．3 The nonhomogeneous equation2．4 The method of variation of parameters2．5 The method ofjudicious guessing2．6 Mecharucalvibrations2．6．1 The Tacoma Bridge disaster2．6．2 Electricalnetworks2．7 A model for the detection of diabetes2．8 Series solutions2．8．1 Singular points， Euler equations2．8．2 Regular singular points， the method of Frobenius2．8．3 Equal roots， and roots differing by an integer2．9 The method of Laplace transforms2．10 Some useful properties of Laplace transforms2．11 Differential equations with discontinuous right-hand sides2．12 The Dirac delta function2．13 The convolution integral2．14 The method of elimination for systems2．15 Higher-order equationsChapter 3 Systems of differential equations3．1 Algebraic properties of solutions of linear systems3．2 Vectorspaces3．3 Dimension of a vector space3．4 Applications of linear algebra to differential equations3．5 The theory of determinants3．6 Solutions of simultaneous linear equations3．7 Linear transformations3．8 The eigenvalue-eigenvector method of finding solutions3．9 Complexroots3．10 Equalroots3．11 Fundamental matrix solutions； eAt3．12 The nonhomogcneous equation； variation of parameters3．13 Solving systems by Laplace transformsChapter 4 Qualitative theory of differential equations4．1 Introduction4．2 Stability oflinear systems4．3 Stability of equilibrium solutions4．4 Thephase-plane4．5 Mathematical theories of war4．5．1 L．F．Richardson’s theory of conflict4．5．2 Lanchester’s combat models and the battle of Iwo Jima4．6 Qualitative properties of orbits4．7 Phase portraits of linear systems4．8 Long time behavior of solutions； the Poincare～Bendixson Theorem4．9 Introduction to bifurcation theory4．10 Predator-prey problems； or why the percentage of sharks caught in the Mediterranean Sea rose dramatically during World War I4．11 The principle of competitive exclusion in population biology4．12 The Threshold Theorem of epidemiology4．13 A model for the spread of gonorrheaChapter 5 Separation of variables and Fourier series5．1 Two point boundary-value problems5．2 Introduction to partialdifferentialequations5．3 The heat equation； separation of variables5．4 Fourierseries5．5 Even and odd functions5．6 Retum to the heat equation5．7 The wave equation5．8 Laplace’sequationChapter 6 Sturm-Liouville boundary value problems6．1 Introduction6．2 Inner product spaces6．3 Orthogonalbases， Hermitian operators6．4 Sturm-‘LiouvilletheoryAppendix ASome simple facts concerning functions of several variablesAppendix BSequences and seriesAppendix CC ProgramsAnswers to odd-numbered exercisesIndex