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Numerical Methods with Artificial Intelligence Applications VOL-1

Foundations Algorithms and Machine Learning Optimization

This book is 100% completeLast updated on 2026-06-26
Artificial Intelligence is built on mathematics—and numerical methods are at its core. What happens behind gradient descent? How do optimization algorithms converge? Why are interpolation, differentiation, and integration essential for machine learning? Discover the mathematical engine that powers modern AI. Numerical Methods with Artificial Intelligence Applications (Volume 1) transforms…

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About the Book

Artificial Intelligence has transformed the modern technological landscape, yet behind every intelligent system lies a strong mathematical and numerical foundation. Numerical Methods with Artificial Intelligence Applications – Volume 1 bridges the gap between classical numerical computation and cutting-edge AI technologies by presenting numerical algorithms through the lens of modern machine learning, optimization, and intelligent systems.

Unlike traditional numerical methods textbooks that focus primarily on engineering mathematics, this book demonstrates how numerical computation powers today's AI applications—including optimization, regression, neural networks, probabilistic modeling, reinforcement learning, scientific computing, and data-driven decision-making.

Beginning with the fundamentals of numerical computation, floating-point arithmetic, and error analysis, the book systematically develops algorithms for solving nonlinear equations, interpolation, differentiation, numerical integration, and optimization. Each concept is connected to practical Artificial Intelligence applications, enabling readers to understand not only the mathematical theory but also its real-world relevance in modern AI systems.

The text emphasizes algorithmic thinking, convergence analysis, computational efficiency, numerical stability, and machine learning optimization techniques. Numerous examples, illustrations, algorithmic explanations, and AI-oriented case studies make the subject approachable for both beginners and advanced learners.

Whether you are a university student, researcher, AI practitioner, software engineer, or educator, this book provides a solid mathematical foundation required for developing intelligent computational systems.

What You Will Learn

• Mathematical foundations of numerical computation

• Floating-point arithmetic and computational error analysis

• Numerical stability and convergence techniques

• Root-finding algorithms and nonlinear equation solving

• Newton-Raphson, Secant, Bisection, Regula-Falsi, and Fixed Point methods

• AI optimization using numerical techniques

• Polynomial and spline interpolation

• Numerical differentiation for gradient estimation

• Numerical integration methods including Monte Carlo Integration

• Bayesian computation and probabilistic estimation

• Machine Learning optimization concepts

• Numerical algorithms used in Artificial Intelligence

• Practical computational approaches for intelligent systems

Who Should Read This Book?

This book is ideal for:

• Undergraduate and postgraduate Computer Science students

• B.Tech, BCA, MCA, MSc, M.Tech, and Data Science students

• Artificial Intelligence and Machine Learning learners

• Researchers in Computational Science

• Engineering students

• University faculty members

• Competitive examination aspirants

• Software developers

• AI engineers

• Data scientists

• Professionals interested in mathematical foundations of AI

Key Features

✔ AI-integrated Numerical Methods

✔ Beginner-friendly mathematical explanations

✔ Machine Learning-oriented examples

✔ Modern optimization techniques

✔ Step-by-step algorithmic development

✔ Practical computational approaches

✔ Industry-relevant AI applications

✔ Research-oriented content

✔ Suitable for self-learning and university courses

✔ Covers both theory and practical implementation

Why This Book is Different

Most numerical methods books stop at solving mathematical equations. This book goes one step further by showing how those same numerical techniques are used inside Artificial Intelligence, Machine Learning, Deep Learning, Data Science, and Computational Intelligence.

Readers will discover how classical mathematical algorithms continue to power modern AI systems, making this book a unique blend of mathematics, computer science, and artificial intelligence.

Whether your goal is academic excellence, AI research, software development, or building intelligent systems, this book serves as an essential foundation for understanding the numerical backbone of Artificial Intelligence.

Author

About the Author

Anshuman Mishra

Anshuman Kumar Mishra, M.Tech (Computer Science) Assistant Professor, Doranda College, Ranchi University

Prolific Author of 50+ Books on AI, Machine Learning & Computer Science | 20+ Years Experience

Anshuman Kumar Mishra is a dedicated educator, researcher, and highly prolific author with over 20 years of experience in Computer Science and Information Technology. Holding an M.Tech in Computer Science from BIT Mesra, he brings a rare combination of academic depth and practical teaching expertise.

Currently serving as Assistant Professor at Doranda College under Ranchi University, he has mentored thousands of students, helping them build strong foundations in programming, data science, and artificial intelligence. His student-centric teaching style emphasizes conceptual clarity, hands-on practice, and real-world application.

Anshuman is a prolific author with more than 50 books published across a wide spectrum of computer science and emerging technology domains. From foundational programming languages to advanced topics in Artificial Intelligence, Machine Learning, Reinforcement Learning, Decision Theory, and Computer Vision — his books are widely appreciated by students, educators, and professionals for their clear explanations, strong theoretical foundation, and practical approach.

His extensive body of work reflects his deep commitment to making complex subjects accessible and meaningful for learners at all levels. He is particularly recognized for creating well-structured learning paths that help readers progress from beginner to advanced levels with confidence.

Driven by the mission to democratize quality technical education, Anshuman continues to write and update books that bridge the gap between academic theory and industry practice.

When not teaching or writing, he actively follows and explores new developments in AI, Quantum Machine Learning, and Ethical Intelligence systems.

Contents

Table of Contents

Numerical Methods with Artificial Intelligence Applications Foundations, Algorithms, and Machine Learning Optimization VOL-1 ________________________________________ Table of Contents ________________________________________ Chapter 1: Introduction to Numerical Methods in the Age of AI 1-15 1.1 Role of numerical computation in intelligent systems 1.2 Limitations of analytical solutions in AI problems 1.3 Approximation, iteration, and convergence concepts 1.4 Relationship between numerical methods and machine learning 1.5 Numerical pipelines in modern AI systems 1.6 Case studies: optimization, simulation, and prediction ________________________________________ Chapter 2: Floating-Point Arithmetic and Error Analysis 16-34 2.1 Number representation in computers 2.2 Floating-point standards (IEEE 754) 2.3 Absolute, relative, and percentage errors 2.4 Truncation and round-off errors 2.5 Error propagation in iterative algorithms 2.6 Stability and conditioning of numerical methods ________________________________________ Chapter 3: Root Finding and Nonlinear Equation Solving 35-54 3.1 Mathematical formulation of root-finding problems 3.2 Graphical and numerical interpretation of roots 3.3 Convergence criteria and stopping conditions 3.4 Computational complexity of root-finding methods ________________________________________ Chapter 4: Classical Root-Finding Algorithms 55-74 4.1 Bisection method 4.2 Regula–Falsi (false position) method 4.3 Fixed-point iteration method 4.4 Newton–Raphson method 4.5 Secant method 4.6 Comparative analysis of root-finding techniques ________________________________________ Chapter 5: Root Finding in Machine Learning and AI 75-95 5.1 Roots of gradients and stationary points 5.2 Solving optimization equations in regression models 5.3 Newton methods in loss minimization 5.4 Adaptive step-size and damping strategies 5.5 Convergence behavior in large-scale AI models ________________________________________ Chapter 6: Interpolation and Approximation Fundamentals 96-114 6.1 Interpolation versus approximation 6.2 Polynomial interpolation theory 6.3 Interpolation error analysis 6.4 Runge’s phenomenon and numerical instability ________________________________________ Chapter 7: Polynomial and Spline Interpolation Methods 115-135 7.1 Lagrange interpolation 7.2 Newton’s divided difference interpolation 7.3 Forward and backward interpolation formulas 7.4 Piecewise interpolation and splines 7.5 Cubic spline interpolation ________________________________________ Chapter 8: Interpolation Techniques in AI and Data Science 136-156 8.1 Function approximation in regression models 8.2 Interpolation for missing data and sensor data 8.3 Basis functions and kernel approximation 8.4 Relationship between interpolation and neural networks ________________________________________ Chapter 9: Numerical Differentiation 157-177 9.1 Concept of numerical differentiation 9.2 Forward difference method 9.3 Backward difference method 9.4 Central difference method 9.5 Gradient estimation in optimization algorithms ________________________________________ Chapter 10: Numerical Integration Techniques 178-200 10.1 Introduction to numerical integration 10.2 Trapezoidal rule 10.3 Simpson’s one-third rule 10.4 Simpson’s three-eighth rule 10.5 Gaussian quadrature 10.6 Monte Carlo integration ________________________________________ Chapter 11: Integration Methods in Artificial Intelligence 201-220 11.1 Expectation estimation in probabilistic models 11.2 Loss and risk estimation 11.3 Reinforcement learning reward computation 11.4 Bayesian evidence and marginal likelihood estimation ________________________________________ Chapter 12: Fundamentals of Numerical Optimization 221-241 12.1 Formulation of optimization problems 12.2 Convex and non-convex optimization 12.3 Constraints and feasibility regions 12.4 Objective functions in AI systems

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