A first course in partial differential equations with complex variables and transform methods
Book Description
Text presents the general properties of partial differential equations such as characteristics, domains of independence and maximum principles. Solutions.
Table Of Content
I. The one-dimensional wave equation
1. A physical problem and its mathematical models: the vibrating string
2. The one-dimensional wave equation
3. Discussion of the solution: characteristics
4. Reflection and the free boundary problem
5. The nonhomogeneous wave equation
II. Linear second-order partial differential equations in two variables
6. Linearity and superposition
7. Uniqueness for the vibrating string problem
8. Classification of second-order equations with constant coefficients
9. Classification of general second-order operators
III. Some properties of elliptic and parabolic equations
10. Laplace's equation
11. Green's theorem and uniqueness for the Laplace's equation
12. The maximum principle
13. The heat equation
IV. Separation of variables and Fourier series
14. The method of separation of variables