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Preface

Solvable Differential Equations / 1：

Second-Order Differential Equations / 2：

Preliminaries to Series Solutions / 3：

Solution at an Ordinary Point / 4：

Solution at a Singular Point / 5：

Solution at a Singular Point (Cont'd.) / 6：

Legendre Polynomials and Functions / 7：

Chebyshev, Hermite and Laguerre Polynomials / 8：

Bessel Functions / 9：

Hypergeometric Functions / 10：

Piecewise Continuous and Periodic Functions / 11：

Orthogonal Functions and Polynomials / 12：

Orthogonal Functions and Polynomials (Cont'd.) / 13：

Boundary Value Problems / 14：

Boundary Value Problems (Cont'd.) / 15：

Green's Functions / 16：

Regular Perturbations / 17：

Singular Perturbations / 18：

Sturm-Liouville Problems / 19：

Eigenfunction Expansions / 20：

Eigenfunction Expansions (Cont'd.) / 21：

Convergence of the Fourier Series / 22：

Convergence of the Fourier Series (Cont'd.) / 23：

Fourier Series Solutions of Ordinary Differential Equations / 24：

Partial Differential Equations / 25：

First-Order Partial Differential Equations / 26：

Solvable Partial Differential Equations / 27：

The Canonical Forms / 28：

The Method of Separation of Variables / 29：

The One-Dimensional Heat Equation / 30：

The One-Dimensional Heat Equation (Cont'd.) / 31：

The One-Dimensional Wave Equation / 32：

The One-Dimensional Wave Equation (Cont'd.) / 33：

Laplace Equation in Two Dimensions / 34：

Laplace Equation in Polar Coordinates / 35：

Two-Dimensional Heat Equation / 36：

Two-Dimensional Wave Equation / 37：

Laplace Equation in Three Dimensions / 38：

Laplace Equation in Three Dimensions (Cont'd.) / 39：

Nonhomogeneous Equations / 40：

Fourier Integral and Transforms / 41：

Fourier Integral and Transforms (Cont'd.) / 42：

Fourier Transform Method for Partial DEs / 43：

Fourier Transform Method for Partial DEs (Cont'd.) / 44：

Laplace Transforms / 45：

Laplace Transforms (Cont'd.) / 46：

Laplace Transform Method for Ordinary DEs / 47：

Laplace Transform Method for Partial DEs / 48：

Well-Posed Problems / 49：

Verification of Solutions / 50：

References for Further Reading

Index

Preface

Solvable Differential Equations / 1：

Second-Order Differential Equations / 2：

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Preface

Contradictions / 1：

Non-expansive maps / 2：

Continuation methods for contractive and non-expansive mapping / 3：

The theorems of Brouwer, Svhauder and Monch / 4：

Non-linear alternatives of Leray-Schauder type / 5：

Continuation principles for condensing maps / 6：

Fixed point theorems in conical shells / 7：

Fixed point theory in Hausdorff locally convex linear topological spaces / 8：

Contractive and non-expansive multivalued maps / 9：

Multivalued maps with continuous selections / 10：

Multivalued maps with closed graph / 11：

Degree theory / 12：

Bibliography

Index

Preface

Contradictions / 1：

Non-expansive maps / 2：

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