Computer Aided NUMERICAL ANALYSIS

Numerical analysis (numerical analysis) consists of methods used to find approximate solutions for problems that cannot be solved analytically or which are very difficult to solve. In recent years, the use of numerical analysis methods has increased in parallel with the developments in the field of computers. Numerical analysis methods are frequently used in many engineering fields and applied sciences.
In this book, numerical analysis methods and their MATLAB applications are explained.
The book consists of ten main chapters:
In the first chapter, the history of numerical analysis, the basic theorems used, machine numbers and errors are included. In the second part, direct and iterative solution methods for linear equation systems are mentioned. In the third chapter, solution methods for nonlinear equations and systems of nonlinear equations are covered. In the fourth chapter, the theory and applications of interpolation and polynomial approaches are given. In the fifth chapter, the subjects of curve fitting, least squares method, curve fitting with orthogonal polynomials, approximation with trigonometric functions are given. In the sixth chapter, numerical derivative formulas used to find the approximate derivative value are discussed. In the seventh chapter, numerical integral methods are covered to find the approximate integral value. In addition, improper integrals and multiple integrals are also included. In the eighth chapter, one-step and multi-step solution methods for ordinary differential equations and systems of ordinary differential equations are given. In addition, boundary value problems are also discussed. In the ninth chapter, the finite difference method used for numerical solutions of partial differential equations is covered. Finite difference method for Laplace equation, heat equation and wave equation is explained. In the last chapter, MATLAB applications of all numerical methods described in the book are discussed. This section contains all the MATLAB functions and MATLAB codes used. At the end of each chapter, there are exercises and answers related to the topic.
This book is a useful resource for all engineering students using undergraduate and graduate level mathematics, applied mathematics, and numerical analysis.