1. Basic Concepts2. First Order Differential Equations 3. Linear First Order4. Higher Order Linear Differential Equations5. Systems of Linear Differential Equations6. Series Solutions7. Laplace Transforms8. Numerical Methods9. Systems of Autonomous Differential Equations10. Orthogonal Functions and Fourier Series 11. Partial Differential Equations

1. Existence and Uniqueness of Solutions2. Existence and Uniqueness of Solutions (continued)3. Linear Differential Equations4. Linear Systems with Isolated Singularities: Singularities of the First Kind5. Linear Systems with Isolated Singularities: Singularities of the Second Kind6. Asymptotic Behavior of Linear Systems Containing a Large Parameter7. Self-adjoint Eigenvalue Problems on a Finite Interval8. Oscillation and Comparison Theorems for Second-Order Linear Equations and Applications9. Si...

1. New results in potential theory2. Generalized potential theory solutions3. Applications in electromagnetics4. Applications in diffusion and acoustics5. New solutions in contact mechanics6. New solutions in fracture mechanics7. Singular integral equations

Met antwoordenboekjeI. Inleiding. Scherpe hoekenII. Goniometrische verhoudingen van andere dan scherpe hoekenIII. Hoofdwaarden en bijzondere waarden van de goniometrische verhoudingenIV. Algemeene formules voor willekeurige hoekenV. Goniometrische verhoudingenVI. Tafel van de goniometrische verhoudingen en hun logarithmenVII. Optellings-theorema'sVIII. Toepassingen van de optellingstheorema'sIX. Goniometrische VergelijkingenX. Uiterste WaardenXI. Rechthoekige driehoekenXII. Scheefhoekige driehoe...

1. Method of Power Series2. First Order3. Partial4. Cauchy Two Independent Variables5. Fundamental Solution7. Dirichlet and Neumann Problems12. Ticomi's Problem14. Fluid Dynamics

Part of the book series: Grundlehren der mathematischen Wissenschaften (GL volume 141)AlgebraGeometrie und TensorkalkülTensorkalkül nebst AnwendungenInterpolation und genäherte QuadraturApproximation von FunktionenDarstellung von Funktionen in RechenautomatenLineare und nichtlineare Optimierung

I. Uit de geschiedenis der wiskunde - Dr. C.H. van OsII. Getallenstelsels - Dr. F. LoonstraIII. Lineaire algebra - Dr. F. LoonstraIV. Analytische meetkunde - Dr. F. LoonstraV. Analyse - Dr. B. MeulenbeldVI. Getallenrijen - reeksen - Dr. L. KuipersVII. Functietheorie - Dr. H.J.A. DuparcVIII. Gewone differentiaalvergelijkingen - Dr. S.C. van VeenIX. Bijzondere functies - Dr. S.C. van VeenX. Vectoranalyse - Dr. R. TimmanXI. Partiële differentiaalvergelijkingen - Dr. R. TimmanXII. Numerieke analyse...

1. Random Walk and Partial Differential Equations2. First Order3. Classification4. Boundary Value5. Integral Transforms6. Integral Relations7. Green's Functions8. Variational and Other Methods9 Perturbation Methods10 Asymptotoc Methods

1. Examples2. Classification into Types Theory of Characteristics and Normal Form3. Questions of Uniqueness4. Questions of Existence5. Simple Tools from Functional Analysis Applied to Questions of Existence

1. Potentiale in belegungsfreien Aufpukten2. Potentialen in beliebigen Aufpunkten3. Harmonische Fuinktionen4. Differentialgleichungsproblemen der Potentialtheorie

I. The Force of GravityII. Fields of ForceIII. The PotentialIV. The Divergence TheoremV. Properties of Newtonian Potentials at Points of Free SpaceVI. Properties of Newtonian Potentials at Points Occupied by MassesVII. Potentials as Solutions of Laplace's Equation; ElectrostaticsVIII. Harmonic FunctionsIX. Electric Images; Green's FunctionX. Sequences of Harmonic FunctionsXI. Fundamental Existence TheoremsXII. The Logarithmic Potential

1. Fourier Series2. Introduction to Partial Differential Equations3. Boundary Value4. Cylinder and Sphere5. Eigen Functions and Eigen Values6. Problems of Radio

I. Existence of solutionsII. The linear equationIII. Oscillation theoremsIV. Solution in seriesV. Singularities of equationsVI. Contour integral solutionsVII. Legendre functionsVIII. Bessel functionsIX. Asymptotic series

I. Equations of the first order and degreeII. Integral curvesIII. Equations of higher degreeIV. Equations of the second and higher ordersV. Linear equationsVI. Solution in seriesExamplesSolutions

1. Dilogarithm2. Inverse Tangent Integral3. Generalized Inverse Tangent Integral4. Clausen's Integral5. Dilogarithm of Complex Argument6. Trilogarithm7. Higher Order Functions8. Integration9. Reference Data and Tables

A Course of Modern AnalysisAn introduction to the general theory of infinite processes and of analytic functions; with an account of the principal transcendental functionsI. Complex NumbersII. The Theory of ConvergenceIII. Continuous Functions and Uniform ConvergenceIV. The Theory of Riemann IntegrationV. The fundamental properties of Analytic Functions; Taylor's Laurent's and Liouville's TheoremaVI. The Theory of Residues; application to the evaluation of Definite IntegralsVII. The expansion of...

1. Foundations Eigenvalues2. Mathieu Functions3. Spheroid Funtions

1. Grundlagen2. Mathieusche Funktionen3. Sphäroidfuntionen4. Anwendungen der Mathieuschen Funktionen und der Sphäroidfunktionen

1. History2. Analytic Properties3. Algebraic Properties4. Applications

1. Hypergeometrische Funktionen2. Kugelfunktionen3. Lineare homogene Differentialgleichungen4. Infinitares