Numerical Methods with AI

Artificial Intelligence (AI) is becoming increasingly important in education, particularly in mathematics and computation. This book is designed to help readers quickly grasp the key concepts of numerical methods. Numerical methods are an essential subject in many fields of engineering and science, as they provide the foundational knowledge embedded within advanced software widely used in industry and research. The book covers a broad range of topics including: methods for solving systems of linear and nonlinear algebraic equations, finding the roots of transcendental equations, interpolation, least squares regression, integration, differentiation, and the numerical solutions of differential equations. The finite difference, finite element, and finite volume methods are also introduced. Each chapter begins with concise theoretical explanations presented in an accessible manner, followed by problem-solving examples that employ AI tools capable of generating instant results on a computer screen. AI has become an indispensable tool in modern education, especially in an era that demands rapid and flexible learning. A proper understanding of AI, combined with a strong foundation in the theory of numerical methods, creates new opportunities for deeper and more effective learning. This integration empowers learners to extend their knowledge and apply numerical methods to tackle advanced and complex problems.