TY  - BOOK
AU  - Zachmanoglou,E.C.
AU  - Thoe,Dale W.
TI  - Introduction to partial differential equations with applications
T2  - Dover books on advanced mathematics
SN  - 0486652513
AV  - QA377 .Z32 1986
PY  - 1986///
CY  - New York
PB  - Dover Publications
KW  - Differential equations, Partial
N1  - Originally published: Baltimore : Williams and Wilkins, c1976; Includes index; Bibliography: pages 395-396; Chapter 0; Preliminaries; Introduction; 2 Complex numbers; 3 Functions; 4 Polynomials; 5. Complex series and the exponential function; 6. Determinants; 7. Remarks on methods of discovery and proof; Chapter 1; Introduction—; Linear Equations of the First Order; 1. Introduction; 2. Differential equations; 3. Problems associated with differential equations; 4. Linear equations of the first order; 5. The equation y'+ay=0; 6. The equation y'+ay=b(x); 7. The general linear equation of the first order; Chapter 2.  Linear Equations with Constant Coefficients; 1. Introduction; 2. The second order homogeneous equation; 3. Initial value problems for second order equations; 4. Linear dependence and independence; 5. A formula for the Wronskian; 6. The non-homogeneous equation of order two; 7. The homogeneous equation of order n; 8. Initial value problems for n-th order equations; 9. Equations with real constants; 10. The non-homogeneous equation of order n; 11. A special method for solving the non-homogeneous equation; 12. Algebra of constant coefficient operators; Chapter 3.  Linear Equations with Variable Coefficients; 1. Introduction; 2. Initial value problems for the homogeneous equation; 3. Solutions of the homogeneous equation; 4. The Wronskian and linear independence; 5. Reduction of the order of a homogeneous equation; 6. The non-homogeneous equation; 7. Homogeneous equations with analytic coefficients; 8. The Legendre equation; 9. Justification of the power series method; Chapter 4. Linear Equations with Regular Singular Points; 1.Introduction; 2. The Euler equation; 3. Second order equations with regular singular points--an example; 4. Second order equations with regular singular points--the general case; 5. A convergence proof; 6. The exceptional cases; 7. The Bessel equation; 8. The Bessel equation (continued); 9. Regular singular points at infinity; Chapter 5.  Existence and Uniqueness of Solutions to First Order Equations; 1. Introduction; 2. Equations with variables separated; 3. Exact equations; 4. The method of successive approximations; 5. The Lipschitz condition; 6. Convergence of the successive approximations; 7. Non-local existence of solutions; 8. Approximations to, and uniqueness of, solutions; 9. Equations with complex-valued functions; Chapter 6.  Existence and Uniqueness of Solutions to Systems and n-th Order Equations; 1. Introduction; 2. An example--central forces and planetary motion; 3. Some special equations; 4. Complex n-dimensional space; 5. Systems as vector equations; 6. Existence and uniqueness of solutions to systems; 7. Existence and uniqueness for linear systems; 8. Equations of order; References; Answers to Exercises; Index
ER  -