Name of the Student: Fourier Series in the interval (0,2l)

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1 Engineering Mathematics 15 SUBJECT NAME : Transforms and Partial Diff. Eqn. SUBJECT CODE : MA11 MATERIAL NAME : University Questions REGULATION : R8 WEBSITE : UPDATED ON : May-June 15 TEXT BOOK FOR REFFERENCE : Hariganesh Publications (Author: C. Ganesan) To buy the book visit Name of the Student: Branch: Unit I (Fourier Series) Fourier Series in the interval (,l) 1. Epand f ( ) as Fourier series in, and hence deduce that the sum of.... (A/M 11) Tet Book Page No.:.6. Find the Fourier series of f ( ) in, of periodicity. (M/J 1) Tet Book Page No.:.3 for 3. Find the Fourier series epansion of f( ). Also, deduce for that.... (N/D 1) Tet Book Page No.:.1 Prepared by C.Ganesan, M.Sc., M.Phil., (Ph: ) Page 1

2 Engineering Mathematics Find the Fourier Series Epansion of 1 for f( ). (N/D 13) for Tet Book Page No.:.1 5. Determine the Fourier series for the function f ( ) sin in. Tet Book Page No.:.1 6. Find the Fourier series epansion of (N/D 14), 1 f( ). Also, deduce, (N/D 1) Tet Book Page No.: Find the Fourier series for in the interval f ( ). (A/M 1) Tet Book Page No.: Obtain the Fourier series of periodicity 3 for f ( ) in 3. Tet Book Page No.:.33 (N/D 11),(N/D 14) Fourier Series in the interval (-l,l) 1. Find the Fourier series of in, and hence deduce that (M/J 13) Tet Book Page No.:.4. Obtain the Fourier series of f ( ) sin in,. (N/D 11) Tet Book Page No.: Obtain the Fourier series to represent the function f ( ), and 1 deduce. (M/J 1) n1 n 1 8 Tet Book Page No.:.45 Prepared by C.Ganesan, M.Sc., M.Phil., (Ph: ) Page

3 Engineering Mathematics Obtain the Fourier series of the periodic function defined by f( ). Deduce that.... (N/D 9) Tet Book Page No.: Epand 1, - f( ) as a full range Fourier series in the interval 1, 1 1 1,. Hence deduce that.... (M/J 14) Tet Book Page No.: Obtain the Fourier series for the function f( ) given by 1, f( ). 1, Hence deduce that.... (A/M 11) Tet Book Page No.: Find the Fourier series epansion of 1, f( ). (N/D 13) 1, Tet Book Page No.:.61, 8. Find the Fourier series of the function f( ) and hence evaluate sin, (N/D 11)(AUT) Tet Book Page No.: Epand f ( ) as a Fourier series in L L and using this series find the root mean square value of f( ) in the interval. (N/D 9) Tet Book Page No.: Find the Fourier series epansion of in, f ( ). (N/D 1) Tet Book Page No.:.6 Prepared by C.Ganesan, M.Sc., M.Phil., (Ph: ) Page 3

4 Engineering Mathematics Find the Fourier series epansion of f ( ) 1 in the interval 1,1. Tet Book Page No.:.7 (N/D 1) Half Range Fourier Series 1. Obtain the half range cosine series for f ( ) in, and hence show that (N/D 1),(N/D 1),(N/D 14) Tet Book Page No.:.81. Find the half range cosine series of the function f ( ) ( ) in the interval Hence deduce that.... (A/M 1) Tet Book Page No.: Find the half-range Fourier cosine series of f ( ) in the interval (, ) Hence find the sum of the series.... (M/J 1) Tet Book Page No.: Obtain the Fourier cosine series of , 1and hence show that (M/J 13) Tet Book Page No.: Obtain the half range cosine series for f ( ) Tet Book Page No.:.81 in,. (N/D 1),(N/D 1) 6. Obtain the Fourier cosine series epansion of sin in, and hence find the value of (N/D 11) Tet Book Page No.:.83 Prepared by C.Ganesan, M.Sc., M.Phil., (Ph: ) Page 4

5 Engineering Mathematics Find the half-range sine series of f ( ) 4 in the interval,4. Hence deduce the value of the series.... (M/J 14) Tet Book Page No.: Find the half range sine series of f ( ) in,. (N/D 13) Tet Book Page No.: Obtain the sine series for in f( ). (A/M 11) in Tet Book Page No.: Obtain the Fourier cosine series for Tet Book Page No.:.91 k in f( ) k in. (M/J 13) Comple Form of Fourier Series a 1. Find the comple form of the Fourier series of f ( ) e,.(a/m 1) Tet Book Page No.:.113. Show that the comple form of Fourier series for the function f ( ) e when and f ( ) f ( ) sinh n 1 in in f ( ) 1 e. 1 n is n Tet Book Page No.:.113 (N/D 14) 3. Find the comple form of the Fourier series of f ( ) e in 1 1.(N/D 9) Tet Book Page No.: Find the comple form of Fourier series of cosa in,, where " a " is not an integer. (M/J 13) Prepared by C.Ganesan, M.Sc., M.Phil., (Ph: ) Page 5

6 Engineering Mathematics 15 Tet Book Page No.: Epand f ( ) sin Tet Book Page No.:.14 Harmonic Analysis as a comple form Fourier series in,. (M/J 14) 1. Compute upto first harmonics of the Fourier series of f( ) given by the following table Tet Book Page No.:.131 T/6 T/3 T/ T/3 5T/6 T f( ) (N/D 9),(N/D 11). Find the Fourier series as far as the second harmonic to represent the function f( ) with the period 6, given in the following table. (N/D 9),(N/D 1),(M/J 1),(N/D 1) f( ) Tet Book Page No.: Find the Fourier series up to second harmonic for y f ( ) from the following values. Tet Book Page No.:.17 : π/3 π/3 π 4π/3 5 π/3 π y: (A/M 11),(N/D 13),(M/J 14) 4. Calculate the first 3 harmonics of the Fourier of f( ) from the following data (N/D 11) : f( ) : Tet Book Page No.:.133 Prepared by C.Ganesan, M.Sc., M.Phil., (Ph: ) Page 6

7 Engineering Mathematics 15 Unit II (Fourier Transform) Fourier Transform with Deduction 1 if 1 1. Find the Fourier transform of f( ) and hence find the value of if 1 4 sin t 4 dt t. (N/D 9),(A/M 1),(N/D 11),(N/D 1) Tet Book Page No.: 4.. Find the Fourier transform of f( ) given by 1 for a f( ) and using for a sin Parseval s identity prove that t dt t. (A/M 11) Tet Book Page No.: 4. 1 for a sin 3. Find the Fourier transform of f( ) and hence find d.tet for a Book Page No.: 4. (M/J 13) 1 if 1 4. Find the Fourier transform of f( ). Hence evaluate if 1 cos sin cos d 3. (A/M 11) Tet Book Page No.: Find the Fourier transform of 1, 1 f( ). Hence show that, 1 sin s scos s s 3 cos 3 ds s 16 and 6 Tet Book Page No.: 4.4 cos sin d. (N/D 13) 15 Prepared by C.Ganesan, M.Sc., M.Phil., (Ph: ) Page 7

8 Engineering Mathematics 15 a, a 6. Show that the Fourier transform of f( ) is, a sinas as cos as 3 s. Hence deduce that sin t t cos t 3 dt. Using t 4 Perserval s identity show that Tet Book Page No.: 4.5 Integration using Parseval s Identity 1. Evaluate sin t t cos t dt 3 t 15. (N/D 11),(N/D 1) d using Parseval s identity. (M/J 13),(N/D 13),(M/J 14) a Tet Book Page No.: 4.5. Using Parseval s identity evaluate d. (M/J 14) a Tet Book Page No.: Evaluate d 4 5 using transform methods. (N/D 9) Tet Book Page No.: Using Fourier cosine transform method, evaluate dt a t b t.(a/m 1) Tet Book Page No.: Evaluate d using Fourier cosine transforms of a b a e b and e. Tet Book Page No.: 4.67 (N/D 1),(A/M 11) Prepared by C.Ganesan, M.Sc., M.Phil., (Ph: ) Page 8

9 Engineering Mathematics 15 Fourier Transform of Eponential Function& Self Reciprocal Problems 1. Find the Fourier sine transform of a e and hence evaluate Fourier cosine transforms of a e a and e sin a. (N/D 11) Tet Book Page No.: 4.58 a. Find the Fourier cosine and sine transforms of f ( ) e, a and hence deduce the inversion formula. (N/D 1) Tet Book Page No.: Find the Fourier sine transformation of Tet Book Page No.: 4.59 e a wherea. (N/D 11)(AUT) 4. Find the function whose Fourier Sine Transform is a Tet Book Page No.: 4.61 e s as. (N/D 13) 5. Find the Fourier cosine transform of e. (N/D 9),(N/D 11)(AUT) Tet Book Page No.: Show that the Fourier transform of e Tet Book Page No.: Find the Fourier cosine transform of e is e a s. (A/M 1),(M/J 13), a. Hence show that the function e is self-reciprocal. (N/D 1) Tet Book Page No.: Show that e is a self reciprocal with respect to Fourier transform. (N/D 11) Tet Book Page No.: Find the Fourier transform of Tet Book Page No.: 4.31 f( ) 1. (M/J 14) 1 1. Prove that is self reciprocal under Fourier sine and cosine transforms.(n/d 9) Tet Book Page No.: Find Fourier sine and cosine transform of n 1 and hence prove 1 is self reciprocal under Fourier sine and cosine transforms. (M/J 1) Tet Book Page No.: 4.64 Prepared by C.Ganesan, M.Sc., M.Phil., (Ph: ) Page 9

10 Engineering Mathematics 15 Fourier Transform of General Function& Derivations 1. Find the Fourier sine and cosine transform of sin, a f( ). (A/M 1), a Tet Book Page No.: 4.54 for 1. Find the Fourier integral representation of f( ) defined as f ( ) for. e for Tet Book Page No.: 4.33 (N/D 1),(M/J 1) 3. Find the Fourier sine transform of, 1 f ( ), 1. (N/D 1),(A/M 11), Tet Book Page No.: , s 1 4. Solve for f( ) from the integral equation f ( )sin s d, 1 s., s Tet Book Page No.: 4.39 (M/J 14) 5. Solve for f( ) from the integral equation a f ( )cos a d e. (N/D 14) 6. Derive the Parseval s identity for Fourier Transforms. (N/D 1),(M/J 1) Tet Book Page No.: State and prove convolution theorem for Fourier transforms. (N/D 11),(M/J 1) Tet Book Page No.: Verify the convolution theorem under Fourier Transform, for f ( ) g( ) e. (M/J 13) Prepared by C.Ganesan, M.Sc., M.Phil., (Ph: ) Page 1

11 Engineering Mathematics 15 Unit III (Partial Differential Equation) Formation of PDE and Standard Types of PDE 1. Find the partial differential equation of all planes which are at a constant distance a from the origin. (A/M 1) Tet Book Page No.: 1.5. Form the PDE by eliminating the arbitrary function from y z, a by cz. (N/D 1),(M/J 1) Tet Book Page No.: Form the partial differential equation by eliminating arbitrary functions f and from z f ( ct) ( ct). (A/M 11) Tet Book Page No.: Form the PDE by eliminating the arbitrary functions f and g from z f y y g ( ) ( ). (N/D 13) Tet Book Page No.: Form the PDE by eliminating the arbitrary function from the relation z y f log y. (M/J 14) 1 Tet Book Page No.: Solve z p qy p q. (N/D 9) Tet Book Page No.: Find the singular integral of z p qy p q 1. Tet Book Page No.: 1.4 (N/D 11),(M/J 13),(N/D 13) 8. Find the singular integral of Tet Book Page No.: Solve 1 z p qy p pq q. (N/D 1) p q qz (A/M 1) Prepared by C.Ganesan, M.Sc., M.Phil., (Ph: ) Page 11

12 Engineering Mathematics 15 Tet Book Page No.: Solve p z q 11. Solve 9 4. (N/D 14) Tet Book Page No.: 1.53 p q y (A/M 1) Tet Book Page No.: 1.61 z p q y. (N/D 11)(AUT) 1. Solve 13. Solve Tet Book Page No.: 1.69 p y q z. (M/J 14) Tet Book Page No.: 1.71 PDE of Lagrange s Equation 1. Solve the partial differential equation ( mz ny) p ( n z) q y m.(a/m 11) Tet Book Page No.: Solve the partial differential equation y z p y z q z y. Tet Book Page No.: 1.11 (N/D 1),(M/J 1) 3. Solve the partial differential equation ( y z) p y( z ) q z( y). Tet Book Page No.: 1.97 (N/D 11) 4. Solve y z p y z q z y. (N/D 11)(AUT),(M/J 13) Tet Book Page No.: Solve z y p y z q z y. (N/D 14) Tet Book Page No.: Solve ( z) p ( z y) q y. (N/D 1) Tet Book Page No.: Solve( y z) p ( yz ) q ( y)( y). (N/D 9) Prepared by C.Ganesan, M.Sc., M.Phil., (Ph: ) Page 1

13 Engineering Mathematics 15 Tet Book Page No.: Solve y z p yq z. (N/D 13) Tet Book Page No.: 1.16 yz p y z q z y (A/M 1) 9. Solve Tet Book Page No.: 1.11 z p z y q y. (M/J 14) 1. Solve the Lagrange s equation Tet Book Page No.: 1.18 Homogeneous Linear Partial Differential Equation y 1. Solve D DD D z sinh( y) e. (N/D 9) Tet Book Page No.: Solve 4 y D DD D z 3y e. (N/D 13) Tet Book Page No.: Solve D 3DD D z sin 5y Tet Book Page No.:. (N/D 14) 4. Solve D 3 D D 4DD 4D 3 z cos y. (N/D 1),(M/J 1) Tet Book Page No.: y 5. Solve D D z e sin 3y. (A/M 11) Tet Book Page No.: Solve D D D z e 3 y. (N/D 11) Tet Book Page No.: Solve 3 4 cos D DD D z y y. (N/D 1) Tet Book Page No.: Prepared by C.Ganesan, M.Sc., M.Phil., (Ph: ) Page 13

14 Engineering Mathematics Solve 7 6 cos D DD D z y. (N/D 11)(AUT) Tet Book Page No.: Solve D 3 7DD 6D 3 z sin y. (M/J 13) Tet Book Page No.: Solve D DD 6D z ycos. (M/J 13),(M/J 14) Tet Book Page No.: 1.17 Non Homogeneous Linear Partial Differential Equation 1. Solve D D 3D 3D z y 7. (N/D 9) Tet Book Page No.: Solve D DD D D D z sin( y). (A/M 1) Tet Book Page No.: Solve y D DD D 6D 3D z e. (N/D 1),(M/J 1) Tet Book Page No.: Solve D 3DD D D D z y sin( y). (A/M 11) Tet Book Page No.: y Solve D DD D 3D 3D z e. (N/D 11) Tet Book Page No.: Solve y D DD D z e 4. (N/D 1) Tet Book Page No.: Prepared by C.Ganesan, M.Sc., M.Phil., (Ph: ) Page 14

15 Engineering Mathematics 15 Unit IV (Application of Partial Differential Equation) One Dimensional Wave Equation with No Velocity 1. A string is stretched and fastened to points at a distance apart. Motion is started by displacing the string in the form y asin,, from which it is released at time t. Find the displacement at any time t. (M/J 14) Tet Book Page No.: 3.1. A tightly stretched string with fied end points and is initially in a position 3 given by y(,) y sin. It is released from rest from this position. Find the epression for the displacement at any time t. (N/D 1) Tet Book Page No.: A uniform string is stretched and fastened to two points apart. Motion is started by displacing the string into the form of the curve y k( ) and then released from this position at time t. Derive the epression for the displacement of any point of the string at a distance from one end at time t. (A/M 11),(N/D 13) Tet Book Page No.: A string is stretched and fastened to two points and apart. Motion is started y k l from which it is released at time by displacing the string into the form t. Find the displacement of any point on the string at a distance of from one end at time t. (N/D 11)(AUT) Tet Book Page No.: A tightly stretched string of length has its ends fastened at and. The mid point of the string is then taken to height b and released from rest in that position. Find the lateral displacement of a point of the string at time t from the instant of release. (A/M 1) Tet Book Page No.: 3.7 Prepared by C.Ganesan, M.Sc., M.Phil., (Ph: ) Page 15

16 Engineering Mathematics A tightly stretched string of length is fastened at both ends. The midpoint of the string is displaced by a distance b transversely and the string is released from rest in this position. Find an epression for the transverse displacement of the string at any time during the subsequent motion. (N/D 1) Tet Book Page No.: 3.43 One Dimensional Wave Equation with Velocity 1. A tightly stretched string with fied end points and is initially at rest in its equilibrium position. If it is set vibrating giving each point a initial velocity 3 ( ), find the displacement. (N/D 9) Tet Book Page No.: A tightly stretched string between the fied end points and is initially at rest in its equilibrium position. If each of its points is given a velocity k( ), find the displacement y(, t) of the string. (M/J 13) Tet Book Page No.: A tightly stretched string with fied ends points and is initially at rest in its equilibrium position. If it is set vibrating giving each point a velocity ( ), show that (n 1) (n 1) at y(, t) sin sin. (N/D 14) a (n1) 4 4 n1 Tet Book Page No.: 3.44 (Similar Problem) 4. A tightly stretched string of length is initially at rest in its equilibrium position and 3 each of its points is given the velocityv sin.find the displacement (, ) y t. Tet Book Page No.: 3.3 (N/D 11) One Dimensional Heat Equation with Both Ends Are Change to Zero Temperature 1. Find the solution to the equation u a t Prepared by C.Ganesan, M.Sc., M.Phil., (Ph: ) Page 16 u that satisfies the conditions, / u(,t), u(,t), for t and u (,). (N/D 13), / Tet Book Page No.: 3.53

17 Engineering Mathematics 15. A rod, 3 cm long has its ends A and B kept at ⁰C and 8⁰C respectively, until steady state conditions prevail. The temperature at each end is then suddenly reduced to ⁰C and kept so. Find the resulting temperature function is a regular function u(, t) taking at A. (N/D 9) Tet Book Page No.: 3.57 One Dimensional Heat Equation with Both Ends Are Change to Non Zero Temperature 1. A bar of 1 cm long, with insulated sides has its ends A and B maintained at temperatures 5 C and 1 C respectively, until steady-state conditions prevail. The temperature at A is suddenly raised to 9 C and at B is lowered to 6 C. Find the temperature distribution in the bar thereafter. (N/D 11)(AUT) Tet Book Page No.: The ends A and B of a rod 4 cm long have their temperatures kept at C and 8 C respectively, until steady state condition prevails. The temperature of the end B is then suddenly reduced to 4 C and kept so, while that of the end A is kept at C. Find the subsequent temperature distribution u(, t) in the rod. (M/J 1) Tet Book Page No.: 3.7 Two Dimensional Heat Equation 1. A rectangular plate with insulated surface is 1 cm wide and so long compared to its width that may be considered infinite in length without introducing appreciable error. The temperature at short edge y for 5 is given by u and (1 ) for 5 1 the other three edges are kept at C. Find the steady state temperature at any point in the plate. (A/M 1),(M/J 13) Tet Book Page No.: A rectangular plate with insulated surface is cm wide and so long compared to its width that it may be considered infinite in length without introducing an appreciable error. If the temperature of the short edge is given by 1 y for y1 u and the two long edges as well as the other short 1( y) for 1 y edge are kept at C. Find the steady state temperature distribution in the plate. Tet Book Page No.: 3.1 (A/M 11) Prepared by C.Ganesan, M.Sc., M.Phil., (Ph: ) Page 17

18 Engineering Mathematics A square plate is bounded by the lines, y, and y. Its faces are insulated. The temperature along the upper horizontal edge is given by u(,) ( ), while the other two edges are kept at C. Find the steady state temperature distribution in the plate. Tet Book Page No.: 3.83 (N/D 1),(N/D 11),(N/D 14) 4. Find the steady state temperature distribution in a rectangular plate of sides a and b insulated at the lateral surfaces and satisfying the boundary conditions: u(, y) u( a, y), for y b; u(, b) and u(,) ( a ), for a. (N/D 1) Tet Book Page No.: A long rectangular plate with insulated surface is cm wide. If the temperature along one short edge ( y ) is u(,) k( ) degrees, for, while the other two long edges and as well as the other short edge are kept at C, find the steady state temperature function u(, y ). (M/J 1) Tet Book Page No.: An infinitely long rectangular plate with insulated surfaces is 1cm wide. The two long edges and one short edge are kept at C, while the other short edge is kept at u y, y 5 temperature. Find the steady state temperature u 1 y, 5 y 1 distribution in the plate. (M/J 14) Tet Book Page No.: 3.11 Unit V (Z - Transforms) Simple problems on Z - transforms 1. Find Z n( n 1)( n ) Tet Book Page No.: (M/J 1). Find the Z transform of 1. (N/D 13) ( n1)( n) Tet Book Page No.: 5.38 Prepared by C.Ganesan, M.Sc., M.Phil., (Ph: ) Page 18

19 Engineering Mathematics Find the Z transform of cosn andsinn. Hence deduce the Z transforms of n cos n 1 and a sin n. (N/D 1) Tet Book Page No.: 5.1 n Z n and hence deduce Z cos. (M/J 13) 4. Find cos Tet Book Page No.: Find the Z transform of Tet Book Page No.: 5.4 sin n 4 andcos n n 4. (N/D 1) n at 6. Find the Z transforms ofa cos n and e sin bt. (A/M 11) Tet Book Page No.: 5.1; 5.31 n at 7. Find the Z transforms of r cos n and e cos bt. (M/J 14) Tet Book Page No.: 5.38; Find n sin Z na n. (A/M 1) 9. If Z f ( n) F( z), find Z f ( n k) and Z f ( n k) Tet Book Page No.: 5.8. (N/D 11) 1. State and prove the second shifting property of Z-transform. (M/J 13) Tet Book Page No.: State and prove the final value theorem on Z-transform. (N/D 14) Inverse Z - transform by Partial Fraction 1z 1. Find the inverse Z transform of. (N/D 9) z 3z Tet Book Page No.: 5.41 Prepared by C.Ganesan, M.Sc., M.Phil., (Ph: ) Page 19

20 Engineering Mathematics 15. Find the inverse Z transform of 3 z z4 Tet Book Page No.: 5.48 z 3 z. (N/D 9) 3. Find Z z z z 1 ( z1)( z1) and Z 1 z ( z1)( z). (A/M 1) Tet Book Page No.: 5.45; Evaluate 3 Z z 5 for z 5. (N/D 11) Tet Book Page No.: 5.5 Inverse Z - transform by Residue Theorem zz ( 1) 1. Find the inverse Z transform of 3 ( z 1) by residue method. (N/D 1) Tet Book Page No.: 5.61 Inverse Z - transform by Convolution Theorem 1. Using convolution theorem, find the Z 1 of z4 z3 z. (N/D 9) Tet Book Page No.: 5.77 z. Using convolution theorem, find inverse Z transform of. ( z1)( z3) Tet Book Page No.: 5.76 (A/M 11),(N/D 13) z 3. Using convolution theorem, find the inverse Z transform of ( z a). (N/D 1) Tet Book Page No.: z 4. State and prove convolution theorem on Z-transformation. Find Z ( z a)( z b). Tet Book Page No.: 5.75 (N/D 11)(AUT) 1 z 5. Using convolution theorem, find Z. ( z a)( z b) (M/J 13),(M/J 14) Prepared by C.Ganesan, M.Sc., M.Phil., (Ph: ) Page

21 Engineering Mathematics 15 Tet Book Page No.: Using Convolution theorem, find the inverse Z transform of 8z. (z1)(4z1) Tet Book Page No.: 5.78 (M/J 1) 1 8z 7. Using Convolution theorem, find Z. (z1)(4z1) (N/D 14) Tet Book Page No.: 5.81 z 8. Using convolution theorem, find the inverse Z transform of z 4. (A/M 1) Tet Book Page No.: 5.8 Formation & Solution of Difference Equation 1. Form the difference equation from the relation y a b.3 n. (N/D 1) Tet Book Page No.: Derive the difference equation from y A Bn( 3) n. (A/M 11) Tet Book Page No.: Form the difference equation form y n A Bn n n ( ) n. (N/D 13) Tet Book Page No.: Form the difference equation of second order by eliminating the arbitrary constants A and B from y A( ) n Bn. (N/D 11) n Tet Book Page No.: Using Z-transform solve yn 3yn11 yn, y 1 and y1. Tet Book Page No.: 5.87 (M/J 13),(M/J 14) 6. Solve the equation u n n un un given u u 1. (N/D 9),(N/D 1) Tet Book Page No.: Prepared by C.Ganesan, M.Sc., M.Phil., (Ph: ) Page 1

22 Engineering Mathematics Solve by Z transform u 1 n n un un with u and u1 1.(A/M 1) Tet Book Page No.: Solve y n n yn yn with y and y1 1, using Z transform.(n/d 1) Tet Book Page No.: Solve: u n n un un given that u, u1 1. (N/D 11) Tet Book Page No.: Solve u n n un un, given that u, u1 1. (M/J 14) Tet Book Page No.: Solve y( k ) y( k) 1, y() y(1),using Z-transform. (M/J 1) Tet Book Page No.: Using Z-transform solve the difference equation yn yn1 yn n given y y. (N/D 13) 1 Tet Book Page No.: 5.98 n 13. Solve y y. n, using Z-transform. (M/J 1) n Tet Book Page No.: 5.11 n 14. Using Z-transform, solve yn 4yn1 5yn 4n 8 given that y 3 and y 1 5.Tet Book Page No.: 5.11 (N/D 11)(AUT) 15. Solve the difference equation y( n 3) 3 y( n 1) y( n), given that y() 4, y(1) and y() 8. (A/M 11),(N/D 1),(N/D 14) Tet Book Page No.: 5.89 Tet Book for Reference: TRANSFORMS AND PARTIAL DIFFERENTIAL EQUATIONS Publication: Hariganesh Publications Author: C. Ganesan To buy the book visit Prepared by C.Ganesan, M.Sc., M.Phil., (Ph: ) Page

23 Engineering Mathematics All the Best---- Prepared by C.Ganesan, M.Sc., M.Phil., (Ph: ) Page 3