Ads
related to: graph of equations without solution pdf worksheet
Search results
Results from the WOW.Com Content Network
In the mathematical study of partial differential equations, Lewy's example is a celebrated example, due to Hans Lewy, of a linear partial differential equation with no solutions. It shows that the analog of the Cauchy–Kovalevskaya theorem does not hold in the smooth category.
Isoclines are often used as a graphical method of solving ordinary differential equations. In an equation of the form y' = f(x, y), the isoclines are lines in the (x, y) plane obtained by setting f(x, y) equal to a constant. This gives a series of lines (for different constants) along which the solution curves have the same gradient.
Many mathematical problems have been stated but not yet solved. These problems come from many areas of mathematics, such as theoretical physics, computer science, algebra, analysis, combinatorics, algebraic, differential, discrete and Euclidean geometries, graph theory, group theory, model theory, number theory, set theory, Ramsey theory, dynamical systems, and partial differential equations.
If the curve passes through the origin then determine the tangent lines there. For algebraic curves, this can be done by removing all but the terms of lowest order from the equation and solving. Similarly, removing all but the terms of highest order from the equation and solving gives the points where the curve meets the line at infinity.
Solutions of some further graph equations, Vasanti N. Bhat-Nayak, Ranjan N. Naik – Discrete Mathematics, 47 (1983) 169–175; More Results on the Graph Equation G2= G, M Capobianco, SR Kim – Graph Theory, Combinatorics, and Algorithms: Proceedings of …, 1995 – Wiley-Interscience; Graph equation Ln (G)= G, S Simic - Univ. Beograd. Publ.
The Grötzsch graph is a triangle-free graph that cannot be colored with fewer than four colors. Much research about triangle-free graphs has focused on graph coloring. Every bipartite graph (that is, every 2-colorable graph) is triangle-free, and Grötzsch's theorem states that every triangle-free planar graph may be 3-colored. [8]
Ads
related to: graph of equations without solution pdf worksheet