A Course in Ordinary and Partial Differential Equations

Content: Front Matter, Page iii Copyright, Page iv Preface, Pages ix-x SECTION 1 - Classification and Solutions of First-Order Differential Equations, Pages 3-13 SECTION 2 - Elementary Higher-Order Differential Equations, Pages 14-25 SECTION 3 - Existence Theorems, Pages 26-49 SECTION 4 - Singular Solutions, Pages 50-53 SECTION 5 - Linear Equations of Arbitrary Order, Pages 54-60 SECTION 6 - Solutions of Linear Equations, Pages 61-79 SECTION 7 - Linear Systems with Constant Coefficients, Pages 80-97 SECTION 8 - Infinite Series Solutions, Pages 98-131 SECTION 9 - Asymptotic Expansion of Solutions of Linear Differential Equations, Pages 132-145 SECTION 10 - Solutions of Differential Equations by Definite Integrals, Pages 146-153 SECTION 11 - Boundary Value Problems, Pages 154-183 SECTION 12 - Green's Function, Pages 184-198 SECTION 13 - Expansion Theorems, Pages 199-217 SECTION 14 - Nonlinear Differential Equations, Pages 218-250 SECTION 1 - Introduction, Pages 253-267 SECTION 2 - Elementary Second-Order Partial Differential Equations, Pages 268-296 SECTION 3 - Second-Order Hyperbolic Differential Equations, Pages 297-335 SECTION 4 - Second-Order Elliptic Differential Equations, Pages 336-357 SECTION 5 - Second-Order Parabolic Differential Equations, Pages 358-373 SECTION 6 - The Fourier Transform and Its Applications to Partial Differential Equations, Pages 374-400 SECTION 7 - Hilbert Space Approach to Partial Differential Equations, Pages 401-421 SECTION 8 - Distributions and Their Applications to Partial Differential Equations, Pages 422-471 Index, Pages 473-477