xiii magic fix of the numerical method the nd-order runge-kutta method (or heun' method software for solving odes the th-order runge-kutta method more effectsdampingnonlinearityand external forces illustration of linear damping illustration of linear damping with sinusoidal excitation spring-mass system with sliding friction finite difference methodundampedlinear case finite difference methodlinear damping exercises solving partial differential equations finite difference methods reduction of pde to system of odes construction of test problem with known discrete solution implementationforward euler method applicationheat conduction in rod vectorization using odespy to solve the system of odes implicit methods exercises solving nonlinear algebraic equations brute force methods brute force root finding brute force optimization model problem for algebraic equations newton' method deriving and implementing newton' method making more efficient and robust implementation the secant method the bisection method rate of convergence solving multiple nonlinear algebraic equations abstract notation taylor expansions for multi-variable functions newton' method implementation exercises getting access to python required software anaconda and spyder spyder on mac installation of additional packages how to write and run python program