Mathematical Models in the Applied Sciences by A. C. Fowler – A Thorough Grounding in Modelling Techniques for Biology,

Introduction

Mathematical modelling sits at the heart of applied science, transforming real-world challenges into precise mathematical language. Mathematical Models in the Applied Sciences by A. C. Fowler, published by Cambridge University Press, is a comprehensive guide that bridges the gap between abstract theory and practical problem-solving. This hardcover edition is an essential resource for Indian students and researchers who wish to master the art of building, analysing, and interpreting models across diverse scientific fields.

Book Overview

This book offers a rigorous yet accessible journey through the principles of mathematical modelling. Starting with foundational techniques, it systematically explores classical and continuum models drawn from biology, chemical engineering, fluid and solid mechanics, geophysics, medicine, and physics. The author assumes only a basic grounding in calculus and analysis, making it suitable for advanced undergraduate and postgraduate students. Each chapter builds on the previous, equipping readers with the confidence to tackle complex, interdisciplinary problems.

Key Highlights

• Broad Interdisciplinary Scope: Covers models from biology, chemical engineering, geophysics, medicine, physics, and more.
• Practical Approach: Emphasises the entire modelling process—from problem formulation to solution interpretation.
• Classical and Continuum Models: Includes both discrete and continuous systems, with detailed derivations.
• Accessible Prerequisites: Requires only basic calculus and analysis; no advanced mathematics needed.
• Authored by an Expert: A. C. Fowler is a renowned mathematician with decades of teaching and research experience.

Inside the Book

The book is structured to guide the reader step-by-step through the modelling methodology. Early chapters introduce core techniques such as dimensional analysis, scaling, and perturbation methods. Later chapters delve into specific applications: population dynamics in biology, reaction-diffusion systems in chemical engineering, flow in porous media, elasticity in solid mechanics, wave propagation in geophysics, and tumour growth in medicine. Numerous worked examples and exercises reinforce learning, making complex ideas tangible.

Key Topics

• Dimensional analysis and scaling
• Perturbation methods and asymptotic analysis
• Continuum mechanics: fluid flow, heat transfer, and elasticity
• Biological models: population dynamics, epidemics, and pattern formation
• Chemical engineering: reactors, diffusion, and catalysis
• Geophysical models: groundwater flow, glaciers, and mantle convection
• Medical applications: drug delivery, tumour growth, and blood flow
• Classical mechanics: pendulums, springs, and wave equations

Reader Benefits

• Builds Strong Foundations: Develops a systematic, transferable modelling skillset applicable to any field.
• Enhances Problem-Solving: Encourages critical thinking and mathematical reasoning for real-world issues.
• Supports Academic Success: Ideal for coursework, projects, and research in science and engineering disciplines.
• Prepares for Advanced Study: Provides a springboard for specialised topics in applied mathematics and computational science.
• Indian Context Relevance: Examples and applications resonate with challenges in Indian industry, environment, and healthcare.

Learning Outcomes

By the end of this book, readers will be able to formulate mathematical models from verbal descriptions, apply scaling and dimensional analysis to simplify problems, use perturbation methods to find approximate solutions, analyse the behaviour of continuum systems, and interpret model predictions in the context of the original application. They will also gain the confidence to design their own models for novel scientific questions.

Who Should Read

• Undergraduate and postgraduate students in mathematics, engineering, physics, and applied sciences.
• Researchers and professionals in biotechnology, chemical engineering, geophysics, and medicine.
• Teachers and lecturers seeking a comprehensive text for modelling courses.
• Self-learners with a basic calculus background eager to explore applied mathematics.

About the Author

A. C. Fowler is a distinguished applied mathematician and Professor of Mathematics at the University of Oxford. He has authored numerous research papers and books on mathematical modelling, with a particular focus on glaciology, geophysics, and industrial mathematics. His teaching philosophy emphasises clarity, relevance, and the joy of translating real-world phenomena into mathematical insight.

About the Publisher

Cambridge University Press is a world-leading academic publisher with a legacy of over 400 years. Known for its rigorous editorial standards and commitment to knowledge dissemination, Cambridge University Press publishes textbooks and reference works that shape education globally. This hardcover edition reflects the press's dedication to quality and durability, making it a lasting addition to any library.

Conclusion

Mathematical Models in the Applied Sciences is more than a textbook—it is a toolkit for thinking mathematically about the world. Whether you are a student in an Indian university, a researcher tackling environmental or medical challenges, or an engineer seeking deeper analytical skills, this book will empower you to turn complexity into clarity. Order your hardcover copy from Bookshops.in today and take a decisive step toward mastering applied mathematics.