Imagine delving into a realm where abstract mathematical concepts intertwine with the tangible world of engineering marvels – bridges that defy gravity, circuits humming with electricity, and software orchestrating complex systems. This is the journey “Advanced Engineering Mathematics” by Dr. Hossein Behrouzi invites you on. Published in Tehran by the esteemed Nashr-e Elm publication house in 2017, this tome transcends the traditional boundaries of a mathematics textbook. It’s a masterpiece that elegantly blends rigorous theory with captivating real-world applications, making it an indispensable companion for aspiring and seasoned engineers alike.
“Advanced Engineering Mathematics” delves into a rich tapestry of mathematical concepts essential to modern engineering practices. From the intricacies of differential equations – those elegant expressions describing change over time – to the power of linear algebra in solving complex systems, the book provides a comprehensive framework for understanding the mathematical underpinnings of engineering design and analysis.
The book’s structure is meticulously crafted, guiding readers through progressively more advanced topics.
Chapter Breakdown:
Chapter Title | Description | Key Concepts Covered |
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Fundamentals of Calculus | Establishes a firm foundation in differentiation and integration, essential tools for understanding rates of change and accumulation. | Derivatives, Integrals, Fundamental Theorem of Calculus |
Differential Equations | Introduces various types of differential equations and their solutions, providing insights into how systems evolve over time. | Ordinary Differential Equations (ODEs), Partial Differential Equations (PDEs), Solution Techniques |
Linear Algebra | Explores vectors, matrices, and linear transformations – the building blocks for analyzing complex systems and solving simultaneous equations. | Vector Spaces, Eigenvalues, Eigenvectors, Matrix Operations |
Complex Analysis | Delves into the realm of complex numbers, functions, and integrals, revealing their profound applications in fields like signal processing and control theory. | Cauchy-Riemann Equations, Complex Integration, Residue Theorem |
Numerical Methods | Equips readers with powerful computational tools for solving engineering problems that may not have analytical solutions. | Finite Difference Method, Numerical Integration, Root Finding Algorithms |
Beyond its theoretical depth, “Advanced Engineering Mathematics” distinguishes itself through a rich tapestry of real-world examples and applications.
These illustrative scenarios showcase the practical relevance of mathematical concepts:
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Designing an Airplane Wing: Applying Bernoulli’s principle and differential equations to model airflow and optimize wing shape for lift generation.
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Analyzing a Circuit: Using Kirchhoff’s laws and linear algebra to determine currents and voltages in complex electrical networks.
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Predicting Weather Patterns: Employing numerical methods and partial differential equations to simulate atmospheric conditions and forecast weather trends.
These examples highlight the book’s ability to bridge the gap between abstract theory and tangible engineering challenges, making it an invaluable resource for students seeking to understand how mathematics shapes the world around them.
Production Features:
“Advanced Engineering Mathematics” is a testament to the publisher’s commitment to quality and accessibility:
- Clear and Concise Language: The text is written in a clear and concise style that avoids unnecessary jargon, making it accessible to readers with varying mathematical backgrounds.
- Abundant Illustrations: Numerous diagrams, graphs, and tables enhance understanding by visually representing key concepts and relationships.
- Comprehensive Exercises: Each chapter concludes with a carefully curated set of exercises designed to reinforce learning and deepen comprehension.
The book’s physical presentation is equally impressive:
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Durable Binding: A robust binding ensures the book withstands repeated use.
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High-Quality Paper: Crisp, white pages provide a comfortable reading experience.
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Accessible Format: The book is available in both hardcover and paperback editions to suit different preferences.
“Advanced Engineering Mathematics” by Dr. Hossein Behrouzi stands as a beacon of excellence in the field of engineering education. It’s a testament to the power of mathematics to illuminate the complexities of our world, empowering engineers to design innovative solutions for the challenges of tomorrow. This book is not merely a collection of equations and theorems; it’s an invitation to embark on a transformative journey – a journey that will reshape your understanding of engineering and equip you with the tools to shape the future.