Purpose of the course

To give students an introductory knowledge about urban design from the view point of historical, cultural progression stepping to the new modern concepts of the present. The focus is to understand the principles that explain the elements of urban design and its applications in the design process.

..

..

1. Solving ODEs with variable coefficients by power series method
2. Inner product space
3. Adjoint operators
4. Sturm-Liouville theory
5. Orthogonal polynomials and special functions
6. Fourier series 
7. Fourier transformation
8. Laplace transform and its applications

1. Elementary theory of distributions (Convolution and differentiation).
2. Types of partial differential equations
3. Fundamental solutions of some linear differential operators such as the
Laplacian, the heat, and the wave operators.
4. Initial and boundary value problems for parabolic and hyperbolic
equations (existence and uniqueness of solutions)
5. Generalizations and applications.
6. Solutions of mixed problems in Sobolev spaces.

Various types of first order differential equations and their applications. Linear equations of higher order. Systems of linear equations with constant coefficients, Power series methods for solving second order equations with polynomial coefficients. Fourier series, Fourier series for even and odd functions. Complex Fourier series, Fourier integral