This book furthers the understanding of applied numerical methods by emphasizing the use of approximation techniques to address various problems commonly encountered in science and engineering. Its primary objective is to present a range of methods for solving linear systems, nonlinear equations, performing integral calculus, evaluating limits, and approximating functions through polynomial interpolation. A particular focus is placed on explaining each method from an implementation perspective, ensuring that the techniques applied are not only practical but also mathematically sound
The book is accessible to anyone working with applied numerical methods and possessing a foundational mathematical background. It is intended for students in science and technology across various disciplines mathematics, computer science, mechanics, electronics, civil engineering, and more. Written in the form of comprehensive course notes, it features numerous solved examples and applications, along with additional unsolved exercises and, importantly, exam problems with complete solutions
The content is presented in a clear and simple style that allows students to grasp concepts quickly. Each chapter begins with definitions, theorems, and foundational principles of numerical methods, which are then applied through practical exercises. The course content and solved problems have been carefully selected to offer a clear interpretation of both the mathematical foundations and the algorithmic aspects of each method
CHAPITRE I: RESOLUTION OF THE NONLINEAR
CHAPTER II: POLYNOMIAL INTERPOLATION
CHAPTER III: FUNCTION APPROXIMATION
CHAPTER IV : NUMERICAL INTEGRATION
CHAPTER V: RESOLUTION ORDINARY DIFFERENTIAL EQUATIONS
CHAPTER VI: METHOD FOR DIRECT RESOLUTION OF SYSTEMS OF LINEAR EQUATIONS
CHAPTER VII: APPROXIMATE RESOLUTION METHOD FOR SYSTEMS OF LINEAR EQUATIONS