In the first part of the book solution methods for ordinary differential equations (ODEs) are discussed. In Chapter 1 it is explained how one can evaluate the analytical solution of ODEs by using the Symbolic Math toolbox of MATLAB. Hereby, first-order and second order ODEs are considered. The application of numerical methods (Euler, Runge-Kutta, Adams-Bashford, Adams-Moulton and others methods) for solving first-order initial value problems of ODEs is explained in Chapter 2. Hereby, three possibilities are discussed, writing own MATLAB script files, using MATLAB’s built-in ODE solvers, and modeling with Simulink. Chapter 3 is devoted to the solution of second-order ODEs by numerical methods and by using the symbolic toolbox as well as by modeling with Simulink. The topics of Chapters 4, 5, and 6 are possibilities for solving stiff ODEs, higher-order ODEs, coupled ODEs, and implicit ODEs. Chapter 7 gives a comparative analysis of the different ways for solving ODEs which are presented in the previous chapters. The accuracy and efficiency of these approaches is compared by one example. The topic of the second part of the book is the solution of boundary value problems of ODEs by using MATLAB built-in solvers. In the third part (Chapters 9–12) the solution of real-life problems modeled by ODEs is discussed: spring-mass-damper systems, electromechanical and mechanical systems, trajectory problems, Lorenz systems, and Lotka-Volterra problems. In the fourth part of the book the solution of partial differential equations (PDEs) is discussed. Hereby, the one-dimensional heat transfer problem, two-dimensional heat transfer problems as well as one- and two-dimensional wave propagation problems are considered. All presented solution methods are demonstrated by numerous examples. Some of the chapters contain also exercises.