The book "numerical analysis" is designed with the objective of providing a comprehensive and in-depth exploration into the algorithms, methods, and theoretical underpinnings of numerical solutions to mathematical problems. its aim is to bridge the gap between theoretical mathematics and practical application, offering readers insights into how complex, continuous mathematical problems can be approached and solved using numerical methods. this book targets a broad audience, primarily consisting of undergraduate and graduate students in mathematics and computer science who are keen on mastering the fundamentals and advanced concepts of numerical analysis. it serves as an invaluable resource for academics, researchers, and professionals in fields where numerical methods are pivotal, including engineering, physical sciences, and applied mathematics.