Week  Topics  Study Materials  Materials 
1 
Introduction to partial differential equations. The first order linear equations.


O’Neil, P.V., “Beginning Partial Differential Equations”, Second Edition, Wiley, 2008

2 
The first order quasilinear equations. Method of characteristics.


O’Neil, P.V., “Beginning Partial Differential Equations”, Second Edition, Wiley, 2008

3 
Classification of second order linear partial differential equations, canonical forms. The Cauchy problem. Well posedness.


O’Neil, P.V., “Beginning Partial Differential Equations”, Second Edition, Wiley, 2008

4 
The Fourier series. Convergence of Fourier series. Fourier integral.


O’Neil, P.V., “Beginning Partial Differential Equations”, Second Edition, Wiley, 2008

5 
Eigenvalue problem with symmetric boundary conditions. Generalized Fourier series.


O’Neil, P.V., “Beginning Partial Differential Equations”, Second Edition, Wiley, 2008

6 
The Fourier Transform. Convolution.


O’Neil, P.V., “Beginning Partial Differential Equations”, Second Edition, Wiley, 2008

7 
The wave equation on the real line. D'alambert solution of the Cauchy problem. Fourier transform approach.


O’Neil, P.V., “Beginning Partial Differential Equations”, Second Edition, Wiley, 2008

8 
Characteristic triangle and nonhomogenous wave equation. The Wave equation on the half line. Reflection method.


O’Neil, P.V., “Beginning Partial Differential Equations”, Second Edition, Wiley, 2008

9 
The wave equation on a bounded interval. Separation of variables methdod.


O’Neil, P.V., “Beginning Partial Differential Equations”, Second Edition, Wiley, 2008

10 
The Heat equation on the real line and the half line. Obtaining the solution using Fourier transform.


O’Neil, P.V., “Beginning Partial Differential Equations”, Second Edition, Wiley, 2008

11 
The Heat equation on a bounded interval. Weak maximum principle.


O’Neil, P.V., “Beginning Partial Differential Equations”, Second Edition, Wiley, 2008

12 
Dirichlet and Neumann problem for the Laplace equation.


O’Neil, P.V., “Beginning Partial Differential Equations”, Second Edition, Wiley, 2008

13 
The Laplace equation in polar coordinates. Poisson's formula.


O’Neil, P.V., “Beginning Partial Differential Equations”, Second Edition, Wiley, 2008

14 
The Laplace equation in Higher dimensions. Mean value property and the maximum principle.


