**1** |
1. Introduction: Basic Definitions, Typical Problems
2. First Order Equations in Two Independent Variables: Basic properties of the linear equation, solution of linear equations, Cauchy problem, quasi-linear equations, solution of quasi-linear equations,
3. The general first order nonlinear equation, exact solution, general solution and singular solution.
4. Linear Second Order Equations in Two Independent Variables; Cauchy problem, classification of lineear second order equations and their reduction to a canonical form (hyperbolic equations),
5. Continue the reduction of the equations to canonical forms (elliptic and parabolic equations),
6. Hyperbolic Equations -One Dimensional Wave Equation; D’Alembert’s solution, the mixed initial value –boundary value problem for the one-dimensional equation, Cauchy problem, inhomogeneous wave equation
7. Separation of Variables (one dimensional wave equations)
8. Elliptic equations; Laplace equation, max-min principle, boundary value problems,
9. Integral represantations and Green’s functions,
10. Parabolic equations; Initial and boundary value problems, fundamental solutions and Green's functions
11. Hyperbolic Equations: Cauchy and Goursat problems
12. Analytical methods of solutions; Integral transform techniques.
13. Fourier Transformation
14. Laplace Transformation |

**2** |
1. Introduction: Basic Definitions, Typical Problems
2. First Order Equations in Two Independent Variables: Basic properties of the linear equation, solution of linear equations, Cauchy problem, quasi-linear equations, solution of quasi-linear equations,
3. The general first order nonlinear equation, exact solution, general solution and singular solution.
4. Linear Second Order Equations in Two Independent Variables; Cauchy problem, classification of lineear second order equations and their reduction to a canonical form (hyperbolic equations),
5. Continue the reduction of the equations to canonical forms (elliptic and parabolic equations),
6. Hyperbolic Equations -One Dimensional Wave Equation; D’Alembert’s solution, the mixed initial value –boundary value problem for the one-dimensional equation, Cauchy problem, inhomogeneous wave equation
7. Separation of Variables (one dimensional wave equations)
8. Elliptic equations; Laplace equation, max-min principle, boundary value problems,
9. Integral represantations and Green’s functions,
10. Parabolic equations; Initial and boundary value problems, fundamental solutions and Green's functions
11. Hyperbolic Equations: Cauchy and Goursat problems
12. Analytical methods of solutions; Integral transform techniques.
13. Fourier Transformation
14. Laplace Transformation |