'Introduction to Computation and Modeling for Differential Equations, Second Edition' provides a unified and integrated view of numerical analysis, mathematical modeling in applications, and programming to solve differential equations, which is essential in problem-solving across many disciplines such as engineering, physics, and economics. This book successfully introduces readers to the subject through a unique 'Five-M' approach: Modeling, Mathematics, Methods, MATLAB(R), and Multiphysics. This approach facilitates a thorough understanding of how models are created and preprocessed mathematically with scaling, classification, and approximation, and it also illustrates how a problem is solved numerically using the appropriate mathematical methods. The 'Second Edition' includes new topical coverage on variational formulation, the finite element method, examples of discretization, Anstaz methods for parabolic PDEs and elliptic PDEs, Galerkin's method for the model problem, and finite difference and volume methods. Many new real-world examples from scientific and engineering applications, including mechanics, fluid dynamics, solid mechanics, chemical engineering, electromagnetic field theory, and control theory have been added. All presented examples are solved through the use of MATLAB and the interactive scientific computing program Comsol Multiphysics. Numerous illustrations aid in the visualization of the solutions, and a related website features select solutions to problems and MATLAB datasets.