Applied Algebraic and Differential Calculus" is an edited book consisting of 18 open-access articles on mathematical analysis and computational methodologies for solving differential equations, as well as matrix eigenvalue, boundary value, and bifurcation problems. It includes a variety of algebraic and numerical strategies from decomposition to neural network based methods. Reading this book requires some knowledge in advanced calculus, differential equations, matrix computations. This book is intended to reach an academic audience ranging from graduate student to experienced researchers.