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

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’ 40^th 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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