MA1201 – TRANSFORMS AND PARTIAL DIFFERENTIAL EQUATIONS

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MA1201 – TRANSFORMS AND PARTIAL DIFFERENTIAL EQUATIONS
(Common to all branches)
L    T     P    C
3    1      0    4
                                                   
UNIT I           FOURIER SERIES                           9 
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                               9 
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                                           9  
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.

UNIT IV        APPLICATIONS OF PARTIAL DIFFERENTIAL EQUATIONS      9
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. 

UNIT V          Z -TRANSFORMS AND DIFFERENCE EQUATIONS                       9 
Z-transforms  -  Elementary  properties  –  Inverse  Z-transform  –  Convolution  theorem  -
Formation of difference equations – Solution of difference equations using Z-transform.

                
                              L: 45    T: 15   Total: 60  
TEXTBOOKS     
1.        Grewal,   B.S.,   “Higher   Engineering   Mathematics”,   39th   Edition,   Khanna
Publishers, 2007.
2.        Bali,  N.P.  and    Manish  Goyal,  “A  Textbook  of  Engineering  Mathematics”,  7th
Edition, Laxmi Publications (P) Ltd, 2008.

REFERENCES
1.         Ramana,  B.V.,  “Higher  Engineering  Mathematics”,  2nd  Edition,  Tata  McGraw
Hill, 2008.
2.         Glyn James, “Advanced Modern Engineering Mathematics”, 3rd Edition, Pearson
Education, 2007.
3.         Erwin Kreyszig, “Advanced Engineering Mathematics” 8th Edition, Wiley India,
2007.
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