This book discusses the Taylor Series Method for numerical solution of initial and boundary value problems.  A number of differential equations related to problems in physics have been solved numerically, including radioactive decay; simple harmonic motion; damped harmonic motion; driven damped harmonic motion; motion of oscillators in phase space, cyclotron motion; and differential equations for Hyperbolic functions.  In addition, several Hermite polynomials have been reproduced by numerically solving two-point boundary value problems.  Regarding oscillatory motion, the authors present both velocity and displacement of the oscillating particle as functions of time.  For cyclotron motion, the authors simulate trajectory of electrons in magnetic field in real space.  Also, Hermite polynomials H3, H4 and H5 are reproduced by numerically solving two-point boundary value problems.