Principles Of Applied Mathematics: Transformation And Approximation by James P. Keener – A Graduate-Level Guide to Mathe

Introduction

For students and researchers in applied mathematics, science, and engineering, mastering the art of transforming and approximating complex problems is essential. Principles Of Applied Mathematics: Transformation And Approximation by James P. Keener offers a rigorous yet accessible journey into the foundational techniques that power real-world mathematical modeling. Published by CRC Press, this hardcover volume is an indispensable resource for graduate-level study and professional reference in India and beyond.

Book Overview

This book is primarily about the principles that guide problem-solving in applied mathematics. It is designed for beginning graduate students in applied mathematics, science, and engineering, and is appropriate as a one-year course in applied mathematical techniques. The text focuses on two core themes: transformation methods that simplify equations, and approximation methods that yield practical solutions when exact answers are elusive. With clear exposition and numerous examples, Keener bridges abstract theory and tangible application.

Key Highlights

• Comprehensive Coverage: Integrates transformation techniques (Fourier, Laplace, etc.) with approximation methods (asymptotics, perturbation theory).
• Practical Orientation: Every concept is tied to real scientific and engineering problems, making it ideal for Indian students preparing for research or industry.
• Rigorous Yet Readable: Balances mathematical depth with intuitive explanations—perfect for self-study or classroom use.
• Enduring Value: A classic text that remains relevant for modern applied mathematics curricula.

Inside the Book

The content is structured to build from fundamental ideas to advanced applications. Early chapters introduce integral transforms and their properties, followed by detailed explorations of asymptotic expansions, perturbation methods, and boundary layer theory. Each chapter includes worked examples, exercises, and references that encourage deeper investigation. The book’s logical flow helps readers connect transformation and approximation as complementary tools.

Key Topics

• Integral transforms: Fourier, Laplace, and Hankel transforms
• Asymptotic expansions and perturbation methods
• Boundary layer theory and singular perturbations
• Green’s functions and their applications
• Variational principles and calculus of variations
• Difference equations and discrete models
• Approximation of eigenvalues and eigenfunctions

Reader Benefits

• Strengthen Problem-Solving Skills: Learn to choose and apply the right mathematical technique for any given problem.
• Bridge Theory and Practice: Move from abstract equations to concrete solutions used in physics, engineering, and data science.
• Build a Strong Foundation: Ideal for Indian students aiming for competitive exams (like GATE, NET) or advanced research.
• Save Time: A self-contained volume that reduces the need to consult multiple references.

Learning Outcomes

By studying this book, readers will be able to: apply integral transforms to solve differential and integral equations; use asymptotic methods to approximate solutions for nonlinear or high-dimensional problems; analyze boundary layers and singular perturbations in fluid dynamics and other fields; derive and apply Green’s functions for boundary value problems; and critically evaluate approximation errors in mathematical models.

Who Should Read

• Graduate Students in applied mathematics, physics, and engineering disciplines.
• Researchers and Practitioners who use mathematical modeling in their work.
• Advanced Undergraduate Students seeking a rigorous introduction to modern applied mathematics.
• Faculty Members looking for a comprehensive textbook for a one-year course.

About the Author

James P. Keener is a distinguished professor of mathematics known for his contributions to mathematical biology and applied analysis. With decades of teaching experience at the University of Utah, he brings clarity and depth to complex topics. His writing reflects a deep understanding of how students learn and how mathematics serves science.

About the Publisher

CRC Press, an imprint of Taylor & Francis, is a globally respected publisher of scientific and technical books. Known for high-quality content and rigorous editorial standards, CRC Press has been a trusted name in academic publishing for over a century. This hardcover edition ensures durability for years of frequent use.

Conclusion

Principles Of Applied Mathematics: Transformation And Approximation is more than a textbook—it is a companion for anyone serious about applied mathematics. Whether you are a student in an Indian institute, a researcher solving real-world problems, or a professional refreshing your skills, this book equips you with the essential tools. Order your hardcover copy from Bookshops.in today and invest in a resource that will serve you for a lifetime.