Differential Geometry (Math 371)

Differential quadrature solution of nonlinear Klein-Gordon and sine-Gordon equations Pekmen, B.; Tezer, Münevver (2012-08-01) Differential quadrature method (DQM) is proposed to solve the one-dimensional quadratic and cubic Klein-Gordon equations, and two-dimensional sine-Gordon equation. We apply DQM in space direction and also blockwise in time direction. Initial and derivative boundary conditions are also approximated by DQM. DQM provides one to obtain numerical results with very good accuracy using considerably small number of grid points. Numerical solutions are obtained by using Gauss-Chebyshev-Lobatto (GCL) grid points in s...
Differential topology of quotients of complex surfaces by complex conjugation Finashin, Sergey (1998-01-01) The paper contains a brief survey of the author's results on the diffeomorphism type of quotients of complex surfaces by anti-holomorphic involutions. The conjecture of complete decomposability is discussed, which says that if such a quotient is simply connected, then it is completely decomposable, i.e., is diffeomorphic to the connected sum of several copies of the projective plane (possibly, with reversed orientation) and the quadric. ©1998 Plenum Publishing Corporation.
Differential equations on variable time scales Akhmet, Marat (2009-02-01) We introduce a class of differential equations on variable time scales with a transition condition between two consecutive parts of the scale. Conditions for existence and uniqueness of solutions are obtained. Periodicity, boundedness and stability of solutions are considered. The method of investigation is by means of two successive reductions: B-equivalence of the system [E. Akalfn, M.U. Akhmet, The principles of B-smooth discontinuous flows, Computers and Mathematics with Applications 49 (2005) 981-995; ...
Differential - Operator solutions for complex partial differential equations Celebi, O; Sengul, S (1998-07-10) The solutions of complex partial differential equations of order four are obtained by using polynomial differential operators. A correspondence principle is also derived for the solutions of two different differential equations, imposing conditions on the coefficients.
Differential equations with state-dependent piecewise constant argument Akhmet, Marat (Elsevier BV, 2010-06-01) A new class of differential equations with state-dependent piecewise constant argument is introduced. It is an extension of systems with piecewise constant argument. Fundamental theoretical results for the equations the existence and uniqueness of solutions, the existence of periodic solutions, and the stability of the zero solution are obtained. Appropriate examples are constructed.

Citation Formats

Y. Ozan, “Differential Geometry (Math 371),” 00, 2020, Accessed: 00, 2021. [Online]. Available: https://www.youtube.com/playlist?list=PLBMmiR8tC9Um_c_Lw0If5UnKaWbT8aBar.