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The objective of numerical analysis is to solve complex numerical problems using only the simple operations of arithmetic, to develop and evaluate methods for computing numerical results from given data. The methods of computation are called algorithms. An algorithm is a finite sequence of rules for performing computations on a computer such that at each instant the rules determine exactly what the computer has to do next. Numerical methods tend to emphasize the implementation of the algorithms. Thus, applied numerical methods are methods for solving problems on computers by numerical calculations, often giving a table of numbers and /or graphical representations or figures. The purpose of this book is to impart a basic understanding, both physical and mathematical, of the basic theory of numerical analysis/methods and their applications using MATLAB. In this book, an attempt is made to present in a simple and systematic manner the techniques that can be applied to the study of applied numerical methods. Special emphasis is placed on analytical developments, algorithms and computational solutions. The objective of this text book is to introduce students from a variety of disciplines and backgrounds to the vast array of problems that are amenable to numerical solution. The emphasis is placed on application rather than pure theory, which, although kept to a minimum and presented in a mostly heuristic and intuitive manner. This is deemed sufficient for the student to fully understand the workings, efficiency and shortcomings or failings of each technique. The computer language of MATLAB is incorporated throughout the text. Hence, most of the problems are executed in MATLAB code. Since I intended this book as a first course on the numerical methods, the concepts have been presented in simple terms and the solution procedures have been explained in detail.