Interested Articles & Keywords

• C++ source codes
  
• Changing the technology narrative and embracing innovation
  
• 10 easy ways to fail a Ph.D.
  
• The illustrated guide to a Ph.D.
  
• Frameworks for Higher Education Qualifications
  
• Quantifying the evolution of individual scientific impact
  
• How Scientists Can Thrive in the Startup World
  
• Wheel of Emotions

Math

• A Calculated Decision
  
• A new method q-calculus
  
• Bessel Functions Page
  
• Intuition of orthogonal polynomials
  
• Jordan Inequality
  
• Useful inequalities cheat sheet
  
• Some special functions and their applications
  
• Study on special functions in q-analysis
  
• Systems of Holonomic Differential Equations
  
• Table of Functions with Formulae and Curves
  
• What is q-calculus?
  

Videos at Youtube

• Tangent and Secant q-Calculus and (t,q)-Calculus
• q Combinatorics, A new view

Computation

• Acceleration methods for slowly convergent sequences and their applications
• Asymptotics of generalized harmonic numbers
• Computer Assisted Proof in Dynamics
• Development of Verified Numerical Computations for Mathematical Modeling
• Development of Fast Numerical Algorithms for Elementary and Special Functions Retaining High Reliability, High Accuracy, and High Portability
• Double exponential numerical integration technique
• Differential Equations and Linear Algebra (MathWorks webinar)
• Exponential integrator
• New rigorous numerical integration in Arb
• Programming for Computation
  

Keywords

• Asymptotics (Watson lemma, Mellin transform, WKB method, Plancherel-Rotach Asymptotics)
• Binary Splitting
• Clenshaw-Curtis quadrature (Filon-Clenshaw-Curtis, Nystrom-Clenshaw-Curtis etc.)
• Coincidence Theorems (Brouwer, Ky Fan, Nielsen, Reich,...)
• Gauss quadrature (Gauss-Christoffel, Gauss-Lobatto-Legendre-Birkhoff, Gauss-Kronrod, Gauss-Patterson, Gauss-Radau etc.)
• Hypergeometric series (basic/elliptic/hyperbolic, GKZ, Heckman-Opdam etc.)
• Zeta functions (Dedekind, Epstein, Hasse-Weil, Hurwitz, Ihara, Riemann, Selberg etc.)
  

Gauss Quadrature References
Wang, L. L., & Guo, B. Y. (2009). Interpolation approximations based on Gauss–Lobatto–Legendre–Birkhoff quadrature. Journal of Approximation Theory, 161(1), 142-173.
Gautschi, W. (2002, January). Gauss-Radau formulae for Jacobi and Laguerre weight functions. In Computational Science, Mathematics, and Software: Proceedings of the International Symposium on Computational Science in Celebration of the 65th Birthday of John R. Rice, West Lafayette, Indiana, USA, 22-26 May, 1999 (Vol. 1, p. 237). Purdue University Press.
Masjed-Jamei, M., Eslahchi, M. R., & Dehghan, M. (2005). On numerical improvement of Gauss–Radau quadrature rules. Applied Mathematics and Computation, 168(1), 51-64.
Gautschi, W. (1991). On the remainder term for analytic functions of Gauss-Lobatto and Gauss-Radau quadratures. The Rocky Mountain Journal of Mathematics, 209-226.
Gautschi, W., & Li, S. (1990). The remainder term for analytic functions of Gauss-Radau and Gauss-Lobatto quadrature rules with multiple end points. Journal of Computational and Applied Mathematics, 33(3), 315-329.
Gautschi, W., & Li, S. (1991). Gauss—Radau and Gauss—Lobatto quadratures with double end points. Journal of Computational and Applied Mathematics, 34(3), 343-360.

Clenshaw-Curtis Quadrature References
Dominguez, V., Graham, I. G., & Smyshlyaev, V. P. (2011). Stability and error estimates for Filon–Clenshaw–Curtis rules for highly oscillatory integrals. IMA Journal of Numerical Analysis, 31(4), 1253-1280.
Domínguez, V., Graham, I. G., & Kim, T. (2013). Filon--Clenshaw--Curtis rules for highly oscillatory integrals with algebraic singularities and stationary points. SIAM Journal on Numerical Analysis, 51(3), 1542-1566.
Domínguez, V. (2014). Filon–Clenshaw–Curtis rules for a class of highly-oscillatory integrals with logarithmic singularities. Journal of Computational and Applied Mathematics, 261, 299-319.
Xiang, S., He, G., & Cho, Y. J. (2015). On error bounds of Filon-Clenshaw-Curtis quadrature for highly oscillatory integrals. Advances in Computational Mathematics, 41(3), 573-597.
Xiang, S., Cho, Y. J., Wang, H., & Brunner, H. (2011). Clenshaw–Curtis–Filon-type methods for highly oscillatory Bessel transforms and applications. IMA Journal of Numerical Analysis, 31(4), 1281-1314.
Kang, S. Y., Koltracht, I., & Rawitscher, G. (2003). Nyström-Clenshaw-Curtis quadrature for integral equations with discontinuous kernels. Mathematics of Computation, 72(242), 729-756.

Iterative Methods

• Aitken's Process and Steffensen's Acceleration Method
• Interval Newton Method (An introduction can also be viewed at Slideshare)
• Krawczyk method for solving systems of equations (modified versions do exist)

Writing

• Manual for authors of mathematical papers

Keywords About Design

• Policy Based Design
• Polymorphism
• Strategy Pattern