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Prof. Faiz Ahmad
Professor
Department of Mathematics

SNS
National University of Sciences and Technology (NUST)
School of Natural Sciences, H-12, Islamabad
Tel : +92 51 9085 5577

Specialization
Differential Equations

Education
PhD, Mathematics (Manchester, UK)

Education:

    1961     Matric. BISE , Lahore. First position in the Lahore Board.
    1963     Intermediate. Government College, Lahore. Second position in the Lahore Board .
    1966     BSc (Honours). Government College, Lahore. First position in the University of the Punjab and a Roll of Honour of  the Government College. 
    1967     MA (Mathematics). University of the Punjab, Lahore. First position in B.Sc. as well as  M.A. examinations.
    1972     PhD University of Manchester Institute of Science and  Technology, Manchester (England).
 
Positions:
 
31 August 2007-present                       HEC Professor, School of Natural Sciences, NUST,  Islamabad, Pakistan.    
27 March 2006- 30 August 2007          Professor, King Abdulaziz University, Jeddah, Saudi Arabia. 
September 2001- March 2006              Associate Professor King Abdulaziz University, Jeddah, Saudi Arabia.
March   1992-   August  2001              Associate Professor, Quaid-I-Azam University, Islamabad.
October 1987 -  March   1992              Associate Professor,  Government Post-graduate College, Asghar Mall, Rawalpindi.
October  1985-   October 1987            Assistant Professor, Quaid-I-Azam University, Islamabad.
November 1977- August 1985             Assistant Professor, Al-Fateh University, Tripoli, Libya.
October 1974- October 1977               Assistant Professor, Quaid-I-Azam University, Islamabad.
Feb. 1973- July 1973                            Visiting research fellow at the University of Stuttgart, Germany. The visit was sponsored by the I.C.I.
October  1972- September 1974           I.C.I. Research Fellow, University of Manchester Institute of Science and Technology.
October 1969- September 1972           Research student, Department of Mathematics, University of Manchester Institute of Science and 
                                                           Technology,  Manchester, U.K.
 October 1967- September 1969          Lecturer at the Department of Mathematics, University of the Punjab, Lahore, Pakistan 
 
Professional Activities:
 
1. Administrative and Managerial Assignments:
 
  • Worked as the Acting Director General of School of Natural Sciences(SNS) (formerly known as Centre for Advanced Mathematics and Physics),  20 June, 2009 – 3 July 2009 and 11 August 2009 to 25 August, 2009.
  • Worked as the Acting Director General of School of Natural Sciences(SNS) (formerly known as Centre for Advanced Mathematics and Physics), 26 October, 2010- 2 November, 2010.
  • Participated in the Meeting of the Selection Board of NUST, 9-10 April, 2009.
  • In charge of the Library of the Centre Sep. 2010 to Jan. 2011.
  • In charge of the B.S. program of the School January 2011 to November, 2011.
  • Representative of the Centre in the Committee for the uniform course codes being developed at NUST.
  • Served as an expert in the interviews conducted by the IGT Branch of the Pakistan Army for selection of officers in the Army Education Corps, during 15 April-22 April, 2011 at Lahore, Karachi and Rawalpindi.
  • Served as an expert with the Federal Public Service Commission for the review of syllabus for the C.S.S. examination in Applied Mathematics.
  • Served as an expert in the meetings of the Selection Board of International Islamic University, Islamabad on 31st March, 2012 and in December, 2012.
  • Served as an expert in the meeting of the Selection Board of Fatima Jinnah Women University, Rawalpindi, on 19th  July, 2012.
  • Chairman, Hiring Committee for the School.
  • Member, Departmental Tenure Review Committee for the School.
 
2.  Curriculum Development
 
  • Member of the Committee appointed by the Faculty Board of Studies, School of Natural Sciences, NUST. The Committee prepared the four year  B.S. (Mathematics) program which has recently been approved by the Academic Council of NUST.
  • Member of the Board of Studies in Mathematics of Fatima Jinnah Women University, Rawalpindi.
  • Member,  the Board of Studies COMSATS CIIT, Islamabad.
  • Member Board of Post-graduate Studies, University of Engineering and Technology, Taxila.
  • Member Board of Studies in Mathematics, Quaid-i-Azam University, Islamabad.
  • Member Board of Faculty, FAST National University, Islamabad.
  • Convener Curriculum Review Committee for Numerical Analysis Courses, CIIT, COMSATS, Islamabad.

Research Interest:

Study of normal modes in plates and cylinders made of anisotropic elastic materials. Approximate analytical solutions to problems in elasticity. Invariants of the elasticity tensor. Solution of nonlinear ordinary differential equations. Blasius problem.​​

Reviewing and Refreceing:

Reviewer of Mathematical Reviews.
Refereed articles for publication in international journals such as Journal of Acoustical Society of America, Sound and Vibration, Applied Mathematics Letters, Mathematical Problems in Engineering,
Evaluated a Project submitted to the Department of Mathematical Sciences, King Fahad University of Petroleum and Minerals, Dhahran, Saudi Arabia.

Research Students:

Supervision of PhD Thesis

2013 Takassar Hussain Work in progress.
2012 Riaz Ahmad Khan  "Planes and axes of symmetry in an elastic material".
2001 Aftab Khan "Wave propagation in incompressible, transversely   isotropic materials".
 
Supervision of MPhil Thesis
2013    Rida Waheed "Limit cycles in nonlinear differential equations" Completed in January,2013.
2013    Raheela Jumani "Delay differential equations" work in progress.
2013    Syeda Madeeha  Fatima "Analytical solutions of nonlinear differential Equations" work in progress. 
2011    Sumaira Afzal  "Rayleigh- Lamb spectrum of an incompressible orthotropic wave guide".
2010    Khalid Saeed   "Stokes’ first problem and some of its generalizations".
2010    Sidra Rana  "Symmetry planes of an anisotropic material".
2007    Haifa Abdulghani Al- Aleemi "Degeneracy in some nonlinear problems"
2007    Ubaid Jeffeen Al-Qahtani "Application of wavelet theory to differential equations". (M.Sc. at KAAU).
2007    Faisal Zaid Doreiham  " A study of the Blasius equation" (M. Sc. At KAAU).
2006    Hanan Assarooji "Necessary and sufficient conditions for the oscillation of  linear delay differential equations". (M. Sc. Thesis at KAAU).
2006    Suad Omar Alhadhrami "New methods for solving nonlinear differential equations". (M. Sc. Thesis at KAAU).
2003    Rania Alherbi "Oscillation in delay differential equations". ( M. Sc. thesis at KAAU.)
2001    Moniba Shams "Rayleigh waves in a transversely isotropic half-space loaded by a fluid".
2001    Nabila Kauser "Guided waves in a plate immersed in a fluid".
2000    Ehsan ul Haq "Scattering of an acoustic wave from anisotropic bodies".
2000    M. Shakeel "Guided waves in a transversely isotropic medium".
2000    Farkhanda Yousaf"Guided waves in a transversely isotropic plate".
2000    Nagina Kiyani "Guided waves in a fluid- loaded TI plate".
2000    Sherbaz Khan "Torsional waves in a nonhomogeneous half space".
1999    Nadia Aziz "Numerical solution of a laminar boundary layer formed due to flow past a wedge".
1999    Himat Mir "Scattering of an acoustic wave from an isotropic cylinder".
1998    Jamila Sarwar "Fourier analysis of iterative process".
1998    Abida Mansoora "Wave propagation in an anisotropic medium".
1997    M.Saleem Iqbal "Wiener-Hopf technique in boundary value problems".
1996    Shamsul Qamar  "The behavior of elastic surface waves polarized in a plane of material symmetry".
1995    Javed Iqbal "Diffraction of a sinusoidal pulse by a half plane".
1994    Haider Zaman "Half-space subjected to antiplane surface disturbance".
Research ​Publications:
 
S/No ​Reference
​1. F. Ahmad, Periodicity in the solution of Volterra’s equation by spectral method, submitted.
​2. F. Ahmad, Some misconceptions about stability in epidemic models, submitted.
​3. ​Jerome  Laurenta and Daniel Royer, Takasar Hussain and Faiz Ahmad, Laser induced zero-group velocity resonances in transversely isotropic cylinder, Journal of the Acoustical Society of America, Vol. 137, Issue 6, 2015, Pages 3325-3334, IF 1.503
​4. T. Hussain and F. Ahmad, Existence of zero-group velocity modes in an incompressible plate,  Archives of Mechanics 66(2014), 55-65.
​5. T. Hussain M.A. Awan, M. Shams and F. Ahmad,  Lamb modes for an isotropic incompressible plate, Mathematical Problems in Engineering (2013), Article ID 152346. http://dx.doi.org./10.1155/2013/152346.
​6. F. Ahmad and T. Hussain, Anomalous dispersion of the S1 Lamb mode,  Advances in Acoustics and Vibration (2013). Article ID903934, 6 pages, http://dx.doi.org/10.1155/2013/903934.
​7. R.A. Khan and F. Ahmad, Extrema of Young’s modulus in a hexagonal material, Applied Mathematics and Computation 219(2012), 2260-2266.
​8. ​R.A. Khan and F. Ahmad, Extrema of Young’s modulus in a hexagonal material, Applied Mathematics and Computation 219(2012), 2260-2266.
​9. ​T. Hussain and F. Ahmad, Doubly anomalous Lamb modes in an orthotropic plate,  Journal of Acoustical Society of America 132(2012), 641-645.
​10. ​A.A. Lashari and F. Ahmad, False mathematical reasoning in biology,  Journal of Theoretical Biology 307, 211 (2012).
​11. ​R.A. Khan and F. Ahmad, “ Planes and axes of symmetry in elastic materials,” International Journal of Physical Sciences 7 (2012), 1141-1149.
​12. ​F. Ahmad, Uniqueness of the Rayleigh wave speed, Proc. Pakistan Academy of Sciences 48, 107-109 (2011).
​13. ​M.A. Rashid, F. Ahmad and N. Amir, Linear invariants of a Cartesian tensor under SO(2), SO(3) and SO(4), International Journal of Theoretical Physics 50 (2011) 479-488.
​14. ​F. Ahmad, Matrix with prescribed eigenvectors, to appear in Mathematics and Computers in Education, November 2011, 198-203.
​15. ​F. Ahmad and S. Rana, Representation of the elasticity tensor of an anisotropic material possessing an axis of symmetry, to appear in Proceedings Pakistan Academy of Sciences (2011).
​16. ​F. Ahmad, Invariants of a Cartesian tensor of rank 3, Archives of Mechanics 63 (2011), 383-392.
​17. ​F. Ahmad, Cowin-Mehrabadi Theorem in six dimensions,  Archives of Mechanics 62, 215-222 (2010).
​18. ​F. Ahmad, The Cowin-Mehrabadi Theorem for an axis of symmetry, International Journal of Solids and Structure 47 (2010) 3050-3052.
​19. ​F. Ahmad and M.A. Rashid, Counting invariants of a tensor, paper  presented in the IMACS World Congress on Computational and Applied Mathematics and Applications in Science and Engineering held in University of Georgia, Athens, USA, 3-5 August, 2009.
​20. ​F. Ahmad and Riaz Ahmad Khan, “ Eigenvectors of the rotation matrix,”  Quarterly Journal of Mechanics and Applied Mathematics 62 (2009) 297-310. doi:10.1093/ qjmam/hbp009.
​21. ​F. Ahmad and M. A. Rashid, “ Linear invariants of a Cartesian tensor,”  Quarterly Journal of Mechanics and Applied Mathematics 62 (2009) 31-38. Doi:10.1093/qjmam/hb021.
​22. ​F. Ahmad, W. H. Albarakati  “ Polynomial approximations for some elementary functions,”  South East Asia Bulletin of Mathematics 33(2009) 613-621.
​23. ​F. Ahmad, “ A simple analytical solution for the steady flow of a third grade fluid in a porous half space,”  Communications in Nonlinear Science and Numerical Simulation 14 (2009) 2848-2852. doi: 0.1016/j.cnsns.2008.09.029.
​24. ​F. Ahmad and W. H. Al-barakati, “ An approximate analytic solution of the Blasius problem,” Communications in Nonlinear Science and Numerical Simulation 14 (2009) 1021-1024.
​25. ​F. Ahmad, " Degeneracy in the Blasius problem," Electronic Journal of Differential Equations 2007 (2007), No. 79, pp. 1-8.
​26. ​F. Ahmad, and A. S. Alfhaid, "Some comments on the Adomian decomposition method," Journal of Engineering and Applied Sciences 25 (2006), 37-40.
​27. ​F. Ahmad ad W. H. Al-Barakati, " Application of Pade approximation  to the Blasius problem," Proceedings of Pakistan Academy of Sciences 44 (2007)17-19.
​28. ​F. Ahmad, " Application of Crocco-Wang equation to the Blasius problem," Electronic Journal " Technical Acoustics", http://www.ejta.org ,  2007, 2, pp1-11.
​29. ​F. Ahmad and F. D. Zaman, “Exact and asymptotic solutions of the elastic wave propagation problem in a rod,” International Journal of Pure and Applied Mathematics 27 (2006), 127-132 .
​30. ​F. Ahmad, “ Algebraic approximants to exp(z) and other functions,”  Proceedings Pakistan Academy of Sciences 41 (2004), 129-131.
​31. ​F. Ahmad, “ Inequalities for a sum of exponential functions,” Journal of Inequalities in Pure and Applied Mathematics 5(4), Art.107, (2004).
​32. ​F. Ahmad and R. A. Alherbi, “ Oscillation of solutions of delay differential equations with positive and negative coefficients,” International Journal of Mathematics, Game Theory and Algebra 14 (2004), 9-16.
​33. ​F. Ahmad, “ Shape of dispersion curves in the spectrum of Lamb modes,”  Archives of Mechanics 56 (2004), 157-165.
​34. ​F. Ahmad, “ A system of equations with a tridiagonal matrix,”  Applied Mathematics and Computation (2004), 159 (2004), 435-438.
​35. ​F. Ahmad, “ A simple formula for the longitudinal modes in a cylinder,” J. Acoust. Soc. Am. 115(2004), 475-477.
​36. ​F. Ahmad, “ Linear delay equation with a positive and a negative term,” Electronic Journal of Differential Equations 2003(2003), No. 92, pp. 1-6.
​37. ​F. Ahmad, “ A simple formula for the Lamb modes in a plate,” Journal of the Acoustical Society of America 111(2002), 1974-1975.
​38. ​F. Ahmad, “ Invariants and structural invariants of the anisotropic elasticity tensor,” Quarterly Journal of Mechanics and Applied Mathematics 55(2002), 597-606.
​39. ​F. Ahmad, N. Kiyani, F. Yousaf and M. Shams “ Guided waves in a fluid-loaded transversely isotropic plate”  Mathematical Problems in Engineering 8(2002), 151-159.
​40. ​F. Ahmad, S. Asghar and T. Hayat, “ Fracture filled with a viscous fluid,” Acoustics Letters 23, 231-232 (2000).
​41. ​F. Ahmad and H. Mir, “ The gauge condition for the vector potential,” Proc. Pak. Academy of Sciences 38, 1-5(2001).
​42. ​F. Ahmad, “ Acoustic scattering from an elastic cylinder,” Acoustics Letters 23,247-252(2000).
​43. ​F. Ahmad and Ahsan ul Haq, “ Vector potential in spherical polar coordinates,” Journal of the Acoustical Society of America 109, 2270-2271(2001).
​44. ​F. Ahmad and A. Khan, “ Effect of rotation on wave propagation in a transversely isotropic medium,” Mathematical Problems in Engineering 7, 147-154(2001).
​45. ​F. Ahmad, “ Elastic waves in a transversely isotropic bar immersed in a fluid,” Proceedings of the Second International Seminar on Mechanical Vibrations  Islamabad, (ISMV 2000), pp 596-601(2001).
​46. ​A. Khan and F. Ahmad, “Propagation of longitudinal and transverse waves in a TI elastic material rotating about its axis of symmetry,”   J. Acoust. Soc. of Japan 22, 261-264 (2001).
​47. ​F. Ahmad, “ Guided waves in a transversely isotropic cylinder immersed in a fluid,”  Journal Acoustical Society of America 109, 886-890(2001).
​48. ​A. Khan and F. Ahmad, “ Propagation of plane waves in a rotating transversely isotropic  material.( The special case a =0.)  J. Engg. Applied Maths. 19,  23-.26(2000).
​49. ​A. Khan and F. Ahmad, “ Thermoelastic wave propagation in a rotating, incompressible, transversely isotropic medium,” Proceedings of the   Pakistan Academy of Sciences  36, 113-117(1999).
​50. ​A. Khan and F. Ahmad, “ Wave propagation in a transversely isotropic medium rotating about its axis of symmetry,”  J. Engg. Appl. Sci 18., 103-106(1999).
​51. ​F. Ahmad, “ Theory of the Cagniard- de Hoop method,” Pakistan Journal of Scientific and Industrial Research 43, 141-144 (2000).
​52. ​F. Ahmad and A. Rehman, “ Acoustic scattering by transversely isotropic cylinders.” Int. J. Engg. Sci. 38, 325-335 (2000).
​53. ​F. Ahmad  and A. Rehman, “ Scattering of acoustic waves from an anisotropic cylinder,” Paper presented in the First Seminar on Mechanical Vibrations, Sep.21-23, 1998.
​54. ​A. Khan and F. Ahmad, “ Dilatation and shear waves without energy dissipation in a rotating medium,” Mechanics Research Communications 26, 225-227 (1999).
​55. ​F. Ahmad and A. Khan, “ Thermoelastic plane waves in a rotating isotropic medium,” Acta Mechanica, 136,243-247, (1999).
​56. ​A. Khan and F. Ahmad, “ Wave propagation in a rotating incompressible transversely isotropic medium,”   Acoustics Letters 22, 90-94(1998).
​57. ​A. Khan and F. Ahmad, “ Wave propagation in a rotating incompressible transversely isotropic medium,”   Acoustics Letters 22, 90-94(1998).
​58. ​F. Ahmad and A. Khan, “ Thermal effects on wave propagation in an incompressible transversely isotropic material,”  Acoustics Letters 22, 22-25 (1998).
​59. ​A. Rehman and F. Ahmad, “ Representation of the displacement in terms of scalar potentials for use in transversely isotropic materials,” J. Acoust. Soc. Am. 104, 3675-3676(1998).
​60. ​F. Ahmad, “The orthogonal polynomials and the Pade approximation,” Applied Mathematics and Mechanics 19, 663-668(1998).
​61. ​F. Ahmad, “ Easier ways of construction for the square- triangular numbers,” Int. Journal Math. Educ. Sci. Technol.27, 932-934(1996).
​62. ​F. Ahmad and G. Zaman, “ The Cagniard- De Hoop transformation in elastodynamics,” Proceedings of 26th Annual Iranian Conference on Mathematics, Kerman, Editors S. H. Javadpour and M. Radjabalipour, pp. 119-122, 1995.
​63. ​F. Ahmad, “ Cauchy- Riemann equations in polar form,” Int. Journal Math. Educ. Sci. Technol. 26, 759-760(1995).
​64. ​F. Ahmad, A. Khan and S. Asghar, “ Acoustic waves in a moving fluid,” Acoustics Letters 16, 202-203(1993).
​65. ​F. Ahmad, “ Two classes of starlike and convex functions,” Riazi 10, 1-9(1988).
​66. ​F. Ahmad, “ Dr. Mumtaz Hosain Kazi- an obituary,” University of Punjab- Journal of Mathematics 21, i-ii (1988).
​67. ​F. Ahmad, “ Jakubowski starlike integral operator,” Journal of Natural Sciences and Mathematics 28, 157-160(1988).
​68. F. Ahmad, “An integral operator that maps a subclass of starlike functions into itself,” Mat. Visnik 39,361-365(1987).​
​69. ​F Ahmad, “ A subclass of starlike functions,” Honam Math. Journal 9, 71-76(1987)
​70. ​F. Ahmad, “ Starlike integral operators,” Bull. Austral. Math. Soc. 32, 217-224 (1985).
​71. ​F. Ahmad, “ Semiclassical electrodynamics of a two level system,” Phys. Rev.A12, 1539-1545(1975).
​72. ​R. Saunders, R.K. Bullough and F. Ahmad, “Theory of radiation reaction and atom self energies: an operator reaction field,” J.Phys. A8,759-772(1975).
​73. ​F. Ahmad and R.K. Bullough, “ Theory of the Bloch-Siegert shift,” J.Phys. B7,L275-280(1974).
​74. ​F. Ahmad and R.K. Bullough, “Analytical expressions for the Bloch-Siegert shift,” J. Phys. B7, L147-151(1974).
75.​ ​S.S. Hassan, R.K. Bullough and F. Ahmad, “Reaction field theorry of saturation absorption spectroscopy in intense chaotic fields,” Fourth International Conference on Atomic Physics. Abstracts of cotributed papers: Eds. J. Kowalski and H.G. Weber, Heidelberg, 1974 pp. 303-305.
​76. ​F. Ahmad and R.K. Bullough, “Bloch-Siegert shifts in RF spectroscopy,” Fourth International Conference on Atomic Physics. Abstracts of contributed papers :Eds J. Kowalski and H.G. Weber, Heidelberg, 1974, pp. 239-240.
​77. ​F. Ahmad and R.K. Bullough, “ Frequency shifts in a single mode laser,” J.Phys.A7, 1934(1974).
​78. ​F. Ahmad, “On reducing a quartic,” Riv. Math. Univ. Parma (3),1,23-25,(1972)
​79. ​R.K. Bullough, F. Ahmad and J.C. Eilbeck, “Nonlinear radiation reaction superradiance and coherent optical pulse propagation,” Second International Conference on Atomic Physics, IEEE Journal of Quantum Electronics, QE-8,568-569,(1972).
​80. ​R.K. Bullough and F. Ahmad, “Exact solutions of self-induced transparency equations,” Phys. Rev. Letters, 27,330-333 (1971).
Courses Taught
BSc
1. Calculus
2. Discrete Mathematics
3. Ordinary Differential Equations
4. Partial Differential Equations
5. Linear Algebra
6. Special Functions
MSc
1. Advanced Calculus
2. Real Analysis
3. Complex Analysis
4. Ordinary Differential Equations
5. Partial Differential Equations
7. Numerical Methods
8. Numerical Analysis
9. Nonlinear Differential Equations
10. Mechanics
11. Quantum Mechanics
12. Fluid Dynamics.
MPhil
1. Elastodynamics
2. Partial Differential Equations
3. Advanced Complex Analysis
4. Advanced Quantum Mechanics
5. Continuum Mechanics
6. Ordinary Differential Equations