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181301TRANSFORMS AND PARTIAL DIFFERENTIAL EQUATIONS Anna University Of Technology Question Bank,Subject Notes,Lecture Notes

Thursday, August 18, 2011 ·


181301-TRANSFORMS AND PARTIAL DIFFERENTIAL EQUATIONS         

181301-TRANSFORMS AND PARTIAL DIFFERENTIAL EQUATIONS         

181301-TRANSFORMS AND PARTIAL DIFFERENTIAL EQUATIONS         


1.         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 identify – Harmonic Analysis.

2.         Fourier TransformS                                                                             
Fourier integral theorem (without proof) – Fourier transform pair – Sine and
Cosine transforms – Properties – Transforms of simple functions – Convolution theorem – Parseval’s identity.


3.         PARTIAL DIFFERENTIAL EQUATIONS                                                      
Formation of partial differential equations – Lagrange’s linear equation – Solutions of standard types of first order partial differential equations - Linear partial differential equations of second and higher order with constant coefficients.


4.         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.


5.         Z -TRANSFORMs AND DIFFERENCE Equations                                 
Z-transforms - Elementary properties – Inverse Z-transform – Convolution theorem -Formation of difference equations – Solution of difference equations using Z-transform.

                  
TEXT BOOKS
1.    Grewal, B.S, ‘Higher Engineering Mathematics’ 40th Edition,  Khanna publishers, Delhi, (2007)

REFERENCES
1.    Bali.N.P and Manish Goyal ‘A Textbook of Engineering Mathematics’, Seventh Edition, Laxmi Publications(P) Ltd. (2007)
2. Ramana.B.V. ‘Higher Engineering Mathematics’ Tata Mc-GrawHill Publishing Company limited, New Delhi (2007).
3. Glyn James, ‘Advanced Modern Engineering Mathematics’, Third edition-Pearson Education (2007).
4. Erwin Kreyszig ’Advanced Engineering Mathematics’, Eighth edition-Wiley India (2007).


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