FOUNDATION COURSES
TRANSFORMS and Partial Differential EQUATIONS



UNIT I Fourier series                                                                                    

Dirichlet’s conditions – General Fourier series – Odd and even functions – Half range sine series – Half range cosine series – Complex form of Fourier series – Parseval’s identity – harmonic analysis.

 

UNIT II  Fourier Transforms                                                                   

            Fourier integral theorem (without proof) – Fourier transform pair – Sine and Cosine transforms – properties – Transforms of Simple functions – Convolution theorem – Parseval’s identity

 

UNIT III Partial Differential Equations                                                 

Formation of partial difference equations – Solutions of standard types of first order partial differential equations– Lagrange’s linear equation – Linear partial differential equations of second and higher order with constant coefficients

 

UNIT IV Applications of Partial Differential Equations                          

Solutions of one dimensional wave equation – One dimensional equation of heat conduction – Steady state solution of two-dimensional equation of heat conduction (insulated edges excluded) – Fourier series solutions in Cartesian coordinates only.

 

UNIT V Z-Transforms and Applications                                  

Z-Transforms – Elementary properties – Inverse Z-transform – Convolution theorem – formation of difference equations – Solution of difference equations using Z-transform


Online resources:

http://www.fourier-series.com/

http://www.sosmath.com/fourier/fourier1/fourier1.html

http://www.efunda.com/math/fourier_transform/index.cfm

http://ocw.usu.edu/civil_and_environmental_engineering/numerical_methods_in_civil_engineering/IntroToPartialDiffEqns.pdf