Mathematical Modeling & Graph Theory Notes
Topics in our Mathematical Modeling & Graph Theory Notes PDF
In these “Mathematical Modeling & Graph Theory Notes PDF”, you will study how to model physical problems using differential equations and solve them. Also, the use of Computer Algebra Systems (CAS) by which the listed problems can be solved both numerically and analytically.
The topics we will cover will be taken from the following list:
Power Series Solutions: Power series solution of a differential equation about an ordinary point, Solution about a regular singular point, The method of Frobenius, Legendre’s and Bessel’s equations.
Laplace Transforms: Laplace transform and inverse transform, Application to initial value problem up to second order.
Monte Carlo Simulation: Monte Carlo simulation modeling: Simulating deterministic behavior (area under a curve, volume under a surface); Generating random numbers: Middle square method, Linear congruence; Queuing models: Harbor system, Morning rush hour; Overview of optimization modeling; Linear programming model: Geometric solution, Algebraic solution, Simplex method, Sensitivity analysis.
Graph Theory: Graphs, Diagraphs, Networks and subgraphs, Vertex degree, Paths and cycles, Regular and bipartite graphs, Four cube problem, Social networks, Exploring and traveling, Eulerian and Hamiltonian graphs, Applications to dominoes, Diagram tracing puzzles, Knight’s tour problem, Gray codes.