Differential Equations and Vector Calculus : A Theoretical and Practical Approach

Differential Equations and Vector Calculus: A Theoretical and Practical Approach is a comprehensive guide designed to bridge the gap between abstract mathematical theory and its real-world applications. This book explores two foundational areas of mathematics differential equations and vector calculus by providing both theoretical insights and practical methods of solution. It offers a thorough understanding of ordinary and partial differential equations, highlighting their significance in modeling complex systems across physics, engineering, and biology. In addition, the book delves deeply into vector calculus, emphasizing its pivotal role in describing physical phenomena, particularly in fields such as electromagnetism and fluid dynamics. Key topics include gradient, divergence, curl, line integrals, and surface integrals, all presented with clarity and rigor.

Each chapter is equipped with a range of examples, problems, and exercises that enable readers to develop both computational skills and conceptual understanding. The book also provides practical applications of differential equations and vector calculus, allowing students and professionals to see the utility of these mathematical tools in solving real-world problems. Ideal for students and practitioners alike, Differential Equations and Vector Calculus offers an accessible yet detailed approach, blending theory with practical techniques for mastering these crucial areas of mathematics.

Dr. Rajagopal Reddy N is a Professor in Mathematics at Viswam Engineering College (Autonomous), affiliated with JNTUA, India. With over 13 years of rich experience in teaching different contemporary domains of engineering mathematics. He specializes in mathematical modelling, fuzzy graph theory, and AI applications in agriculture. He has published extensively in internationally acclaimed peer-reviewed journals and published several research articles. This textbook is the result of his long-standing commitment to student-centric learning and curriculum enhancement.

Dr. M. Anjan Kumar , Professor & Dean (R&D), Department of Computer Science and Engineering, Viswam Engineering College (Autonomous), Madanapalle, Andhra Pradesh, India. Dr. M. Anjan Kumar, M.Tech (CS), Ph.D. (CSE), is a seasoned academician, researcher, and innovator in Computer Science and Engineering. With over 19 years of academic and industry experience, he currently serves as Professor and Dean of Research & Development at Viswam Engineering College, where he leads initiatives in advanced computing, machine learning, generative AI, and digital transformation. Dr. AnjanKumar has held senior positions including Professor, Head of Department, Dean, and Principal I/C at reputed institutions in India and abroad. His international exposure includes serving as Faculty (R&D) at Botho University, Botswana, alongside key administrative roles in leading engineering colleges. He has successfully supervised multiple Ph.D. scholars, coordinated postgraduate programs, and established Centers of Excellence in IoT & Machine Learning, driving impactful projects such as AI based demographic prediction systems and face recognition attendance monitoring solutions. Through his mentorship and vision, he continues to shape future-ready professionals and foster innovation in computer science education.
Research & Contributions
• Areas of Interest: Agentic-AI, information retrieval systems, machine learning, deep learning, data engineering, and generative AI
• Patents: Multiple patents in India and Australia, covering innovations in cloud storage optimization, iris recognition, IoT security using blockchain, and resource aggregation in cloud computing
• Publications: Extensive contributions to SCI,WoS,Scopus and UGC Care indexed journals and conferences, with notable work on quantum cryptography, explainable AI, and medical image analysis
• Books: Author of Digital DNA: The Blueprint of Computer Organization (2025), Essentials of Machine Learning, and Real World Applications of Machine Learning in Healthcare—part of a Guinness World Record attempt for the “thickest book in the world”
Awards & Recognition
• Best Paper Award – IEEE Bangalore, 2023 (Brain Tumor Segmentation using CNN)
• Young Researcher Award – Global Education Awards, 2019
• Multiple accolades including Best Professor (2019), Best Faculty (2017–2019), and nominations for the Bharath Jyothi Award

Professional Memberships

Active member of global associations including SDIWC, IAENG, ICSES, IAASSE, and UACEE, contributing to the advancement of computer science research worldwide. Research Funding Coordinator for ATAL Faculty Development Program (FDP) titled Empowering Digital Transformation: Supercomputing, AI, and Data Science, sanctioned with funding of ₹100,000, scheduled from 7–12 September 2025.