In this book titled ¿Solving Problems in Science and Engineering by Matrix Method¿, the boundary value problems governed by the linear differential equations in Science and Engineering are solved by the application of the Matrix Method. This book is intended for the students of undergraduate, master's, and doctorate who study Modern Physics, Quantum Mechanics, Heat Transfer, Network Analysis, and others. In this book, we have presented the methodology of the Matrix method with examples so that the readers understand the way how matrix method works. we have considered the problem of one-dimensional conduction of heat through different fin surfaces, from Modern Physics we have considered the problem of motion of damped harmonic oscillator and Quantum Mechanics related problems like infinite potential well, half-infinite potential well, vertical step potential, from Network Analysis we have considered the problem of RLC network circuit connected to current or voltage sources, design of Snubber circuit. No doubt, solving boundary value problems by the Matrix Method is a tedious task, but it is very interesting to find the solutions by this method.