This book provides a comprehensive approach for engineering mathematics emphasizing fundamental concepts. The book is the first two complementary textbooks. Volume 1 introduces MATLAB software, source of errors in calculations, root finding, solution of nonlinear algebraic equations, interpolation, curve fitting, numerical derivative, numerical integral and eigenvalue problems. Distinct from similar books, unique sections are covered in each chapter such as solution of nonlinear algebraic systems, interpolation and curve fitting methods for multivariate functions such as Kriging, response surface methodology and artificial neural networks, quadrature based numerical derivative and integral methods. To deepen conceptual understanding and improve overall learning, example problems are solved in each chapter illustrating both theory and software-based methods. MATLAB programs developed by the author are additionally provided in appendices to implement the methods and show the examples of program development for engineering applications.