Advanced Numerical Methods and Mathematical Modeling

English | 2025 | ISBN: 979-8308298670 | 178 Pages | PDF | 10 MB

Advanced Numerical Methods and Mathematical Modeling: Comprehensive Techniques in Matrix Algebra, Interpolation, Iterative Methods, Optimization, and Numerical Integration

Unlock the full potential of computational mathematics with Advanced Numerical Methods and Mathematical Modeling, an indispensable reference for students, researchers, and professionals alike. This book meticulously covers a vast array of critical topics in numerical analysis, offering profound insights and expert-level techniques.

From foundational concepts in Matrix Algebra and Numerical Methods to cutting-edge approaches in Optimization and Numerical Integration, this comprehensive volume is designed to equip readers with a solid understanding of both theory and practical applications. It delves into topics such as Gaussian Elimination, Matrix Decompositions, Least Squares Methods, and Iterative Solving of Linear Systems, while also offering a detailed examination of interpolation techniques, from polynomial to spline methods.

Incorporating an in-depth exploration of iterative methods for solving nonlinear equations, the book also provides valuable guidance on methods such as Newton’s Method, Secant Method, and Quasi-Newton Methods, ensuring a complete toolkit for tackling complex mathematical challenges. The book extends into the realm of optimization, covering algorithms like Nelder-Mead, Gradient Descent, and Conjugate Gradient, essential for solving real-world optimization problems.

Moreover, the text addresses the numerical solution of differential equations, presenting both basic and advanced techniques for solving ordinary and partial differential equations, making it a crucial guide for those working in engineering, physics, finance, and applied sciences.