Numerical Methods with Artificial Intelligence Applications

Foundations, Algorithms, and Machine Learning Optimization (Vol. 1)

Artificial Intelligence is built upon mathematics, optimization, and numerical computation. Every modern AI system—from Machine Learning models and Deep Learning networks to Data Science applications and Scientific Computing—depends on powerful numerical algorithms for accurate prediction, optimization, and intelligent decision-making.

Numerical Methods with Artificial Intelligence Applications: Foundations, Algorithms, and Machine Learning Optimization (Vol. 1) has been carefully designed to connect traditional numerical methods with the latest Artificial Intelligence technologies. Rather than teaching numerical analysis as an isolated mathematical subject, this book demonstrates how numerical algorithms serve as the computational backbone of AI, Machine Learning, Optimization, Scientific Computing, Data Analytics, Robotics, and Intelligent Systems.

Written in a clear, structured, and student-friendly style, the book is suitable for university curricula, competitive examinations, self-learning, faculty reference, and industrial applications. Every chapter emphasizes conceptual understanding, mathematical reasoning, computational efficiency, and practical AI relevance.

What You’ll Learn

✔ Introduction to Numerical Methods in Artificial Intelligence

✔ Mathematical Foundations of Intelligent Computing

✔ Floating Point Arithmetic and IEEE 754 Standards

✔ Absolute, Relative and Percentage Error Analysis

✔ Round-Off and Truncation Errors

✔ Error Propagation and Numerical Stability

✔ Conditioning of Numerical Algorithms

✔ Root Finding Techniques

✔ Bisection Method

✔ Regula-Falsi Method

✔ Fixed Point Iteration

✔ Newton-Raphson Method

✔ Secant Method

✔ Convergence Analysis

✔ Computational Complexity

✔ Numerical Optimization

✔ Gradient-Based Optimization

✔ Machine Learning Optimization

✔ Loss Function Minimization

✔ Stationary Point Computation

✔ Polynomial Interpolation

✔ Lagrange Interpolation

✔ Newton Divided Difference

✔ Forward and Backward Interpolation

✔ Cubic Spline Interpolation

✔ Function Approximation

✔ Kernel Approximation

✔ Numerical Differentiation

✔ Forward Difference Method

✔ Backward Difference Method

✔ Central Difference Method

✔ Gradient Estimation

✔ Numerical Integration

✔ Trapezoidal Rule

✔ Simpson’s One-Third Rule

✔ Simpson’s Three-Eighth Rule

✔ Gaussian Quadrature

✔ Monte Carlo Integration

✔ Bayesian Computation

✔ Reinforcement Learning Reward Estimation

✔ Convex Optimization

✔ Non-Convex Optimization

✔ AI Optimization Algorithms

✔ Machine Learning Mathematics

✔ Computational Intelligence

Chapter 1

Introduction to Numerical Methods in the Age of AI

Chapter 2

Floating Point Arithmetic and Error Analysis

Chapter 3

Root Finding and Nonlinear Equation Solving

Chapter 4

Classical Root Finding Algorithms

Chapter 5

Root Finding in Machine Learning and Artificial Intelligence

Chapter 6

Interpolation and Approximation Fundamentals

Chapter 7

Polynomial and Spline Interpolation Methods

Chapter 8

Interpolation Techniques in Artificial Intelligence and Data Science

Chapter 9

Numerical Differentiation

Chapter 10

Numerical Integration Techniques

Chapter 11

Integration Methods in Artificial Intelligence

Chapter 12

Fundamentals of Numerical Optimization

Who Should Read This Book?

This book is ideal for:

B.Tech Students
BCA Students
MCA Students
B.Sc. Computer Science Students
B.Sc. Information Technology Students
M.Tech Students
Artificial Intelligence Students
Machine Learning Students
Data Science Students
Computer Science Researchers
Software Engineers
AI Engineers
Data Analysts
Faculty Members
University Teachers
Research Scholars
Engineering Professionals
Scientific Computing Professionals
Competitive Examination Aspirants

Book Features

✅ Beginner-Friendly Language

✅ Industry-Oriented Content

✅ AI-Integrated Numerical Methods

✅ Modern Machine Learning Applications

✅ Step-by-Step Mathematical Concepts

✅ Practical Computational Examples

✅ Optimization Techniques for AI

✅ Scientific Computing Applications

✅ Data Science Case Studies

✅ Research-Oriented Approach

✅ University Curriculum Aligned

✅ Suitable for Self-Study

✅ Excellent for Projects, Assignments, and Research

Why This Book?

Most traditional Numerical Methods books focus only on mathematical derivations. This book goes beyond conventional numerical analysis by integrating Artificial Intelligence, Machine Learning, Optimization, Data Science, and Computational Intelligence into every major topic. Readers not only learn the theory behind numerical algorithms but also understand how these algorithms are applied in real-world AI systems, predictive analytics, optimization problems, and intelligent computing applications.

Whether you are preparing for university examinations, research work, competitive exams, or building a career in Artificial Intelligence and Data Science, this book provides a strong computational foundation required in today’s technology-driven world.

Book Details

Book Title: Numerical Methods with Artificial Intelligence Applications

Subtitle: Foundations, Algorithms, and Machine Learning Optimization

Volume: Vol. 1

Author: Anshuman Mishra

Publisher: Anshuman Mishra

Publication Year: 2025

Language: English

Category: Artificial Intelligence, Numerical Methods, Machine Learning, Data Science, Computer Science, Applied Mathematics

Newton Raphson Method

Numerical Methods with Artificial Intelligence Applications VOL-1